T H E
SSSSS OOOOOO FFFFFFFFFFFFF AAAAAAA
SSSSSSSSSS OOOOOOOOOOOO FFFFFFFFFFFF AAAAAAAA
SSSSSSSSSSS OOOOOOOOOOOOOO FFFFFFFFFFFF AAAA AAAA
SSSS S OOOOOO OOOOO FFFF AAAA AAAA
SSSSS OOOOO OOOO FFFFF AAAA AAAA
SSSSSSSSSS OOOO OOOOO FFFFFFFFFFFF AAAA AAAA
SSSSSSSSS OOOOO OOOO FFFFFFFFFFFF AAAAAAAAAAAAA
SSSSS OOOO OOOO FFFF AAAAAAAAAAAAAA
S SSSS OOOOO OOOOO FFFF AAAAAAAAAAAAAAA
SSSSSSSSSSS OOOOOOOOOOOOO FFFF AAAA AAAAA
SSSSSSSSS OOOOOOOOOO FFFF AAAA AAAAA
SSSS OOOOO FFFF AAAA AAAAA
S O F T W A R E
L I B R A R I E S
International Astronomical Union
Division 1: Fundamental Astronomy
Commission 19: Rotation of the Earth
Standards Of Fundamental Astronomy Board
8th Release
2010 September 5
contents.lis 2008 September 30
--------
CONTENTS
--------
1) Introduction
2) The SOFA Astronomy Library
3) The SOFA Vector/Matrix Library
4) The individual routines
A1 The SOFA copyright notice
A2 Constants
A3 SOFA Review Board membership
intro.lis 2010 September 5
-------------------------------
THE IAU-SOFA SOFTWARE LIBRARIES
-------------------------------
SOFA stands for "Standards Of Fundamental Astronomy". The SOFA
software libraries are a collection of subprograms, in source-
code form, which implement official IAU algorithms for fundamental-
astronomy computations. The subprograms at present comprise 131
"astronomy" routines supported by 55 "vector/matrix" routines,
available in both Fortran77 and C implementations.
THE SOFA INITIATIVE
SOFA is an IAU Service which operates under Division 1 (Fundamental
Astronomy) and reports through Commission 19 (Rotation of the Earth).
The IAU set up the SOFA initiative at the 1994 General Assembly, to
promulgate an authoritative set of fundamental-astronomy constants and
algorithms. At the subsequent General Assembly, in 1997, the
appointment of a SOFA Review Board and the selection of a site for the
SOFA Center (the outlet for SOFA products) were announced.
The SOFA initiative was originally proposed by the IAU Working Group on
Astronomical Standards (WGAS), under the chairmanship of
Toshio Fukushima. The proposal was for "...new arrangements to
establish and maintain an accessible and authoritative set of constants,
algorithms and procedures that implement standard models used in
fundamental astronomy". The SOFA Software Libraries implement the
"algorithms" part of the SOFA initiative. They were developed under the
supervision of an international panel called the SOFA Review Board. The
current membership of this panel is listed in an appendix.
A feature of the original SOFA software proposals was that the products
would be self-contained and not depend on other software. This includes
basic documentation, which, like the present file, will mostly be plain
ASCII text. It should also be noted that there is no assumption that
the software will be used on a particular computer and Operating System.
Although OS-related facilities may be present (Unix make files for
instance, use by the SOFA Center of automatic code management systems,
HTML versions of some documentation), the routines themselves will be
visible as individual text files and will run on a variety of platforms.
ALGORITHMS
The SOFA Review Board's initial goal has been to create a set of
callable subprograms. Whether "subroutines" or "functions", they are
all referred to simply as "routines". They are designed for use by
software developers wishing to write complete applications; no
runnable, free-standing applications are included in SOFA's present
plans.
The algorithms are drawn from a variety of sources. Because most of the
routines so far developed have either been standard "text-book"
operations or implement well-documented standard algorithms, it has not
been necessary to invite the whole community to submit algorithms,
though consultation with authorities has occurred where necessary. It
should also be noted that consistency with the conventions published by
the International Earth Rotation Service was a stipulation in the
original SOFA proposals, further constraining the software designs.
This state of affairs will continue to exist for some time, as there is
a large backlog of agreed extensions to work on. However, in the future
the Board may decide to call for proposals, and is in the meantime
willing to look into any suggestions that are received by the SOFA
Center.
SCOPE
The routines currently available are listed in the next two chapters of
this document.
The "astronomy" library comprises 131 routines (plus one obsolete
Fortran routine that now appears under a revised name). The areas
addressed include calendars, time scales, ephemerides, precession-
nutation, star space-motion, star catalog transformations and
geodetic/geocentric transformations.
The "vector-matrix" library, comprising 55 routines, contains a
collection of simple tools for manipulating the vectors, matrices and
angles used by the astronomy routines.
There is no explicit commitment by SOFA to support historical models,
though as time goes on a legacy of superseded models will naturally
accumulate. There is, for example, no support of B1950/FK4 star
coordinates, or pre-1976 precession models, though these capabilities
could be added were there significant demand.
Though the SOFA software libraries are rather limited in scope, and are
likely to remain so for a considerable time, they do offer distinct
advantages to prospective users. In particular, the routines are:
* authoritative: they are IAU-backed and have been constructed with
great care;
* practical: they are straightforward to use in spite of being
precise and rigorous (to some stated degree);
* accessible and supported: they are downloadable from an easy-to-
find place, they are in an integrated and consistent form, they
come with adequate internal documentation, and help for users is
available.
VERSIONS
Once it has been published, an issue is never revised or updated, and
remains accessible indefinitely. Subsequent issues may, however,
include corrected versions under the original routine name and
filenames. However, where a different model is introduced, it will have
a different name.
The issues will be referred to by the date when they were announced.
The frequency of re-issue will be decided by the Board, taking into
account the importance of the changes and the impact on the user
community.
DOCUMENTATION
At present there is little free-standing documentation about individual
routines. However, each routine has preamble comments which specify in
detail what the routine does and how it is used.
The file sofa_pn.pdf describes the SOFA tools for precession-nutation
and other aspects of Earth attitude and includes example code and (see
the appendix) diagrams showing the interrelationships between the
routines supporting the latest (IAU 2006/2000A) models.
PROGRAMMING LANGUAGES AND STANDARDS
The SOFA routines are available in two programming languages at present:
Fortran77 and ANSI C. Related software in other languages is under
consideration.
The Fortran code conforms to ANSI X3.9-1978 in all but two minor
respects: each has an IMPLICIT NONE declaration, and its name has a
prefix of "iau_" and may be longer than 6 characters. A global edit to
erase both of these will produce ANSI-compliant code with no change in
its function.
Coding style, and restrictions on the range of language features, have
been much debated by the Board, and the results comply with the majority
view. There is (at present) no document that defines the standards, but
the code itself offers a wide range of examples of what is acceptable.
The Fortran routines contain explicit numerical constants (the INCLUDE
statement is not part of ANSI Fortran77). These are drawn from the
file consts.lis, which is listed in an appendix. Constants for the
SOFA/C functions are defined in a header file sofam.h.
The naming convention is such that a SOFA routine referred to
generically as "EXAMPL" exists as a Fortran subprogram iau_EXAMPL and a
C function iauExampl. The calls for the two versions are very similar,
with the same arguments in the same order. In a few cases, the C
equivalent of a Fortran SUBROUTINE subprogram uses a return value rather
than an argument.
Each language version includes a "testbed" main-program that can be used
to verify that the SOFA routines have been correctly compiled on the end
user's system. The Fortran and C versions are called t_sofa_f.for and
t_sofa_c.c respectively. The testbeds execute every SOFA routine and
check that the results are within expected accuracy margins. It is not
possible to guarantee that all platforms will meet the rather stringent
criteria that have been used, and an occasional warning message may be
encountered on some systems.
COPYRIGHT ISSUES
Copyright for all of the SOFA software and documentation is owned by the
IAU SOFA Review Board. The Software is made available free of charge
for all classes of user, including commercial. However, there are
strict rules designed to avoid unauthorized variants coming into
circulation. It is permissible to distribute derived works and other
modifications, but they must be clearly marked to avoid confusion with
the SOFA originals.
Further details are included in the block of comments which concludes
every routine. The text is also set out in an appendix to the present
document.
ACCURACY
The SOFA policy is to organize the calculations so that the machine
accuracy is fully exploited. The gap between the precision of the
underlying model or theory and the computational resolution has to be
kept as large as possible, hopefully leaving several orders of
magnitude of headroom.
The SOFA routines in some cases involve design compromises between rigor
and ease of use (and also speed, though nowadays this is seldom a major
concern).
ACKNOWLEDGEMENTS
The Board is indebted to a number of contributors, who are acknowledged
in the preamble comments of the routines concerned.
The Board's effort is provided by the members' individual institutes.
Resources for operating the SOFA Center are provided by Her Majesty's
Nautical Almanac Office, operated by the United Kingdom Hydrographic
Office.
sofa_lib.lis 2010 September 5
----------------------
SOFA Astronomy Library
----------------------
PREFACE
The routines described here comprise the SOFA astronomy library. Their
general appearance and coding style conforms to conventions agreed by
the SOFA Review Board, and their functions, names and algorithms have
been ratified by the Board. Procedures for soliciting and agreeing
additions to the library are still evolving.
PROGRAMMING LANGUAGES
The SOFA routines are available in two programming languages at present:
Fortran 77 and ANSI C.
Except for a single obsolete Fortran routine, which has no C equivalent,
there is a one-to-one relationship between the two language versions.
The naming convention is such that a SOFA routine referred to
generically as "EXAMPL" exists as a Fortran subprogram iau_EXAMPL and a
C function iauExampl. The calls for the two versions are very similar,
with the same arguments in the same order. In a few cases, the C
equivalent of a Fortran SUBROUTINE subprogram uses a return value rather
than an argument.
GENERAL PRINCIPLES
The principal function of the SOFA Astronomy Library is to provide
definitive algorithms. A secondary function is to provide software
suitable for convenient direct use by writers of astronomical
applications.
The astronomy routines call on the SOFA vector/matrix library routines,
which are separately listed.
The routines are designed to exploit the full floating-point accuracy
of the machines on which they run, and not to rely on compiler
optimizations. Within these constraints, the intention is that the code
corresponds to the published formulation (if any).
Dates are always Julian Dates (except in calendar conversion routines)
and are expressed as two double precision numbers which sum to the
required value.
A distinction is made between routines that implement IAU-approved
models and those that use those models to create other results. The
former are referred to as "canonical models" in the preamble comments;
the latter are described as "support routines".
Using the library requires knowledge of positional astronomy and
time-scales. These topics are covered in "Explanatory Supplement to the
Astronomical Almanac", P. Kenneth Seidelmann (ed.), University Science
Books, 1992. Recent developments are documented in the journals, and
references to the relevant papers are given in the SOFA code as
required. The IERS Conventions are also an essential reference. The
routines concerned with Earth attitude (precession-nutation etc.) are
described in the SOFA document sofa_pn.pdf.
ROUTINES
Calendars
CAL2JD Gregorian calendar to Julian Day number
EPB Julian Date to Besselian Epoch
EPB2JD Besselian Epoch to Julian Date
EPJ Julian Date to Julian Epoch
EPJ2JD Julian Epoch to Julian Date
JD2CAL Julian Date to Gregorian year, month, day, fraction
JDCALF Julian Date to Gregorian date for formatted output
Time scales
D2DTF format 2-part JD for output
DAT Delta(AT) (=TAI-UTC) for a given UTC date
DTDB TDB-TT
DTF2D encode time and date fields into 2-part JD
TAITT TAI to TT
TAIUT1 TAI to UT1
TAIUTC TAI to UTC
TCBTDB TCB to TDB
TCGTT TCG to TT
TDBTCB TDB to TCB
TDBTT TDB to TT
TTTAI TT to TAI
TTTCG TT to TCG
TTTDB TT to TDB
TTUT1 TT to UT1
UT1TAI UT1 to TAI
UT1TT UT1 to TT
UT1UTC UT1 to UTC
UTCTAI UTC to TAI
UTCUT1 UTC to UT1
Earth rotation angle and sidereal time
EE00 equation of the equinoxes, IAU 2000
EE00A equation of the equinoxes, IAU 2000A
EE00B equation of the equinoxes, IAU 2000B
EE06A equation of the equinoxes, IAU 2006/2000A
EECT00 equation of the equinoxes complementary terms, IAU 2000
EQEQ94 equation of the equinoxes, IAU 1994
ERA00 Earth rotation angle, IAU 2000
GMST00 Greenwich mean sidereal time, IAU 2000
GMST06 Greenwich mean sidereal time, IAU 2006
GMST82 Greenwich mean sidereal time, IAU 1982
GST00A Greenwich apparent sidereal time, IAU 2000A
GST00B Greenwich apparent sidereal time, IAU 2000B
GST06 Greenwich apparent ST, IAU 2006, given NPB matrix
GST06A Greenwich apparent sidereal time, IAU 2006/2000A
GST94 Greenwich apparent sidereal time, IAU 1994
Ephemerides (limited precision)
EPV00 Earth position and velocity
PLAN94 major-planet position and velocity
Precession, nutation, polar motion
BI00 frame bias components, IAU 2000
BP00 frame bias and precession matrices, IAU 2000
BP06 frame bias and precession matrices, IAU 2006
BPN2XY extract CIP X,Y coordinates from NPB matrix
C2I00A celestial-to-intermediate matrix, IAU 2000A
C2I00B celestial-to-intermediate matrix, IAU 2000B
C2I06A celestial-to-intermediate matrix, IAU 2006/2000A
C2IBPN celestial-to-intermediate matrix, given NPB matrix, IAU 2000
C2IXY celestial-to-intermediate matrix, given X,Y, IAU 2000
C2IXYS celestial-to-intermediate matrix, given X,Y and s
C2T00A celestial-to-terrestrial matrix, IAU 2000A
C2T00B celestial-to-terrestrial matrix, IAU 2000B
C2T06A celestial-to-terrestrial matrix, IAU 2006/2000A
C2TCIO form CIO-based celestial-to-terrestrial matrix
C2TEQX form equinox-based celestial-to-terrestrial matrix
C2TPE celestial-to-terrestrial matrix given nutation, IAU 2000
C2TXY celestial-to-terrestrial matrix given CIP, IAU 2000
EO06A equation of the origins, IAU 2006/2000A
EORS equation of the origins, given NPB matrix and s
FW2M Fukushima-Williams angles to r-matrix
FW2XY Fukushima-Williams angles to X,Y
NUM00A nutation matrix, IAU 2000A
NUM00B nutation matrix, IAU 2000B
NUM06A nutation matrix, IAU 2006/2000A
NUMAT form nutation matrix
NUT00A nutation, IAU 2000A
NUT00B nutation, IAU 2000B
NUT06A nutation, IAU 2006/2000A
NUT80 nutation, IAU 1980
NUTM80 nutation matrix, IAU 1980
OBL06 mean obliquity, IAU 2006
OBL80 mean obliquity, IAU 1980
PB06 zeta,z,theta precession angles, IAU 2006, including bias
PFW06 bias-precession Fukushima-Williams angles, IAU 2006
PMAT00 precession matrix (including frame bias), IAU 2000
PMAT06 PB matrix, IAU 2006
PMAT76 precession matrix, IAU 1976
PN00 bias/precession/nutation results, IAU 2000
PN00A bias/precession/nutation, IAU 2000A
PN00B bias/precession/nutation, IAU 2000B
PN06 bias/precession/nutation results, IAU 2006
PN06A bias/precession/nutation results, IAU 2006/2000A
PNM00A classical NPB matrix, IAU 2000A
PNM00B classical NPB matrix, IAU 2000B
PNM06A classical NPB matrix, IAU 2006/2000A
PNM80 precession/nutation matrix, IAU 1976/1980
P06E precession angles, IAU 2006, equinox based
POM00 polar motion matrix
PR00 IAU 2000 precession adjustments
PREC76 accumulated precession angles, IAU 1976
S00 the CIO locator s, given X,Y, IAU 2000A
S00A the CIO locator s, IAU 2000A
S00B the CIO locator s, IAU 2000B
S06 the CIO locator s, given X,Y, IAU 2006
S06A the CIO locator s, IAU 2006/2000A
SP00 the TIO locator s', IERS 2003
XY06 CIP, IAU 2006/2000A, from series
XYS00A CIP and s, IAU 2000A
XYS00B CIP and s, IAU 2000B
XYS06A CIP and s, IAU 2006/2000A
Fundamental arguments for nutation etc.
FAD03 mean elongation of the Moon from the Sun
FAE03 mean longitude of Earth
FAF03 mean argument of the latitude of the Moon
FAJU03 mean longitude of Jupiter
FAL03 mean anomaly of the Moon
FALP03 mean anomaly of the Sun
FAMA03 mean longitude of Mars
FAME03 mean longitude of Mercury
FANE03 mean longitude of Neptune
FAOM03 mean longitude of the Moon's ascending node
FAPA03 general accumulated precession in longitude
FASA03 mean longitude of Saturn
FAUR03 mean longitude of Uranus
FAVE03 mean longitude of Venus
Star space motion
PVSTAR space motion pv-vector to star catalog data
STARPV star catalog data to space motion pv-vector
Star catalog conversions
FK52H transform FK5 star data into the Hipparcos system
FK5HIP FK5 to Hipparcos rotation and spin
FK5HZ FK5 to Hipparcos assuming zero Hipparcos proper motion
H2FK5 transform Hipparcos star data into the FK5 system
HFK5Z Hipparcos to FK5 assuming zero Hipparcos proper motion
STARPM proper motion between two epochs
Geodetic/geocentric
EFORM a,f for a nominated Earth reference ellipsoid
GC2GD geocentric to geodetic for a nominated ellipsoid
GC2GDE geocentric to geodetic given ellipsoid a,f
GD2GC geodetic to geocentric for a nominated ellipsoid
GD2GCE geodetic to geocentric given ellipsoid a,f
Obsolete
C2TCEO former name of C2TCIO
CALLS: FORTRAN VERSION
CALL iau_BI00 ( DPSIBI, DEPSBI, DRA )
CALL iau_BP00 ( DATE1, DATE2, RB, RP, RBP )
CALL iau_BP06 ( DATE1, DATE2, RB, RP, RBP )
CALL iau_BPN2XY ( RBPN, X, Y )
CALL iau_C2I00A ( DATE1, DATE2, RC2I )
CALL iau_C2I00B ( DATE1, DATE2, RC2I )
CALL iau_C2I06A ( DATE1, DATE2, RC2I )
CALL iau_C2IBPN ( DATE1, DATE2, RBPN, RC2I )
CALL iau_C2IXY ( DATE1, DATE2, X, Y, RC2I )
CALL iau_C2IXYS ( X, Y, S, RC2I )
CALL iau_C2T00A ( TTA, TTB, UTA, UTB, XP, YP, RC2T )
CALL iau_C2T00B ( TTA, TTB, UTA, UTB, XP, YP, RC2T )
CALL iau_C2T06A ( TTA, TTB, UTA, UTB, XP, YP, RC2T )
CALL iau_C2TCEO ( RC2I, ERA, RPOM, RC2T )
CALL iau_C2TCIO ( RC2I, ERA, RPOM, RC2T )
CALL iau_C2TEQX ( RBPN, GST, RPOM, RC2T )
CALL iau_C2TPE ( TTA, TTB, UTA, UTB, DPSI, DEPS, XP, YP, RC2T )
CALL iau_C2TXY ( TTA, TTB, UTA, UTB, X, Y, XP, YP, RC2T )
CALL iau_CAL2JD ( IY, IM, ID, DJM0, DJM, J )
CALL iau_D2DTF ( SCALE, NDP, D1, D2, IY, IM, ID, IHMSF, J )
CALL iau_DAT ( IY, IM, ID, FD, DELTAT, J )
D = iau_DTDB ( DATE1, DATE2, UT, ELONG, U, V )
CALL iau_DTF2D ( SCALE, IY, IM, ID, IHR, IMN, SEC, D1, D2, J )
D = iau_EE00 ( DATE1, DATE2, EPSA, DPSI )
D = iau_EE00A ( DATE1, DATE2 )
D = iau_EE00B ( DATE1, DATE2 )
D = iau_EE06A ( DATE1, DATE2 )
D = iau_EECT00 ( DATE1, DATE2 )
CALL iau_EFORM ( N, A, F, J )
D = iau_EO06A ( DATE1, DATE2 )
D = iau_EORS ( RNPB, S )
D = iau_EPB ( DJ1, DJ2 )
CALL iau_EPB2JD ( EPB, DJM0, DJM )
D = iau_EPJ ( DJ1, DJ2 )
CALL iau_EPJ2JD ( EPJ, DJM0, DJM )
CALL iau_EPV00 ( DJ1, DJ2, PVH, PVB, J )
D = iau_EQEQ94 ( DATE1, DATE2 )
D = iau_ERA00 ( DJ1, DJ2 )
D = iau_FAD03 ( T )
D = iau_FAE03 ( T )
D = iau_FAF03 ( T )
D = iau_FAJU03 ( T )
D = iau_FAL03 ( T )
D = iau_FALP03 ( T )
D = iau_FAMA03 ( T )
D = iau_FAME03 ( T )
D = iau_FANE03 ( T )
D = iau_FAOM03 ( T )
D = iau_FAPA03 ( T )
D = iau_FASA03 ( T )
D = iau_FAUR03 ( T )
D = iau_FAVE03 ( T )
CALL iau_FK52H ( R5, D5, DR5, DD5, PX5, RV5,
: RH, DH, DRH, DDH, PXH, RVH )
CALL iau_FK5HIP ( R5H, S5H )
CALL iau_FK5HZ ( R5, D5, DATE1, DATE2, RH, DH )
CALL iau_FW2M ( GAMB, PHIB, PSI, EPS, R )
CALL iau_FW2XY ( GAMB, PHIB, PSI, EPS, X, Y )
CALL iau_GC2GD ( N, XYZ, ELONG, PHI, HEIGHT, J )
CALL iau_GC2GDE ( A, F, XYZ, ELONG, PHI, HEIGHT, J )
CALL iau_GD2GC ( N, ELONG, PHI, HEIGHT, XYZ, J )
CALL iau_GD2GCE ( A, F, ELONG, PHI, HEIGHT, XYZ, J )
D = iau_GMST00 ( UTA, UTB, TTA, TTB )
D = iau_GMST06 ( UTA, UTB, TTA, TTB )
D = iau_GMST82 ( UTA, UTB )
D = iau_GST00A ( UTA, UTB, TTA, TTB )
D = iau_GST00B ( UTA, UTB )
D = iau_GST06 ( UTA, UTB, TTA, TTB, RNPB )
D = iau_GST06A ( UTA, UTB, TTA, TTB )
D = iau_GST94 ( UTA, UTB )
CALL iau_H2FK5 ( RH, DH, DRH, DDH, PXH, RVH,
: R5, D5, DR5, DD5, PX5, RV5 )
CALL iau_HFK5Z ( RH, DH, DATE1, DATE2, R5, D5, DR5, DD5 )
CALL iau_JD2CAL ( DJ1, DJ2, IY, IM, ID, FD, J )
CALL iau_JDCALF ( NDP, DJ1, DJ2, IYMDF, J )
CALL iau_NUM00A ( DATE1, DATE2, RMATN )
CALL iau_NUM00B ( DATE1, DATE2, RMATN )
CALL iau_NUM06A ( DATE1, DATE2, RMATN )
CALL iau_NUMAT ( EPSA, DPSI, DEPS, RMATN )
CALL iau_NUT00A ( DATE1, DATE2, DPSI, DEPS )
CALL iau_NUT00B ( DATE1, DATE2, DPSI, DEPS )
CALL iau_NUT06A ( DATE1, DATE2, DPSI, DEPS )
CALL iau_NUT80 ( DATE1, DATE2, DPSI, DEPS )
CALL iau_NUTM80 ( DATE1, DATE2, RMATN )
D = iau_OBL06 ( DATE1, DATE2 )
D = iau_OBL80 ( DATE1, DATE2 )
CALL iau_PB06 ( DATE1, DATE2, BZETA, BZ, BTHETA )
CALL iau_PFW06 ( DATE1, DATE2, GAMB, PHIB, PSIB, EPSA )
CALL iau_PLAN94 ( DATE1, DATE2, NP, PV, J )
CALL iau_PMAT00 ( DATE1, DATE2, RBP )
CALL iau_PMAT06 ( DATE1, DATE2, RBP )
CALL iau_PMAT76 ( DATE1, DATE2, RMATP )
CALL iau_PN00 ( DATE1, DATE2, DPSI, DEPS,
: EPSA, RB, RP, RBP, RN, RBPN )
CALL iau_PN00A ( DATE1, DATE2,
: DPSI, DEPS, EPSA, RB, RP, RBP, RN, RBPN )
CALL iau_PN00B ( DATE1, DATE2,
: DPSI, DEPS, EPSA, RB, RP, RBP, RN, RBPN )
CALL iau_PN06 ( DATE1, DATE2, DPSI, DEPS,
: EPSA, RB, RP, RBP, RN, RBPN )
CALL iau_PN06A ( DATE1, DATE2,
DPSI, DEPS, RB, RP, RBP, RN, RBPN )
CALL iau_PNM00A ( DATE1, DATE2, RBPN )
CALL iau_PNM00B ( DATE1, DATE2, RBPN )
CALL iau_PNM06A ( DATE1, DATE2, RNPB )
CALL iau_PNM80 ( DATE1, DATE2, RMATPN )
CALL iau_P06E ( DATE1, DATE2,
: EPS0, PSIA, OMA, BPA, BQA, PIA, BPIA,
: EPSA, CHIA, ZA, ZETAA, THETAA, PA, GAM, PHI, PSI )
CALL iau_POM00 ( XP, YP, SP, RPOM )
CALL iau_PR00 ( DATE1, DATE2, DPSIPR, DEPSPR )
CALL iau_PREC76 ( EP01, EP02, EP11, EP12, ZETA, Z, THETA )
CALL iau_PVSTAR ( PV, RA, DEC, PMR, PMD, PX, RV, J )
D = iau_S00 ( DATE1, DATE2, X, Y )
D = iau_S00A ( DATE1, DATE2 )
D = iau_S00B ( DATE1, DATE2 )
D = iau_S06 ( DATE1, DATE2, X, Y )
D = iau_S06A ( DATE1, DATE2 )
D = iau_SP00 ( DATE1, DATE2 )
CALL iau_STARPM ( RA1, DEC1, PMR1, PMD1, PX1, RV1,
: EP1A, EP1B, EP2A, EP2B,
: RA2, DEC2, PMR2, PMD2, PX2, RV2, J )
CALL iau_STARPV ( RA, DEC, PMR, PMD, PX, RV, PV, J )
CALL iau_TAITT ( TAI1, TAI2, TT1, TT2, J )
CALL iau_TAIUT1 ( TAI1, TAI2, DTA, UT11, UT12, J )
CALL iau_TAIUTC ( TAI1, TAI2, UTC1, UTC2, J )
CALL iau_TCBTDB ( TCB1, TCB2, TDB1, TDB2, J )
CALL iau_TCGTT ( TCG1, TCG2, TT1, TT2, J )
CALL iau_TDBTCB ( TDB1, TDB2, TCB1, TCB2, J )
CALL iau_TDBTT ( TDB1, TDB2, DTR, TT1, TT2, J )
CALL iau_TTTAI ( TT1, TT2, TAI1, TAI2, J )
CALL iau_TTTCG ( TT1, TT2, TCG1, TCG2, J )
CALL iau_TTTDB ( TT1, TT2, DTR, TDB1, TDB2, J )
CALL iau_TTUT1 ( TT1, TT2, DT, UT11, UT12, J )
CALL iau_UT1TAI ( UT11, UT12, TAI1, TAI2, J )
CALL iau_UT1TT ( UT11, UT12, DT, TT1, TT2, J )
CALL iau_UT1UTC ( UT11, UT12, DUT, UTC1, UTC2, J )
CALL iau_UTCTAI ( UTC1, UTC2, DTA, TAI1, TAI2, J )
CALL iau_UTCUT1 ( UTC1, UTC2, DUT, UT11, UT12, J )
CALL iau_XY06 ( DATE1, DATE2, X, Y )
CALL iau_XYS00A ( DATE1, DATE2, X, Y, S )
CALL iau_XYS00B ( DATE1, DATE2, X, Y, S )
CALL iau_XYS06A ( DATE1, DATE2, X, Y, S )
CALLS: C VERSION
iauBi00 ( &dpsibi, &depsbi, &dra );
iauBp00 ( date1, date2, rb, rp, rbp );
iauBp06 ( date1, date2, rb, rp, rbp );
iauBpn2xy ( rbpn, &x, &y );
iauC2i00a ( date1, date2, rc2i );
iauC2i00b ( date1, date2, rc2i );
iauC2i06a ( date1, date2, rc2i );
iauC2ibpn ( date1, date2, rbpn, rc2i );
iauC2ixy ( date1, date2, x, y, rc2i );
iauC2ixys ( x, y, s, rc2i );
iauC2t00a ( tta, ttb, uta, utb, xp, yp, rc2t );
iauC2t00b ( tta, ttb, uta, utb, xp, yp, rc2t );
iauC2t06a ( tta, ttb, uta, utb, xp, yp, rc2t );
iauC2tcio ( rc2i, era, rpom, rc2t );
iauC2teqx ( rbpn, gst, rpom, rc2t );
iauC2tpe ( tta, ttb, uta, utb, dpsi, deps, xp, yp, rc2t );
iauC2txy ( tta, ttb, uta, utb, x, y, xp, yp, rc2t );
i = iauCal2jd ( iy, im, id, &djm0, &djm );
i = iauD2dtf ( scale, ndp, d1, d2, &iy, &im, &id, ihmsf );
i = iauDat ( iy, im, id, fd, &deltat );
d = iauDtdb ( date1, date2, ut, elong, u, v );
i = iauDtf2d ( scale, iy, im, id, ihr, imn, sec, &d1, &d2 );
d = iauEe00 ( date1, date2, epsa, dpsi );
d = iauEe00a ( date1, date2 );
d = iauEe00b ( date1, date2 );
d = iauEe06 ( date1, date2 );
d = iauEect00 ( date1, date2 );
i = iauEform ( n, &a, &f );
d = iauEo06 ( date1, date2 );
d = iauEors ( rnpb, s );
d = iauEpb ( dj1, dj2 );
iauEpb2jd ( epb, &djm0, &djm );
d = iauEpj ( dj1, dj2 );
iauEpj2jd ( epj, &djm0, &djm );
i = iauEpv00 ( dj1, dj2, pvh, pvb );
d = iauEqeq94 ( date1, date2 );
d = iauEra00 ( dj1, dj2 );
d = iauFad03 ( t );
d = iauFae03 ( t );
d = iauFaf03 ( t );
d = iauFaju03 ( t );
d = iauFal03 ( t );
d = iauFalp03 ( t );
d = iauFama03 ( t );
d = iauFame03 ( t );
d = iauFane03 ( t );
d = iauFaom03 ( t );
d = iauFapa03 ( t );
d = iauFasa03 ( t );
d = iauFaur03 ( t );
d = iauFave03 ( t );
iauFk52h ( r5, d5, dr5, dd5, px5, rv5,
&rh, &dh, &drh, &ddh, &pxh, &rvh );
iauFk5hip ( r5h, s5h );
iauFk5hz ( r5, d5, date1, date2, &rh, &dh );
iauFw2m ( gamb, phib, psi, eps, r );
iauFw2xy ( gamb, phib, psi, eps, &x, &y );
i = iauGc2gd ( n, xyz, &elong, &phi, &height );
i = iauGc2gde ( a, f, xyz, &elong, &phi, &height );
i = iauGd2gc ( n, elong, phi, height, xyz );
i = iauGd2gce ( a, f, elong, phi, height, xyz );
d = iauGmst00 ( uta, utb, tta, ttb );
d = iauGmst06 ( uta, utb, tta, ttb );
d = iauGmst82 ( uta, utb );
d = iauGst00a ( uta, utb, tta, ttb );
d = iauGst00b ( uta, utb );
d = iauGst06 ( uta, utb, tta, ttb, rnpb );
d = iauGst06a ( uta, utb, tta, ttb );
d = iauGst94 ( uta, utb );
iauH2fk5 ( rh, dh, drh, ddh, pxh, rvh,
&r5, &d5, &dr5, &dd5, &px5, &rv5 );
iauHfk5z ( rh, dh, date1, date2,
&r5, &d5, &dr5, &dd5 );
i = iauJd2cal ( dj1, dj2, &iy, &im, &id, &fd );
i = iauJdcalf ( ndp, dj1, dj2, iymdf );
iauNum00a ( date1, date2, rmatn );
iauNum00b ( date1, date2, rmatn );
iauNum06a ( date1, date2, rmatn );
iauNumat ( epsa, dpsi, deps, rmatn );
iauNut00a ( date1, date2, &dpsi, &deps );
iauNut00b ( date1, date2, &dpsi, &deps );
iauNut06a ( date1, date2, &dpsi, &deps );
iauNut80 ( date1, date2, &dpsi, &deps );
iauNutm80 ( date1, date2, rmatn );
d = iauObl06 ( date1, date2 );
d = iauObl80 ( date1, date2 );
iauPb06 ( date1, date2, &bzeta, &bz, &btheta );
iauPfw06 ( date1, date2, &gamb, &phib, &psib, &epsa );
i = iauPlan94 ( date1, date2, np, pv );
iauPmat00 ( date1, date2, rbp );
iauPmat06 ( date1, date2, rbp );
iauPmat76 ( date1, date2, rmatp );
iauPn00 ( date1, date2, dpsi, deps,
&epsa, rb, rp, rbp, rn, rbpn );
iauPn00a ( date1, date2,
&dpsi, &deps, &epsa, rb, rp, rbp, rn, rbpn );
iauPn00b ( date1, date2,
&dpsi, &deps, &epsa, rb, rp, rbp, rn, rbpn );
iauPn06 ( date1, date2, dpsi, deps,
&epsa, rb, rp, rbp, rn, rbpn );
iauPn06a ( date1, date2,
&dpsi, &deps, &epsa, rb, rp, rbp, rn, rbpn );
iauPnm00a ( date1, date2, rbpn );
iauPnm00b ( date1, date2, rbpn );
iauPnm06a ( date1, date2, rnpb );
iauPnm80 ( date1, date2, rmatpn );
iauP06e ( date1, date2,
&eps0, &psia, &oma, &bpa, &bqa, &pia, &bpia,
&epsa, &chia, &za, &zetaa, &thetaa, &pa,
&gam, &phi, &psi );
iauPom00 ( xp, yp, sp, rpom );
iauPr00 ( date1, date2, &dpsipr, &depspr );
iauPrec76 ( ep01, ep02, ep11, ep12, &zeta, &z, &theta );
i = iauPvstar ( pv, &ra, &dec, &pmr, &pmd, &px, &rv );
d = iauS00 ( date1, date2, x, y );
d = iauS00a ( date1, date2 );
d = iauS00b ( date1, date2 );
d = iauS06 ( date1, date2, x, y );
d = iauS06a ( date1, date2 );
d = iauSp00 ( date1, date2 );
i = iauStarpm ( ra1, dec1, pmr1, pmd1, px1, rv1,
ep1a, ep1b, ep2a, ep2b,
&ra2, &dec2, &pmr2, &pmd2, &px2, &rv2 );
i = iauStarpv ( ra, dec, pmr, pmd, px, rv, pv );
i = iauTaitt ( tai1, tai2, &tt1, &tt2 );
i = iauTaiut1 ( tai1, tai2, dta, &ut11, &ut12 );
i = iauTaiutc ( tai1, tai2, &utc1, &utc2 );
i = iauTcbtdb ( tcb1, tcb2, &tdb1, &tdb2 );
i = iauTcgtt ( tcg1, tcg2, &tt1, &tt2 );
i = iauTdbtcb ( tdb1, tdb2, &tcb1, &tcb2 );
i = iauTdbtt ( tdb1, tdb2, dtr, &tt1, &tt2 );
i = iauTttai ( tt1, tt2, &tai1, &tai2 );
i = iauTttcg ( tt1, tt2, &tcg1, &tcg2 );
i = iauTttdb ( tt1, tt2, dtr, &tdb1, &tdb2 );
i = iauTtut1 ( tt1, tt2, dt, &ut11, &ut12 );
i = iauUt1tai ( ut11, ut12, &tai1, &tai2 );
i = iauUt1tt ( ut11, ut12, dt, &tt1, &tt2 );
i = iauUt1utc ( ut11, ut12, dut, &utc1, &utc2 );
i = iauUtctai ( utc1, utc2, dta, &tai1, &tai2 );
i = iauUtcut1 ( utc1, utc2, dut, &ut11, &ut12 );
iauXy06 ( date1, date2, &x, &y );
iauXys00a ( date1, date2, &x, &y, &s );
iauXys00b ( date1, date2, &x, &y, &s );
iauXys06a ( date1, date2, &x, &y, &s );
sofa_vml.lis 2010 September 5
--------------------------
SOFA Vector/Matrix Library
--------------------------
PREFACE
The routines described here comprise the SOFA vector/matrix library.
Their general appearance and coding style conforms to conventions
agreed by the SOFA Review Board, and their functions, names and
algorithms have been ratified by the Board. Procedures for
soliciting and agreeing additions to the library are still evolving.
PROGRAMMING LANGUAGES
The SOFA routines are available in two programming languages at present:
Fortran 77 and ANSI C.
There is a one-to-one relationship between the two language versions.
The naming convention is such that a SOFA routine referred to
generically as "EXAMPL" exists as a Fortran subprogram iau_EXAMPL and a
C function iauExampl. The calls for the two versions are very similar,
with the same arguments in the same order. In a few cases, the C
equivalent of a Fortran SUBROUTINE subprogram uses a return value rather
than an argument.
GENERAL PRINCIPLES
The library consists mostly of routines which operate on ordinary
Cartesian vectors (x,y,z) and 3x3 rotation matrices. However, there is
also support for vectors which represent velocity as well as position
and vectors which represent rotation instead of position. The vectors
which represent both position and velocity may be considered still to
have dimensions (3), but to comprise elements each of which is two
numbers, representing the value itself and the time derivative. Thus:
* "Position" or "p" vectors (or just plain 3-vectors) have dimension
(3) in Fortran and [3] in C.
* "Position/velocity" or "pv" vectors have dimensions (3,2) in Fortran
and [2][3] in C.
* "Rotation" or "r" matrices have dimensions (3,3) in Fortran and [3][3]
in C. When used for rotation, they are "orthogonal"; the inverse of
such a matrix is equal to the transpose. Most of the routines in
this library do not assume that r-matrices are necessarily orthogonal
and in fact work on any 3x3 matrix.
* "Rotation" or "r" vectors have dimensions (3) in Fortran and [3] in C.
Such vectors are a combination of the Euler axis and angle and are
convertible to and from r-matrices. The direction is the axis of
rotation and the magnitude is the angle of rotation, in radians.
Because the amount of rotation can be scaled up and down simply by
multiplying the vector by a scalar, r-vectors are useful for
representing spins about an axis which is fixed.
* The above rules mean that in terms of memory address, the three
velocity components of a pv-vector follow the three position
components. Application code is permitted to exploit this and all
other knowledge of the internal layouts: that x, y and z appear in
that order and are in a right-handed Cartesian coordinate system etc.
For example, the cp function (copy a p-vector) can be used to copy
the velocity component of a pv-vector (indeed, this is how the
CPV routine is coded).
* The routines provided do not completely fill the range of operations
that link all the various vector and matrix options, but are confined
to functions that are required by other parts of the SOFA software or
which are likely to prove useful.
In addition to the vector/matrix routines, the library contains some
routines related to spherical angles, including conversions to and
from sexagesimal format.
Using the library requires knowledge of vector/matrix methods, spherical
trigonometry, and methods of attitude representation. These topics are
covered in many textbooks, including "Spacecraft Attitude Determination
and Control", James R. Wertz (ed.), Astrophysics and Space Science
Library, Vol. 73, D. Reidel Publishing Company, 1986.
OPERATIONS INVOLVING P-VECTORS AND R-MATRICES
Initialize
ZP zero p-vector
ZR initialize r-matrix to null
IR initialize r-matrix to identity
Copy/extend/extract
CP copy p-vector
CR copy r-matrix
Build rotations
RX rotate r-matrix about x
RY rotate r-matrix about y
RZ rotate r-matrix about z
Spherical/Cartesian conversions
S2C spherical to unit vector
C2S unit vector to spherical
S2P spherical to p-vector
P2S p-vector to spherical
Operations on vectors
PPP p-vector plus p-vector
PMP p-vector minus p-vector
PPSP p-vector plus scaled p-vector
PDP inner (=scalar=dot) product of two p-vectors
PXP outer (=vector=cross) product of two p-vectors
PM modulus of p-vector
PN normalize p-vector returning modulus
SXP multiply p-vector by scalar
Operations on matrices
RXR r-matrix multiply
TR transpose r-matrix
Matrix-vector products
RXP product of r-matrix and p-vector
TRXP product of transpose of r-matrix and p-vector
Separation and position-angle
SEPP angular separation from p-vectors
SEPS angular separation from spherical coordinates
PAP position-angle from p-vectors
PAS position-angle from spherical coordinates
Rotation vectors
RV2M r-vector to r-matrix
RM2V r-matrix to r-vector
OPERATIONS INVOLVING PV-VECTORS
Initialize
ZPV zero pv-vector
Copy/extend/extract
CPV copy pv-vector
P2PV append zero velocity to p-vector
PV2P discard velocity component of pv-vector
Spherical/Cartesian conversions
S2PV spherical to pv-vector
PV2S pv-vector to spherical
Operations on vectors
PVPPV pv-vector plus pv-vector
PVMPV pv-vector minus pv-vector
PVDPV inner (=scalar=dot) product of two pv-vectors
PVXPV outer (=vector=cross) product of two pv-vectors
PVM modulus of pv-vector
SXPV multiply pv-vector by scalar
S2XPV multiply pv-vector by two scalars
PVU update pv-vector
PVUP update pv-vector discarding velocity
Matrix-vector products
RXPV product of r-matrix and pv-vector
TRXPV product of transpose of r-matrix and pv-vector
OPERATIONS ON ANGLES
ANP normalize radians to range 0 to 2pi
ANPM normalize radians to range -pi to +pi
A2TF decompose radians into hours, minutes, seconds
A2AF decompose radians into degrees, arcminutes, arcseconds
AF2A degrees, arcminutes, arcseconds to radians
D2TF decompose days into hours, minutes, seconds
TF2A hours, minutes, seconds to radians
TF2D hours, minutes, seconds to days
CALLS: FORTRAN VERSION
CALL iau_A2AF ( NDP, ANGLE, SIGN, IDMSF )
CALL iau_A2TF ( NDP, ANGLE, SIGN, IHMSF )
CALL iau_AF2A ( S, IDEG, IAMIN, ASEC, RAD, J )
D = iau_ANP ( A )
D = iau_ANPM ( A )
CALL iau_C2S ( P, THETA, PHI )
CALL iau_CP ( P, C )
CALL iau_CPV ( PV, C )
CALL iau_CR ( R, C )
CALL iau_D2TF ( NDP, DAYS, SIGN, IHMSF )
CALL iau_IR ( R )
CALL iau_P2PV ( P, PV )
CALL iau_P2S ( P, THETA, PHI, R )
CALL iau_PAP ( A, B, THETA )
CALL iau_PAS ( AL, AP, BL, BP, THETA )
CALL iau_PDP ( A, B, ADB )
CALL iau_PM ( P, R )
CALL iau_PMP ( A, B, AMB )
CALL iau_PN ( P, R, U )
CALL iau_PPP ( A, B, APB )
CALL iau_PPSP ( A, S, B, APSB )
CALL iau_PV2P ( PV, P )
CALL iau_PV2S ( PV, THETA, PHI, R, TD, PD, RD )
CALL iau_PVDPV ( A, B, ADB )
CALL iau_PVM ( PV, R, S )
CALL iau_PVMPV ( A, B, AMB )
CALL iau_PVPPV ( A, B, APB )
CALL iau_PVU ( DT, PV, UPV )
CALL iau_PVUP ( DT, PV, P )
CALL iau_PVXPV ( A, B, AXB )
CALL iau_PXP ( A, B, AXB )
CALL iau_RM2V ( R, P )
CALL iau_RV2M ( P, R )
CALL iau_RX ( PHI, R )
CALL iau_RXP ( R, P, RP )
CALL iau_RXPV ( R, PV, RPV )
CALL iau_RXR ( A, B, ATB )
CALL iau_RY ( THETA, R )
CALL iau_RZ ( PSI, R )
CALL iau_S2C ( THETA, PHI, C )
CALL iau_S2P ( THETA, PHI, R, P )
CALL iau_S2PV ( THETA, PHI, R, TD, PD, RD, PV )
CALL iau_S2XPV ( S1, S2, PV )
CALL iau_SEPP ( A, B, S )
CALL iau_SEPS ( AL, AP, BL, BP, S )
CALL iau_SXP ( S, P, SP )
CALL iau_SXPV ( S, PV, SPV )
CALL iau_TF2A ( S, IHOUR, IMIN, SEC, RAD, J )
CALL iau_TF2D ( S, IHOUR, IMIN, SEC, DAYS, J )
CALL iau_TR ( R, RT )
CALL iau_TRXP ( R, P, TRP )
CALL iau_TRXPV ( R, PV, TRPV )
CALL iau_ZP ( P )
CALL iau_ZPV ( PV )
CALL iau_ZR ( R )
CALLS: C VERSION
iauA2af ( ndp, angle, &sign, idmsf );
iauA2tf ( ndp, angle, &sign, ihmsf );
i = iauAf2a ( s, ideg, iamin, asec, &rad );
d = iauAnp ( a );
d = iauAnpm ( a );
iauC2s ( p, &theta, &phi );
iauCp ( p, c );
iauCpv ( pv, c );
iauCr ( r, c );
iauD2tf ( ndp, days, &sign, ihmsf );
iauIr ( r );
iauP2pv ( p, pv );
iauP2s ( p, &theta, &phi, &r );
d = iauPap ( a, b );
d = iauPas ( al, ap, bl, bp );
d = iauPdp ( a, b );
d = iauPm ( p );
iauPmp ( a, b, amb );
iauPn ( p, &r, u );
iauPpp ( a, b, apb );
iauPpsp ( a, s, b, apsb );
iauPv2p ( pv, p );
iauPv2s ( pv, &theta, &phi, &r, &td, &pd, &rd );
iauPvdpv ( a, b, adb );
iauPvm ( pv, &r, &s );
iauPvmpv ( a, b, amb );
iauPvppv ( a, b, apb );
iauPvu ( dt, pv, upv );
iauPvup ( dt, pv, p );
iauPvxpv ( a, b, axb );
iauPxp ( a, b, axb );
iauRm2v ( r, p );
iauRv2m ( p, r );
iauRx ( phi, r );
iauRxp ( r, p, rp );
iauRxpv ( r, pv, rpv );
iauRxr ( a, b, atb );
iauRy ( theta, r );
iauRz ( psi, r );
iauS2c ( theta, phi, c );
iauS2p ( theta, phi, r, p );
iauS2pv ( theta, phi, r, td, pd, rd, pV );
iauS2xpv ( s1, s2, pv );
d = iauSepp ( a, b );
d = iauSeps ( al, ap, bl, bp );
iauSxp ( s, p, sp );
iauSxpv ( s, pv, spv );
i = iauTf2a ( s, ihour, imin, sec, &rad );
i = iauTf2d ( s, ihour, imin, sec, &days );
iauTr ( r, rt );
iauTrxp ( r, p, trp );
iauTrxpv ( r, pv, trpv );
iauZp ( p );
iauZpv ( pv );
iauZr ( r );
void iauA2af(int ndp, double angle, char *sign, int idmsf[4])
/*
** - - - - - - - -
** i a u A 2 a f
** - - - - - - - -
**
** Decompose radians into degrees, arcminutes, arcseconds, fraction.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** ndp int resolution (Note 1)
** angle double angle in radians
**
** Returned:
** sign char '+' or '-'
** idmsf int[4] degrees, arcminutes, arcseconds, fraction
**
** Called:
** iauD2tf decompose days to hms
**
** Notes:
**
** 1) The argument ndp is interpreted as follows:
**
** ndp resolution
** : ...0000 00 00
** -7 1000 00 00
** -6 100 00 00
** -5 10 00 00
** -4 1 00 00
** -3 0 10 00
** -2 0 01 00
** -1 0 00 10
** 0 0 00 01
** 1 0 00 00.1
** 2 0 00 00.01
** 3 0 00 00.001
** : 0 00 00.000...
**
** 2) The largest positive useful value for ndp is determined by the
** size of angle, the format of doubles on the target platform, and
** the risk of overflowing idmsf[3]. On a typical platform, for
** angle up to 2pi, the available floating-point precision might
** correspond to ndp=12. However, the practical limit is typically
** ndp=9, set by the capacity of a 32-bit int, or ndp=4 if int is
** only 16 bits.
**
** 3) The absolute value of angle may exceed 2pi. In cases where it
** does not, it is up to the caller to test for and handle the
** case where angle is very nearly 2pi and rounds up to 360 degrees,
** by testing for idmsf[0]=360 and setting idmsf[0-3] to zero.
**
*/
void iauA2tf(int ndp, double angle, char *sign, int ihmsf[4])
/*
** - - - - - - - -
** i a u A 2 t f
** - - - - - - - -
**
** Decompose radians into hours, minutes, seconds, fraction.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** ndp int resolution (Note 1)
** angle double angle in radians
**
** Returned:
** sign char '+' or '-'
** ihmsf int[4] hours, minutes, seconds, fraction
**
** Called:
** iauD2tf decompose days to hms
**
** Notes:
**
** 1) The argument ndp is interpreted as follows:
**
** ndp resolution
** : ...0000 00 00
** -7 1000 00 00
** -6 100 00 00
** -5 10 00 00
** -4 1 00 00
** -3 0 10 00
** -2 0 01 00
** -1 0 00 10
** 0 0 00 01
** 1 0 00 00.1
** 2 0 00 00.01
** 3 0 00 00.001
** : 0 00 00.000...
**
** 2) The largest positive useful value for ndp is determined by the
** size of angle, the format of doubles on the target platform, and
** the risk of overflowing ihmsf[3]. On a typical platform, for
** angle up to 2pi, the available floating-point precision might
** correspond to ndp=12. However, the practical limit is typically
** ndp=9, set by the capacity of a 32-bit int, or ndp=4 if int is
** only 16 bits.
**
** 3) The absolute value of angle may exceed 2pi. In cases where it
** does not, it is up to the caller to test for and handle the
** case where angle is very nearly 2pi and rounds up to 24 hours,
** by testing for ihmsf[0]=24 and setting ihmsf(0-3) to zero.
**
*/
int iauAf2a(int s, int ideg, int iamin, double asec, double *rad)
/*
** - - - - - - - -
** i a u A f 2 a
** - - - - - - - -
**
** Convert degrees, arcminutes, arcseconds to radians.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** s int sign: '-' = negative, otherwise positive
** ideg int degrees
** iamin int arcminutes
** asec double arcseconds
**
** Returned:
** rad double angle in radians
**
** Returned (function value):
** int status: 0 = OK
** 1 = ideg outside range 0-359
** 2 = iamin outside range 0-59
** 3 = asec outside range 0-59.999...
**
** Notes:
**
** 1) The result is computed even if any of the range checks fail.
**
** 2) Negative ideg, iamin and/or asec produce a warning status, but
** the absolute value is used in the conversion.
**
*/
double iauAnp(double a)
/*
** - - - - - - -
** i a u A n p
** - - - - - - -
**
** Normalize angle into the range 0 <= a < 2pi.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** a double angle (radians)
**
** Returned (function value):
** double angle in range 0-2pi
**
*/
double iauAnpm(double a)
/*
** - - - - - - - -
** i a u A n p m
** - - - - - - - -
**
** Normalize angle into the range -pi <= a < +pi.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** a double angle (radians)
**
** Returned (function value):
** double angle in range +/-pi
**
*/
void iauBi00(double *dpsibi, double *depsbi, double *dra)
/*
** - - - - - - - -
** i a u B i 0 0
** - - - - - - - -
**
** Frame bias components of IAU 2000 precession-nutation models (part
** of MHB2000 with additions).
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Returned:
** dpsibi,depsbi double longitude and obliquity corrections
** dra double the ICRS RA of the J2000.0 mean equinox
**
** Notes:
**
** 1) The frame bias corrections in longitude and obliquity (radians)
** are required in order to correct for the offset between the GCRS
** pole and the mean J2000.0 pole. They define, with respect to the
** GCRS frame, a J2000.0 mean pole that is consistent with the rest
** of the IAU 2000A precession-nutation model.
**
** 2) In addition to the displacement of the pole, the complete
** description of the frame bias requires also an offset in right
** ascension. This is not part of the IAU 2000A model, and is from
** Chapront et al. (2002). It is returned in radians.
**
** 3) This is a supplemented implementation of one aspect of the IAU
** 2000A nutation model, formally adopted by the IAU General
** Assembly in 2000, namely MHB2000 (Mathews et al. 2002).
**
** References:
**
** Chapront, J., Chapront-Touze, M. & Francou, G., Astron.
** Astrophys., 387, 700, 2002.
**
** Mathews, P.M., Herring, T.A., Buffet, B.A., "Modeling of nutation
** and precession New nutation series for nonrigid Earth and
** insights into the Earth's interior", J.Geophys.Res., 107, B4,
** 2002. The MHB2000 code itself was obtained on 9th September 2002
** from ftp://maia.usno.navy.mil/conv2000/chapter5/IAU2000A.
**
*/
void iauBp00(double date1, double date2,
double rb[3][3], double rp[3][3], double rbp[3][3])
/*
** - - - - - - - -
** i a u B p 0 0
** - - - - - - - -
**
** Frame bias and precession, IAU 2000.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** rb double[3][3] frame bias matrix (Note 2)
** rp double[3][3] precession matrix (Note 3)
** rbp double[3][3] bias-precession matrix (Note 4)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The matrix rb transforms vectors from GCRS to mean J2000.0 by
** applying frame bias.
**
** 3) The matrix rp transforms vectors from J2000.0 mean equator and
** equinox to mean equator and equinox of date by applying
** precession.
**
** 4) The matrix rbp transforms vectors from GCRS to mean equator and
** equinox of date by applying frame bias then precession. It is
** the product rp x rb.
**
** 5) It is permissible to re-use the same array in the returned
** arguments. The arrays are filled in the order given.
**
** Called:
** iauBi00 frame bias components, IAU 2000
** iauPr00 IAU 2000 precession adjustments
** iauIr initialize r-matrix to identity
** iauRx rotate around X-axis
** iauRy rotate around Y-axis
** iauRz rotate around Z-axis
** iauCr copy r-matrix
** iauRxr product of two r-matrices
**
** Reference:
** "Expressions for the Celestial Intermediate Pole and Celestial
** Ephemeris Origin consistent with the IAU 2000A precession-
** nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
**
** n.b. The celestial ephemeris origin (CEO) was renamed "celestial
** intermediate origin" (CIO) by IAU 2006 Resolution 2.
**
*/
void iauBp06(double date1, double date2,
double rb[3][3], double rp[3][3], double rbp[3][3])
/*
** - - - - - - - -
** i a u B p 0 6
** - - - - - - - -
**
** Frame bias and precession, IAU 2006.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** rb double[3][3] frame bias matrix (Note 2)
** rp double[3][3] precession matrix (Note 3)
** rbp double[3][3] bias-precession matrix (Note 4)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The matrix rb transforms vectors from GCRS to mean J2000.0 by
** applying frame bias.
**
** 3) The matrix rp transforms vectors from mean J2000.0 to mean of
** date by applying precession.
**
** 4) The matrix rbp transforms vectors from GCRS to mean of date by
** applying frame bias then precession. It is the product rp x rb.
**
** Called:
** iauPfw06 bias-precession F-W angles, IAU 2006
** iauFw2m F-W angles to r-matrix
** iauPmat06 PB matrix, IAU 2006
** iauTr transpose r-matrix
** iauRxr product of two r-matrices
**
** References:
**
** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
**
** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
**
*/
void iauBpn2xy(double rbpn[3][3], double *x, double *y)
/*
** - - - - - - - - - -
** i a u B p n 2 x y
** - - - - - - - - - -
**
** Extract from the bias-precession-nutation matrix the X,Y coordinates
** of the Celestial Intermediate Pole.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** rbpn double[3][3] celestial-to-true matrix (Note 1)
**
** Returned:
** x,y double Celestial Intermediate Pole (Note 2)
**
** Notes:
**
** 1) The matrix rbpn transforms vectors from GCRS to true equator (and
** CIO or equinox) of date, and therefore the Celestial Intermediate
** Pole unit vector is the bottom row of the matrix.
**
** 2) The arguments x,y are components of the Celestial Intermediate
** Pole unit vector in the Geocentric Celestial Reference System.
**
** Reference:
**
** "Expressions for the Celestial Intermediate Pole and Celestial
** Ephemeris Origin consistent with the IAU 2000A precession-
** nutation model", Astron.Astrophys. 400, 1145-1154
** (2003)
**
** n.b. The celestial ephemeris origin (CEO) was renamed "celestial
** intermediate origin" (CIO) by IAU 2006 Resolution 2.
**
*/
void iauC2i00a(double date1, double date2, double rc2i[3][3])
/*
** - - - - - - - - - -
** i a u C 2 i 0 0 a
** - - - - - - - - - -
**
** Form the celestial-to-intermediate matrix for a given date using the
** IAU 2000A precession-nutation model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** rc2i double[3][3] celestial-to-intermediate matrix (Note 2)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The matrix rc2i is the first stage in the transformation from
** celestial to terrestrial coordinates:
**
** [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
**
** = rc2t * [CRS]
**
** where [CRS] is a vector in the Geocentric Celestial Reference
** System and [TRS] is a vector in the International Terrestrial
** Reference System (see IERS Conventions 2003), ERA is the Earth
** Rotation Angle and RPOM is the polar motion matrix.
**
** 3) A faster, but slightly less accurate result (about 1 mas), can be
** obtained by using instead the iauC2i00b function.
**
** Called:
** iauPnm00a classical NPB matrix, IAU 2000A
** iauC2ibpn celestial-to-intermediate matrix, given NPB matrix
**
** References:
**
** "Expressions for the Celestial Intermediate Pole and Celestial
** Ephemeris Origin consistent with the IAU 2000A precession-
** nutation model", Astron.Astrophys. 400, 1145-1154
** (2003)
**
** n.b. The celestial ephemeris origin (CEO) was renamed "celestial
** intermediate origin" (CIO) by IAU 2006 Resolution 2.
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
*/
void iauC2i00b(double date1, double date2, double rc2i[3][3])
/*
** - - - - - - - - - -
** i a u C 2 i 0 0 b
** - - - - - - - - - -
**
** Form the celestial-to-intermediate matrix for a given date using the
** IAU 2000B precession-nutation model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** rc2i double[3][3] celestial-to-intermediate matrix (Note 2)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The matrix rc2i is the first stage in the transformation from
** celestial to terrestrial coordinates:
**
** [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
**
** = rc2t * [CRS]
**
** where [CRS] is a vector in the Geocentric Celestial Reference
** System and [TRS] is a vector in the International Terrestrial
** Reference System (see IERS Conventions 2003), ERA is the Earth
** Rotation Angle and RPOM is the polar motion matrix.
**
** 3) The present function is faster, but slightly less accurate (about
** 1 mas), than the iauC2i00a function.
**
** Called:
** iauPnm00b classical NPB matrix, IAU 2000B
** iauC2ibpn celestial-to-intermediate matrix, given NPB matrix
**
** References:
**
** "Expressions for the Celestial Intermediate Pole and Celestial
** Ephemeris Origin consistent with the IAU 2000A precession-
** nutation model", Astron.Astrophys. 400, 1145-1154
** (2003)
**
** n.b. The celestial ephemeris origin (CEO) was renamed "celestial
** intermediate origin" (CIO) by IAU 2006 Resolution 2.
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
*/
void iauC2i06a(double date1, double date2, double rc2i[3][3])
/*
** - - - - - - - - - -
** i a u _ c 2 i 0 6 a
** - - - - - - - - - -
**
** Form the celestial-to-intermediate matrix for a given date using the
** IAU 2006 precession and IAU 2000A nutation models.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** rc2i double[3][3] celestial-to-intermediate matrix (Note 2)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The matrix rc2i is the first stage in the transformation from
** celestial to terrestrial coordinates:
**
** [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
**
** = RC2T * [CRS]
**
** where [CRS] is a vector in the Geocentric Celestial Reference
** System and [TRS] is a vector in the International Terrestrial
** Reference System (see IERS Conventions 2003), ERA is the Earth
** Rotation Angle and RPOM is the polar motion matrix.
**
** Called:
** iauPnm06a classical NPB matrix, IAU 2006/2000A
** iauBpn2xy extract CIP X,Y coordinates from NPB matrix
** iauS06 the CIO locator s, Given X,Y, IAU 2006
** iauC2ixys celestial-to-intermediate matrix, Given X,Y and s
**
** References:
**
** McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003),
** IERS Technical Note No. 32, BKG
**
*/
void iauC2ibpn(double date1, double date2, double rbpn[3][3],
double rc2i[3][3])
/*
** - - - - - - - - - -
** i a u C 2 i b p n
** - - - - - - - - - -
**
** Form the celestial-to-intermediate matrix for a given date given
** the bias-precession-nutation matrix. IAU 2000.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
** rbpn double[3][3] celestial-to-true matrix (Note 2)
**
** Returned:
** rc2i double[3][3] celestial-to-intermediate matrix (Note 3)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The matrix rbpn transforms vectors from GCRS to true equator (and
** CIO or equinox) of date. Only the CIP (bottom row) is used.
**
** 3) The matrix rc2i is the first stage in the transformation from
** celestial to terrestrial coordinates:
**
** [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
**
** = RC2T * [CRS]
**
** where [CRS] is a vector in the Geocentric Celestial Reference
** System and [TRS] is a vector in the International Terrestrial
** Reference System (see IERS Conventions 2003), ERA is the Earth
** Rotation Angle and RPOM is the polar motion matrix.
**
** 4) Although its name does not include "00", This function is in fact
** specific to the IAU 2000 models.
**
** Called:
** iauBpn2xy extract CIP X,Y coordinates from NPB matrix
** iauC2ixy celestial-to-intermediate matrix, given X,Y
**
** References:
** "Expressions for the Celestial Intermediate Pole and Celestial
** Ephemeris Origin consistent with the IAU 2000A precession-
** nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
**
** n.b. The celestial ephemeris origin (CEO) was renamed "celestial
** intermediate origin" (CIO) by IAU 2006 Resolution 2.
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
*/
void iauC2ixy(double date1, double date2, double x, double y,
double rc2i[3][3])
/*
** - - - - - - - - -
** i a u C 2 i x y
** - - - - - - - - -
**
** Form the celestial to intermediate-frame-of-date matrix for a given
** date when the CIP X,Y coordinates are known. IAU 2000.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
** x,y double Celestial Intermediate Pole (Note 2)
**
** Returned:
** rc2i double[3][3] celestial-to-intermediate matrix (Note 3)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The Celestial Intermediate Pole coordinates are the x,y components
** of the unit vector in the Geocentric Celestial Reference System.
**
** 3) The matrix rc2i is the first stage in the transformation from
** celestial to terrestrial coordinates:
**
** [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
**
** = RC2T * [CRS]
**
** where [CRS] is a vector in the Geocentric Celestial Reference
** System and [TRS] is a vector in the International Terrestrial
** Reference System (see IERS Conventions 2003), ERA is the Earth
** Rotation Angle and RPOM is the polar motion matrix.
**
** 4) Although its name does not include "00", This function is in fact
** specific to the IAU 2000 models.
**
** Called:
** iauC2ixys celestial-to-intermediate matrix, given X,Y and s
** iauS00 the CIO locator s, given X,Y, IAU 2000A
**
** Reference:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
*/
void iauC2ixys(double x, double y, double s, double rc2i[3][3])
/*
** - - - - - - - - - -
** i a u C 2 i x y s
** - - - - - - - - - -
**
** Form the celestial to intermediate-frame-of-date matrix given the CIP
** X,Y and the CIO locator s.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** x,y double Celestial Intermediate Pole (Note 1)
** s double the CIO locator s (Note 2)
**
** Returned:
** rc2i double[3][3] celestial-to-intermediate matrix (Note 3)
**
** Notes:
**
** 1) The Celestial Intermediate Pole coordinates are the x,y
** components of the unit vector in the Geocentric Celestial
** Reference System.
**
** 2) The CIO locator s (in radians) positions the Celestial
** Intermediate Origin on the equator of the CIP.
**
** 3) The matrix rc2i is the first stage in the transformation from
** celestial to terrestrial coordinates:
**
** [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
**
** = RC2T * [CRS]
**
** where [CRS] is a vector in the Geocentric Celestial Reference
** System and [TRS] is a vector in the International Terrestrial
** Reference System (see IERS Conventions 2003), ERA is the Earth
** Rotation Angle and RPOM is the polar motion matrix.
**
** Called:
** iauIr initialize r-matrix to identity
** iauRz rotate around Z-axis
** iauRy rotate around Y-axis
**
** Reference:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
*/
void iauC2s(double p[3], double *theta, double *phi)
/*
** - - - - - - -
** i a u C 2 s
** - - - - - - -
**
** P-vector to spherical coordinates.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** p double[3] p-vector
**
** Returned:
** theta double longitude angle (radians)
** phi double latitude angle (radians)
**
** Notes:
**
** 1) The vector p can have any magnitude; only its direction is used.
**
** 2) If p is null, zero theta and phi are returned.
**
** 3) At either pole, zero theta is returned.
**
*/
void iauC2t00a(double tta, double ttb, double uta, double utb,
double xp, double yp, double rc2t[3][3])
/*
** - - - - - - - - - -
** i a u C 2 t 0 0 a
** - - - - - - - - - -
**
** Form the celestial to terrestrial matrix given the date, the UT1 and
** the polar motion, using the IAU 2000A nutation model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** tta,ttb double TT as a 2-part Julian Date (Note 1)
** uta,utb double UT1 as a 2-part Julian Date (Note 1)
** xp,yp double coordinates of the pole (radians, Note 2)
**
** Returned:
** rc2t double[3][3] celestial-to-terrestrial matrix (Note 3)
**
** Notes:
**
** 1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates,
** apportioned in any convenient way between the arguments uta and
** utb. For example, JD(UT1)=2450123.7 could be expressed in any of
** these ways, among others:
**
** uta utb
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution is
** acceptable. The J2000 and MJD methods are good compromises
** between resolution and convenience. In the case of uta,utb, the
** date & time method is best matched to the Earth rotation angle
** algorithm used: maximum precision is delivered when the uta
** argument is for 0hrs UT1 on the day in question and the utb
** argument lies in the range 0 to 1, or vice versa.
**
** 2) The arguments xp and yp are the coordinates (in radians) of the
** Celestial Intermediate Pole with respect to the International
** Terrestrial Reference System (see IERS Conventions 2003),
** measured along the meridians to 0 and 90 deg west respectively.
**
** 3) The matrix rc2t transforms from celestial to terrestrial
** coordinates:
**
** [TRS] = RPOM * R_3(ERA) * RC2I * [CRS]
**
** = rc2t * [CRS]
**
** where [CRS] is a vector in the Geocentric Celestial Reference
** System and [TRS] is a vector in the International Terrestrial
** Reference System (see IERS Conventions 2003), RC2I is the
** celestial-to-intermediate matrix, ERA is the Earth rotation
** angle and RPOM is the polar motion matrix.
**
** 4) A faster, but slightly less accurate result (about 1 mas), can
** be obtained by using instead the iauC2t00b function.
**
** Called:
** iauC2i00a celestial-to-intermediate matrix, IAU 2000A
** iauEra00 Earth rotation angle, IAU 2000
** iauSp00 the TIO locator s', IERS 2000
** iauPom00 polar motion matrix
** iauC2tcio form CIO-based celestial-to-terrestrial matrix
**
** Reference:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
*/
void iauC2t00b(double tta, double ttb, double uta, double utb,
double xp, double yp, double rc2t[3][3])
/*
** - - - - - - - - - -
** i a u C 2 t 0 0 b
** - - - - - - - - - -
**
** Form the celestial to terrestrial matrix given the date, the UT1 and
** the polar motion, using the IAU 2000B nutation model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** tta,ttb double TT as a 2-part Julian Date (Note 1)
** uta,utb double UT1 as a 2-part Julian Date (Note 1)
** xp,yp double coordinates of the pole (radians, Note 2)
**
** Returned:
** rc2t double[3][3] celestial-to-terrestrial matrix (Note 3)
**
** Notes:
**
** 1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates,
** apportioned in any convenient way between the arguments uta and
** utb. For example, JD(UT1)=2450123.7 could be expressed in any of
** these ways, among others:
**
** uta utb
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution is
** acceptable. The J2000 and MJD methods are good compromises
** between resolution and convenience. In the case of uta,utb, the
** date & time method is best matched to the Earth rotation angle
** algorithm used: maximum precision is delivered when the uta
** argument is for 0hrs UT1 on the day in question and the utb
** argument lies in the range 0 to 1, or vice versa.
**
** 2) The arguments xp and yp are the coordinates (in radians) of the
** Celestial Intermediate Pole with respect to the International
** Terrestrial Reference System (see IERS Conventions 2003),
** measured along the meridians to 0 and 90 deg west respectively.
**
** 3) The matrix rc2t transforms from celestial to terrestrial
** coordinates:
**
** [TRS] = RPOM * R_3(ERA) * RC2I * [CRS]
**
** = rc2t * [CRS]
**
** where [CRS] is a vector in the Geocentric Celestial Reference
** System and [TRS] is a vector in the International Terrestrial
** Reference System (see IERS Conventions 2003), RC2I is the
** celestial-to-intermediate matrix, ERA is the Earth rotation
** angle and RPOM is the polar motion matrix.
**
** 4) The present function is faster, but slightly less accurate (about
** 1 mas), than the iauC2t00a function.
**
** Called:
** iauC2i00b celestial-to-intermediate matrix, IAU 2000B
** iauEra00 Earth rotation angle, IAU 2000
** iauPom00 polar motion matrix
** iauC2tcio form CIO-based celestial-to-terrestrial matrix
**
** Reference:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
*/
void iauC2t06a(double tta, double ttb, double uta, double utb,
double xp, double yp, double rc2t[3][3])
/*
** - - - - - - - - - -
** i a u C 2 t 0 6 a
** - - - - - - - - - -
**
** Form the celestial to terrestrial matrix given the date, the UT1 and
** the polar motion, using the IAU 2006 precession and IAU 2000A
** nutation models.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** tta,ttb double TT as a 2-part Julian Date (Note 1)
** uta,utb double UT1 as a 2-part Julian Date (Note 1)
** xp,yp double coordinates of the pole (radians, Note 2)
**
** Returned:
** rc2t double[3][3] celestial-to-terrestrial matrix (Note 3)
**
** Notes:
**
** 1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates,
** apportioned in any convenient way between the arguments uta and
** utb. For example, JD(UT1)=2450123.7 could be expressed in any of
** these ways, among others:
**
** uta utb
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution is
** acceptable. The J2000 and MJD methods are good compromises
** between resolution and convenience. In the case of uta,utb, the
** date & time method is best matched to the Earth rotation angle
** algorithm used: maximum precision is delivered when the uta
** argument is for 0hrs UT1 on the day in question and the utb
** argument lies in the range 0 to 1, or vice versa.
**
** 2) The arguments xp and yp are the coordinates (in radians) of the
** Celestial Intermediate Pole with respect to the International
** Terrestrial Reference System (see IERS Conventions 2003),
** measured along the meridians to 0 and 90 deg west respectively.
**
** 3) The matrix rc2t transforms from celestial to terrestrial
** coordinates:
**
** [TRS] = RPOM * R_3(ERA) * RC2I * [CRS]
**
** = rc2t * [CRS]
**
** where [CRS] is a vector in the Geocentric Celestial Reference
** System and [TRS] is a vector in the International Terrestrial
** Reference System (see IERS Conventions 2003), RC2I is the
** celestial-to-intermediate matrix, ERA is the Earth rotation
** angle and RPOM is the polar motion matrix.
**
** Called:
** iauC2i06a celestial-to-intermediate matrix, IAU 2006/2000A
** iauEra00 Earth rotation angle, IAU 2000
** iauSp00 the TIO locator s', IERS 2000
** iauPom00 polar motion matrix
** iauC2tcio form CIO-based celestial-to-terrestrial matrix
**
** Reference:
**
** McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003),
** IERS Technical Note No. 32, BKG
**
*/
void iauC2tcio(double rc2i[3][3], double era, double rpom[3][3],
double rc2t[3][3])
/*
** - - - - - - - - - -
** i a u C 2 t c i o
** - - - - - - - - - -
**
** Assemble the celestial to terrestrial matrix from CIO-based
** components (the celestial-to-intermediate matrix, the Earth Rotation
** Angle and the polar motion matrix).
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** rc2i double[3][3] celestial-to-intermediate matrix
** era double Earth rotation angle
** rpom double[3][3] polar-motion matrix
**
** Returned:
** rc2t double[3][3] celestial-to-terrestrial matrix
**
** Notes:
**
** 1) This function constructs the rotation matrix that transforms
** vectors in the celestial system into vectors in the terrestrial
** system. It does so starting from precomputed components, namely
** the matrix which rotates from celestial coordinates to the
** intermediate frame, the Earth rotation angle and the polar motion
** matrix. One use of the present function is when generating a
** series of celestial-to-terrestrial matrices where only the Earth
** Rotation Angle changes, avoiding the considerable overhead of
** recomputing the precession-nutation more often than necessary to
** achieve given accuracy objectives.
**
** 2) The relationship between the arguments is as follows:
**
** [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
**
** = rc2t * [CRS]
**
** where [CRS] is a vector in the Geocentric Celestial Reference
** System and [TRS] is a vector in the International Terrestrial
** Reference System (see IERS Conventions 2003).
**
** Called:
** iauCr copy r-matrix
** iauRz rotate around Z-axis
** iauRxr product of two r-matrices
**
** Reference:
**
** McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003),
** IERS Technical Note No. 32, BKG
**
*/
void iauC2teqx(double rbpn[3][3], double gst, double rpom[3][3],
double rc2t[3][3])
/*
** - - - - - - - - - -
** i a u C 2 t e q x
** - - - - - - - - - -
**
** Assemble the celestial to terrestrial matrix from equinox-based
** components (the celestial-to-true matrix, the Greenwich Apparent
** Sidereal Time and the polar motion matrix).
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** rbpn double[3][3] celestial-to-true matrix
** gst double Greenwich (apparent) Sidereal Time
** rpom double[3][3] polar-motion matrix
**
** Returned:
** rc2t double[3][3] celestial-to-terrestrial matrix (Note 2)
**
** Notes:
**
** 1) This function constructs the rotation matrix that transforms
** vectors in the celestial system into vectors in the terrestrial
** system. It does so starting from precomputed components, namely
** the matrix which rotates from celestial coordinates to the
** true equator and equinox of date, the Greenwich Apparent Sidereal
** Time and the polar motion matrix. One use of the present function
** is when generating a series of celestial-to-terrestrial matrices
** where only the Sidereal Time changes, avoiding the considerable
** overhead of recomputing the precession-nutation more often than
** necessary to achieve given accuracy objectives.
**
** 2) The relationship between the arguments is as follows:
**
** [TRS] = rpom * R_3(gst) * rbpn * [CRS]
**
** = rc2t * [CRS]
**
** where [CRS] is a vector in the Geocentric Celestial Reference
** System and [TRS] is a vector in the International Terrestrial
** Reference System (see IERS Conventions 2003).
**
** Called:
** iauCr copy r-matrix
** iauRz rotate around Z-axis
** iauRxr product of two r-matrices
**
** Reference:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
*/
void iauC2tpe(double tta, double ttb, double uta, double utb,
double dpsi, double deps, double xp, double yp,
double rc2t[3][3])
/*
** - - - - - - - - -
** i a u C 2 t p e
** - - - - - - - - -
**
** Form the celestial to terrestrial matrix given the date, the UT1,
** the nutation and the polar motion. IAU 2000.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** tta,ttb double TT as a 2-part Julian Date (Note 1)
** uta,utb double UT1 as a 2-part Julian Date (Note 1)
** dpsi,deps double nutation (Note 2)
** xp,yp double coordinates of the pole (radians, Note 3)
**
** Returned:
** rc2t double[3][3] celestial-to-terrestrial matrix (Note 4)
**
** Notes:
**
** 1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates,
** apportioned in any convenient way between the arguments uta and
** utb. For example, JD(UT1)=2450123.7 could be expressed in any of
** these ways, among others:
**
** uta utb
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution is
** acceptable. The J2000 and MJD methods are good compromises
** between resolution and convenience. In the case of uta,utb, the
** date & time method is best matched to the Earth rotation angle
** algorithm used: maximum precision is delivered when the uta
** argument is for 0hrs UT1 on the day in question and the utb
** argument lies in the range 0 to 1, or vice versa.
**
** 2) The caller is responsible for providing the nutation components;
** they are in longitude and obliquity, in radians and are with
** respect to the equinox and ecliptic of date. For high-accuracy
** applications, free core nutation should be included as well as
** any other relevant corrections to the position of the CIP.
**
** 3) The arguments xp and yp are the coordinates (in radians) of the
** Celestial Intermediate Pole with respect to the International
** Terrestrial Reference System (see IERS Conventions 2003),
** measured along the meridians to 0 and 90 deg west respectively.
**
** 4) The matrix rc2t transforms from celestial to terrestrial
** coordinates:
**
** [TRS] = RPOM * R_3(GST) * RBPN * [CRS]
**
** = rc2t * [CRS]
**
** where [CRS] is a vector in the Geocentric Celestial Reference
** System and [TRS] is a vector in the International Terrestrial
** Reference System (see IERS Conventions 2003), RBPN is the
** bias-precession-nutation matrix, GST is the Greenwich (apparent)
** Sidereal Time and RPOM is the polar motion matrix.
**
** 5) Although its name does not include "00", This function is in fact
** specific to the IAU 2000 models.
**
** Called:
** iauPn00 bias/precession/nutation results, IAU 2000
** iauGmst00 Greenwich mean sidereal time, IAU 2000
** iauSp00 the TIO locator s', IERS 2000
** iauEe00 equation of the equinoxes, IAU 2000
** iauPom00 polar motion matrix
** iauC2teqx form equinox-based celestial-to-terrestrial matrix
**
** Reference:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
*/
void iauC2txy(double tta, double ttb, double uta, double utb,
double x, double y, double xp, double yp,
double rc2t[3][3])
/*
** - - - - - - - - -
** i a u C 2 t x y
** - - - - - - - - -
**
** Form the celestial to terrestrial matrix given the date, the UT1,
** the CIP coordinates and the polar motion. IAU 2000.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** tta,ttb double TT as a 2-part Julian Date (Note 1)
** uta,utb double UT1 as a 2-part Julian Date (Note 1)
** x,y double Celestial Intermediate Pole (Note 2)
** xp,yp double coordinates of the pole (radians, Note 3)
**
** Returned:
** rc2t double[3][3] celestial-to-terrestrial matrix (Note 4)
**
** Notes:
**
** 1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates,
** apportioned in any convenient way between the arguments uta and
** utb. For example, JD(UT1)=2450123.7 could be expressed in any o
** these ways, among others:
**
** uta utb
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution is
** acceptable. The J2000 and MJD methods are good compromises
** between resolution and convenience. In the case of uta,utb, the
** date & time method is best matched to the Earth rotation angle
** algorithm used: maximum precision is delivered when the uta
** argument is for 0hrs UT1 on the day in question and the utb
** argument lies in the range 0 to 1, or vice versa.
**
** 2) The Celestial Intermediate Pole coordinates are the x,y
** components of the unit vector in the Geocentric Celestial
** Reference System.
**
** 3) The arguments xp and yp are the coordinates (in radians) of the
** Celestial Intermediate Pole with respect to the International
** Terrestrial Reference System (see IERS Conventions 2003),
** measured along the meridians to 0 and 90 deg west respectively.
**
** 4) The matrix rc2t transforms from celestial to terrestrial
** coordinates:
**
** [TRS] = RPOM * R_3(ERA) * RC2I * [CRS]
**
** = rc2t * [CRS]
**
** where [CRS] is a vector in the Geocentric Celestial Reference
** System and [TRS] is a vector in the International Terrestrial
** Reference System (see IERS Conventions 2003), ERA is the Earth
** Rotation Angle and RPOM is the polar motion matrix.
**
** 5) Although its name does not include "00", This function is in fact
** specific to the IAU 2000 models.
**
** Called:
** iauC2ixy celestial-to-intermediate matrix, given X,Y
** iauEra00 Earth rotation angle, IAU 2000
** iauSp00 the TIO locator s', IERS 2000
** iauPom00 polar motion matrix
** iauC2tcio form CIO-based celestial-to-terrestrial matrix
**
** Reference:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
*/
int iauCal2jd(int iy, int im, int id, double *djm0, double *djm)
/*
** - - - - - - - - - -
** i a u C a l 2 j d
** - - - - - - - - - -
**
** Gregorian Calendar to Julian Date.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** iy,im,id int year, month, day in Gregorian calendar (Note 1)
**
** Returned:
** djm0 double MJD zero-point: always 2400000.5
** djm double Modified Julian Date for 0 hrs
**
** Returned (function value):
** int status:
** 0 = OK
** -1 = bad year (Note 3: JD not computed)
** -2 = bad month (JD not computed)
** -3 = bad day (JD computed)
**
** Notes:
**
** 1) The algorithm used is valid from -4800 March 1, but this
** implementation rejects dates before -4799 January 1.
**
** 2) The Julian Date is returned in two pieces, in the usual SOFA
** manner, which is designed to preserve time resolution. The
** Julian Date is available as a single number by adding djm0 and
** djm.
**
** 3) In early eras the conversion is from the "Proleptic Gregorian
** Calendar"; no account is taken of the date(s) of adoption of
** the Gregorian Calendar, nor is the AD/BC numbering convention
** observed.
**
** Reference:
**
** Explanatory Supplement to the Astronomical Almanac,
** P. Kenneth Seidelmann (ed), University Science Books (1992),
** Section 12.92 (p604).
**
*/
void iauCp(double p[3], double c[3])
/*
** - - - - - -
** i a u C p
** - - - - - -
**
** Copy a p-vector.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** p double[3] p-vector to be copied
**
** Returned:
** c double[3] copy
**
*/
void iauCpv(double pv[2][3], double c[2][3])
/*
** - - - - - - -
** i a u C p v
** - - - - - - -
**
** Copy a position/velocity vector.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** pv double[2][3] position/velocity vector to be copied
**
** Returned:
** c double[2][3] copy
**
** Called:
** iauCp copy p-vector
**
*/
void iauCr(double r[3][3], double c[3][3])
/*
** - - - - - -
** i a u C r
** - - - - - -
**
** Copy an r-matrix.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** r double[3][3] r-matrix to be copied
**
** Returned:
** char[] double[3][3] copy
**
** Called:
** iauCp copy p-vector
**
*/
int iauD2dtf(char *scale, int ndp, double d1, double d2,
int *iy, int *im, int *id, int ihmsf[4])
/*
** - - - - - - - - -
** i a u D 2 d t f
** - - - - - - - - -
**
** Format for output a 2-part Julian Date (or in the case of UTC a
** quasi-JD form that includes special provision for leap seconds).
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** scale char[] time scale ID (Note 1)
** ndp int resolution (Note 2)
** d1,d2 double time as a 2-part Julian Date (Notes 3,4)
**
** Returned:
** iy,im,id int year, month, day in Gregorian calendar (Note 5)
** ihmsf int[4] hours, minutes, seconds, fraction (Note 1)
**
** Returned (function value):
** int status: +1 = dubious year (Note 5)
** 0 = OK
** -1 = unacceptable date (Note 6)
**
** Notes:
**
** 1) scale identifies the time scale. Only the value "UTC" (in upper
** case) is significant, and enables handling of leap seconds (see
** Note 4).
**
** 2) ndp is the number of decimal places in the seconds field, and can
** have negative as well as positive values, such as:
**
** ndp resolution
** -4 1 00 00
** -3 0 10 00
** -2 0 01 00
** -1 0 00 10
** 0 0 00 01
** 1 0 00 00.1
** 2 0 00 00.01
** 3 0 00 00.001
**
** The limits are platform dependent, but a safe range is -5 to +9.
**
** 3) d1+d2 is Julian Date, apportioned in any convenient way between
** the two arguments, for example where d1 is the Julian Day Number
** and d2 is the fraction of a day. In the case of UTC, where the
** use of JD is problematical, special conventions apply: see the
** next note.
**
** 4) JD cannot unambiguously represent UTC during a leap second unless
** special measures are taken. The SOFA internal convention is that
** the quasi-JD day represents UTC days whether the length is 86399,
** 86400 or 86401 SI seconds.
**
** 5) The warning status "dubious year" flags UTCs that predate the
** introduction of the time scale and that are too far in the future
** to be trusted. See iauDat for further details.
**
** 6) For calendar conventions and limitations, see iauCal2jd.
**
** Called:
** iauJd2cal JD to Gregorian calendar
** iauD2tf decompose days to hms
** iauDat delta(AT) = TAI-UTC
**
*/
void iauD2tf(int ndp, double days, char *sign, int ihmsf[4])
/*
** - - - - - - - -
** i a u D 2 t f
** - - - - - - - -
**
** Decompose days to hours, minutes, seconds, fraction.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** ndp int resolution (Note 1)
** days double interval in days
**
** Returned:
** sign char '+' or '-'
** ihmsf int[4] hours, minutes, seconds, fraction
**
** Notes:
**
** 1) The argument ndp is interpreted as follows:
**
** ndp resolution
** : ...0000 00 00
** -7 1000 00 00
** -6 100 00 00
** -5 10 00 00
** -4 1 00 00
** -3 0 10 00
** -2 0 01 00
** -1 0 00 10
** 0 0 00 01
** 1 0 00 00.1
** 2 0 00 00.01
** 3 0 00 00.001
** : 0 00 00.000...
**
** 2) The largest positive useful value for ndp is determined by the
** size of days, the format of double on the target platform, and
** the risk of overflowing ihmsf[3]. On a typical platform, for
** days up to 1.0, the available floating-point precision might
** correspond to ndp=12. However, the practical limit is typically
** ndp=9, set by the capacity of a 32-bit int, or ndp=4 if int is
** only 16 bits.
**
** 3) The absolute value of days may exceed 1.0. In cases where it
** does not, it is up to the caller to test for and handle the
** case where days is very nearly 1.0 and rounds up to 24 hours,
** by testing for ihms[0]=24 and setting ihmsf[0-3] to zero.
**
*/
int iauDat(int iy, int im, int id, double fd, double *deltat )
/*
** - - - - - - -
** i a u D a t
** - - - - - - -
**
** For a given UTC date, calculate delta(AT) = TAI-UTC.
**
** :------------------------------------------:
** : :
** : IMPORTANT :
** : :
** : A new version of this function must be :
** : produced whenever a new leap second is :
** : announced. There are four items to :
** : change on each such occasion: :
** : :
** : 1) A new line must be added to the set :
** : of statements that initialize the :
** : array "changes". :
** : :
** : 2) The parameter IYV must be set to :
** : the current year. :
** : :
** : 3) The "Latest leap second" comment :
** : below must be set to the new leap :
** : second date. :
** : :
** : 4) The "This revision" comment, later, :
** : must be set to the current date. :
** : :
** : Change (2) must also be carried out :
** : whenever the function is re-issued, :
** : even if no leap seconds have been :
** : added. :
** : :
** : Latest leap second: 2008 December 31 :
** : :
** :__________________________________________:
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** iy int UTC: year (Notes 1 and 2)
** im int month (Note 2)
** id int day (Notes 2 and 3)
** fd double fraction of day (Note 4)
**
** Returned:
** deltat double TAI minus UTC, seconds
**
** Returned (function value):
** int status (Note 5):
** 1 = dubious year (Note 1)
** 0 = OK
** -1 = bad year
** -2 = bad month
** -3 = bad day (Note 3)
** -4 = bad fraction (Note 4)
**
** Notes:
**
** 1) UTC began at 1960 January 1.0 (JD 2436934.5) and it is improper
** to call the function with an earlier date. If this is attempted,
** zero is returned together with a warning status.
**
** Because leap seconds cannot, in principle, be predicted in
** advance, a reliable check for dates beyond the valid range is
** impossible. To guard against gross errors, a year five or more
** after the release year of the present function (see parameter
** IYV) is considered dubious. In this case a warning status is
** returned but the result is computed in the normal way.
**
** For both too-early and too-late years, the warning status is
** j=+1. This is distinct from the error status j=-1, which
** signifies a year so early that JD could not be computed.
**
** 2) If the specified date is for a day which ends with a leap second,
** the UTC-TAI value returned is for the period leading up to the
** leap second. If the date is for a day which begins as a leap
** second ends, the UTC-TAI returned is for the period following the
** leap second.
**
** 3) The day number must be in the normal calendar range, for example
** 1 through 30 for April. The "almanac" convention of allowing
** such dates as January 0 and December 32 is not supported in this
** function, in order to avoid confusion near leap seconds.
**
** 4) The fraction of day is used only for dates before the
** introduction of leap seconds, the first of which occurred at the
** end of 1971. It is tested for validity (zero to less than 1 is
** the valid range) even if not used; if invalid, zero is used and
** status j=-4 is returned. For many applications, setting fd to
** zero is acceptable; the resulting error is always less than 3 ms
** (and occurs only pre-1972).
**
** 5) The status value returned in the case where there are multiple
** errors refers to the first error detected. For example, if the
** month and day are 13 and 32 respectively, j=-2 (bad month)
** will be returned.
**
** 6) In cases where a valid result is not available, zero is returned.
**
** References:
**
** 1) For dates from 1961 January 1 onwards, the expressions from the
** file ftp://maia.usno.navy.mil/ser7/tai-utc.dat are used.
**
** 2) The 5ms timestep at 1961 January 1 is taken from 2.58.1 (p87) of
** the 1992 Explanatory Supplement.
**
** Called:
** iauCal2jd Gregorian calendar to Julian Day number
**
*/
double iauDtdb(double date1, double date2,
double ut, double elong, double u, double v)
/*
** - - - - - - - -
** i a u D t d b
** - - - - - - - -
**
** An approximation to TDB-TT, the difference between barycentric
** dynamical time and terrestrial time, for an observer on the Earth.
**
** The different time scales - proper, coordinate and realized - are
** related to each other:
**
** TAI <- physically realized
** :
** offset <- observed (nominally +32.184s)
** :
** TT <- terrestrial time
** :
** rate adjustment (L_G) <- definition of TT
** :
** TCG <- time scale for GCRS
** :
** "periodic" terms <- iauDtdb is an implementation
** :
** rate adjustment (L_C) <- function of solar-system ephemeris
** :
** TCB <- time scale for BCRS
** :
** rate adjustment (-L_B) <- definition of TDB
** :
** TDB <- TCB scaled to track TT
** :
** "periodic" terms <- -iau_DTDB is an approximation
** :
** TT <- terrestrial time
**
** Adopted values for the various constants can be found in the IERS
** Conventions (McCarthy & Petit 2003).
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support routine.
**
** Given:
** date1,date2 double date, TDB (Notes 1-3)
** ut double universal time (UT1, fraction of one day)
** elong double longitude (east positive, radians)
** u double distance from Earth spin axis (km)
** v double distance north of equatorial plane (km)
**
** Returned (function value):
** double TDB-TT (seconds)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** Although the date is, formally, barycentric dynamical time (TDB),
** the terrestrial dynamical time (TT) can be used with no practical
** effect on the accuracy of the prediction.
**
** 2) TT can be regarded as a coordinate time that is realized as an
** offset of 32.184s from International Atomic Time, TAI. TT is a
** specific linear transformation of geocentric coordinate time TCG,
** which is the time scale for the Geocentric Celestial Reference
** System, GCRS.
**
** 3) TDB is a coordinate time, and is a specific linear transformation
** of barycentric coordinate time TCB, which is the time scale for
** the Barycentric Celestial Reference System, BCRS.
**
** 4) The difference TCG-TCB depends on the masses and positions of the
** bodies of the solar system and the velocity of the Earth. It is
** dominated by a rate difference, the residual being of a periodic
** character. The latter, which is modeled by the present function,
** comprises a main (annual) sinusoidal term of amplitude
** approximately 0.00166 seconds, plus planetary terms up to about
** 20 microseconds, and lunar and diurnal terms up to 2 microseconds.
** These effects come from the changing transverse Doppler effect
** and gravitational red-shift as the observer (on the Earth's
** surface) experiences variations in speed (with respect to the
** BCRS) and gravitational potential.
**
** 5) TDB can be regarded as the same as TCB but with a rate adjustment
** to keep it close to TT, which is convenient for many applications.
** The history of successive attempts to define TDB is set out in
** Resolution 3 adopted by the IAU General Assembly in 2006, which
** defines a fixed TDB(TCB) transformation that is consistent with
** contemporary solar-system ephemerides. Future ephemerides will
** imply slightly changed transformations between TCG and TCB, which
** could introduce a linear drift between TDB and TT; however, any
** such drift is unlikely to exceed 1 nanosecond per century.
**
** 6) The geocentric TDB-TT model used in the present function is that of
** Fairhead & Bretagnon (1990), in its full form. It was originally
** supplied by Fairhead (private communications with P.T.Wallace,
** 1990) as a Fortran subroutine. The present C function contains an
** adaptation of the Fairhead code. The numerical results are
** essentially unaffected by the changes, the differences with
** respect to the Fairhead & Bretagnon original being at the 1e-20 s
** level.
**
** The topocentric part of the model is from Moyer (1981) and
** Murray (1983), with fundamental arguments adapted from
** Simon et al. 1994. It is an approximation to the expression
** ( v / c ) . ( r / c ), where v is the barycentric velocity of
** the Earth, r is the geocentric position of the observer and
** c is the speed of light.
**
** By supplying zeroes for u and v, the topocentric part of the
** model can be nullified, and the function will return the Fairhead
** & Bretagnon result alone.
**
** 7) During the interval 1950-2050, the absolute accuracy is better
** than +/- 3 nanoseconds relative to time ephemerides obtained by
** direct numerical integrations based on the JPL DE405 solar system
** ephemeris.
**
** 8) It must be stressed that the present function is merely a model,
** and that numerical integration of solar-system ephemerides is the
** definitive method for predicting the relationship between TCG and
** TCB and hence between TT and TDB.
**
** References:
**
** Fairhead, L., & Bretagnon, P., Astron.Astrophys., 229, 240-247
** (1990).
**
** IAU 2006 Resolution 3.
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** Moyer, T.D., Cel.Mech., 23, 33 (1981).
**
** Murray, C.A., Vectorial Astrometry, Adam Hilger (1983).
**
** Seidelmann, P.K. et al., Explanatory Supplement to the
** Astronomical Almanac, Chapter 2, University Science Books (1992).
**
** Simon, J.L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
** Francou, G. & Laskar, J., Astron.Astrophys., 282, 663-683 (1994).
**
*/
int iauDtf2d(char *scale, int iy, int im, int id,
int ihr, int imn, double sec, double *d1, double *d2)
/*
** - - - - - - - - -
** i a u D t f 2 d
** - - - - - - - - -
**
** Encode date and time fields into 2-part Julian Date (or in the case
** of UTC a quasi-JD form that includes special provision for leap
** seconds).
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** scale char[] time scale ID (Note 1)
** iy,im,id int year, month, day in Gregorian calendar (Note 2)
** ihr,imn int hour, minute
** sec double seconds
**
** Returned:
** dj1,dj2 double 2-part Julian Date (Notes 3,4)
**
** Returned (function value):
** int status: +3 = both of next two
** +2 = time is after end of day (Note 5)
** +1 = dubious year (Note 6)
** 0 = OK
** -1 = bad year
** -2 = bad month
** -3 = bad day
** -4 = bad hour
** -5 = bad minute
** -6 = bad second (<0)
**
** Notes:
**
** 1) scale identifies the time scale. Only the value "UTC" (in upper
** case) is significant, and enables handling of leap seconds (see
** Note 4).
**
** 2) For calendar conventions and limitations, see iauCal2jd.
**
** 3) The sum of the results, d1+d2, is Julian Date, where normally d1
** is the Julian Day Number and d2 is the fraction of a day. In the
** case of UTC, where the use of JD is problematical, special
** conventions apply: see the next note.
**
** 4) JD cannot unambiguously represent UTC during a leap second unless
** special measures are taken. The SOFA internal convention is that
** the quasi-JD day represents UTC days whether the length is 86399,
** 86400 or 86401 SI seconds.
**
** 5) The warning status "time is after end of day" usually means that
** the sec argument is greater than 60.0. However, in a day ending
** in a leap second the limit changes to 61.0 (or 59.0 in the case
** of a negative leap second).
**
** 6) The warning status "dubious year" flags UTCs that predate the
** introduction of the time scale and that are too far in the future
** to be trusted. See iauDat for further details.
**
** 7) Only in the case of continuous and regular time scales (TAI, TT,
** TCG, TCB and TDB) is the result DJ1+DJ2 a Julian Date, strictly
** speaking. In the other cases (UT1 and UTC) the result must be
** used with circumspection; in particular the difference between
** two such results cannot be interpreted as a precise time
** interval.
**
** Called:
** iauCal2jd Gregorian calendar to JD
** iauDat delta(AT) = TAI-UTC
** iauJd2cal JD to Gregorian calendar
**
*/
double iauEe00(double date1, double date2, double epsa, double dpsi)
/*
** - - - - - - - -
** i a u E e 0 0
** - - - - - - - -
**
** The equation of the equinoxes, compatible with IAU 2000 resolutions,
** given the nutation in longitude and the mean obliquity.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
** epsa double mean obliquity (Note 2)
** dpsi double nutation in longitude (Note 3)
**
** Returned (function value):
** double equation of the equinoxes (Note 4)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The obliquity, in radians, is mean of date.
**
** 3) The result, which is in radians, operates in the following sense:
**
** Greenwich apparent ST = GMST + equation of the equinoxes
**
** 4) The result is compatible with the IAU 2000 resolutions. For
** further details, see IERS Conventions 2003 and Capitaine et al.
** (2002).
**
** Called:
** iauEect00 equation of the equinoxes complementary terms
**
** References:
**
** Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
** implement the IAU 2000 definition of UT1", Astronomy &
** Astrophysics, 406, 1135-1149 (2003)
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
*/
double iauEe00a(double date1, double date2)
/*
** - - - - - - - - -
** i a u E e 0 0 a
** - - - - - - - - -
**
** Equation of the equinoxes, compatible with IAU 2000 resolutions.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned (function value):
** double equation of the equinoxes (Note 2)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The result, which is in radians, operates in the following sense:
**
** Greenwich apparent ST = GMST + equation of the equinoxes
**
** 3) The result is compatible with the IAU 2000 resolutions. For
** further details, see IERS Conventions 2003 and Capitaine et al.
** (2002).
**
** Called:
** iauPr00 IAU 2000 precession adjustments
** iauObl80 mean obliquity, IAU 1980
** iauNut00a nutation, IAU 2000A
** iauEe00 equation of the equinoxes, IAU 2000
**
** References:
**
** Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
** implement the IAU 2000 definition of UT1", Astronomy &
** Astrophysics, 406, 1135-1149 (2003).
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004).
**
*/
double iauEe00b(double date1, double date2)
/*
** - - - - - - - - -
** i a u E e 0 0 b
** - - - - - - - - -
**
** Equation of the equinoxes, compatible with IAU 2000 resolutions but
** using the truncated nutation model IAU 2000B.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned (function value):
** double equation of the equinoxes (Note 2)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The result, which is in radians, operates in the following sense:
**
** Greenwich apparent ST = GMST + equation of the equinoxes
**
** 3) The result is compatible with the IAU 2000 resolutions except
** that accuracy has been compromised for the sake of speed. For
** further details, see McCarthy & Luzum (2001), IERS Conventions
** 2003 and Capitaine et al. (2003).
**
** Called:
** iauPr00 IAU 2000 precession adjustments
** iauObl80 mean obliquity, IAU 1980
** iauNut00b nutation, IAU 2000B
** iauEe00 equation of the equinoxes, IAU 2000
**
** References:
**
** Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
** implement the IAU 2000 definition of UT1", Astronomy &
** Astrophysics, 406, 1135-1149 (2003)
**
** McCarthy, D.D. & Luzum, B.J., "An abridged model of the
** precession-nutation of the celestial pole", Celestial Mechanics &
** Dynamical Astronomy, 85, 37-49 (2003)
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
*/
double iauEe06a(double date1, double date2)
/*
** - - - - - - - - -
** i a u E e 0 6 a
** - - - - - - - - -
**
** Equation of the equinoxes, compatible with IAU 2000 resolutions and
** IAU 2006/2000A precession-nutation.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned (function value):
** double equation of the equinoxes (Note 2)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The result, which is in radians, operates in the following sense:
**
** Greenwich apparent ST = GMST + equation of the equinoxes
**
** Called:
** iauAnpm normalize angle into range +/- pi
** iauGst06a Greenwich apparent sidereal time, IAU 2006/2000A
** iauGmst06 Greenwich mean sidereal time, IAU 2006
**
** Reference:
**
** McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003),
** IERS Technical Note No. 32, BKG
**
*/
double iauEect00(double date1, double date2)
/*
** - - - - - - - - - -
** i a u E e c t 0 0
** - - - - - - - - - -
**
** Equation of the equinoxes complementary terms, consistent with
** IAU 2000 resolutions.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned (function value):
** double complementary terms (Note 2)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The "complementary terms" are part of the equation of the
** equinoxes (EE), classically the difference between apparent and
** mean Sidereal Time:
**
** GAST = GMST + EE
**
** with:
**
** EE = dpsi * cos(eps)
**
** where dpsi is the nutation in longitude and eps is the obliquity
** of date. However, if the rotation of the Earth were constant in
** an inertial frame the classical formulation would lead to
** apparent irregularities in the UT1 timescale traceable to side-
** effects of precession-nutation. In order to eliminate these
** effects from UT1, "complementary terms" were introduced in 1994
** (IAU, 1994) and took effect from 1997 (Capitaine and Gontier,
** 1993):
**
** GAST = GMST + CT + EE
**
** By convention, the complementary terms are included as part of
** the equation of the equinoxes rather than as part of the mean
** Sidereal Time. This slightly compromises the "geometrical"
** interpretation of mean sidereal time but is otherwise
** inconsequential.
**
** The present function computes CT in the above expression,
** compatible with IAU 2000 resolutions (Capitaine et al., 2002, and
** IERS Conventions 2003).
**
** Called:
** iauFal03 mean anomaly of the Moon
** iauFalp03 mean anomaly of the Sun
** iauFaf03 mean argument of the latitude of the Moon
** iauFad03 mean elongation of the Moon from the Sun
** iauFaom03 mean longitude of the Moon's ascending node
** iauFave03 mean longitude of Venus
** iauFae03 mean longitude of Earth
** iauFapa03 general accumulated precession in longitude
**
** References:
**
** Capitaine, N. & Gontier, A.-M., Astron. Astrophys., 275,
** 645-650 (1993)
**
** Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
** implement the IAU 2000 definition of UT1", Astronomy &
** Astrophysics, 406, 1135-1149 (2003)
**
** IAU Resolution C7, Recommendation 3 (1994)
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
*/
int iauEform ( int n, double *a, double *f )
/*
** - - - - - - - - -
** i a u E f o r m
** - - - - - - - - -
**
** Earth reference ellipsoids.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: canonical.
**
** Given:
** n int ellipsoid identifier (Note 1)
**
** Returned:
** a double equatorial radius (meters, Note 2)
** f double flattening (Note 2)
**
** Returned (function value):
** int status:
** 0 = OK
** -1 = illegal identifier (Note 3)
**
** Notes:
**
** 1) The identifier n is a number that specifies the choice of
** reference ellipsoid. The following are supported:
**
** n ellipsoid
**
** 1 WGS84
** 2 GRS80
** 3 WGS72
**
** The number n has no significance outside the SOFA software.
**
** 2) The ellipsoid parameters are returned in the form of equatorial
** radius in meters (a) and flattening (f). The latter is a number
** around 0.00335, i.e. around 1/298.
**
** 3) For the case where an unsupported n value is supplied, zero a and
** f are returned, as well as error status.
**
** References:
**
** Department of Defense World Geodetic System 1984, National
** Imagery and Mapping Agency Technical Report 8350.2, Third
** Edition, p3-2.
**
** Moritz, H., Bull. Geodesique 66-2, 187 (1992).
**
** The Department of Defense World Geodetic System 1972, World
** Geodetic System Committee, May 1974.
**
** Explanatory Supplement to the Astronomical Almanac,
** P. Kenneth Seidelmann (ed), University Science Books (1992),
** p220.
**
*/
double iauEo06a(double date1, double date2)
/*
** - - - - - - - - -
** i a u E o 0 6 a
** - - - - - - - - -
**
** Equation of the origins, IAU 2006 precession and IAU 2000A nutation.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned (function value):
** double equation of the origins in radians
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The equation of the origins is the distance between the true
** equinox and the celestial intermediate origin and, equivalently,
** the difference between Earth rotation angle and Greenwich
** apparent sidereal time (ERA-GST). It comprises the precession
** (since J2000.0) in right ascension plus the equation of the
** equinoxes (including the small correction terms).
**
** Called:
** iauPnm06a classical NPB matrix, IAU 2006/2000A
** iauBpn2xy extract CIP X,Y coordinates from NPB matrix
** iauS06 the CIO locator s, given X,Y, IAU 2006
** iauEors equation of the origins, Given NPB matrix and s
**
** References:
**
** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
**
** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
**
*/
double iauEors(double rnpb[3][3], double s)
/*
** - - - - - - - -
** i a u E o r s
** - - - - - - - -
**
** Equation of the origins, given the classical NPB matrix and the
** quantity s.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** rnpb double[3][3] classical nutation x precession x bias matrix
** s double the quantity s (the CIO locator)
**
** Returned (function value):
** double the equation of the origins in radians.
**
** Notes:
**
** 1) The equation of the origins is the distance between the true
** equinox and the celestial intermediate origin and, equivalently,
** the difference between Earth rotation angle and Greenwich
** apparent sidereal time (ERA-GST). It comprises the precession
** (since J2000.0) in right ascension plus the equation of the
** equinoxes (including the small correction terms).
**
** 2) The algorithm is from Wallace & Capitaine (2006).
**
** References:
**
** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
**
** Wallace, P. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
**
*/
double iauEpb(double dj1, double dj2)
/*
** - - - - - - -
** i a u E p b
** - - - - - - -
**
** Julian Date to Besselian Epoch.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** dj1,dj2 double Julian Date (see note)
**
** Returned (function value):
** double Besselian Epoch.
**
** Note:
**
** The Julian Date is supplied in two pieces, in the usual SOFA
** manner, which is designed to preserve time resolution. The
** Julian Date is available as a single number by adding dj1 and
** dj2. The maximum resolution is achieved if dj1 is 2451545D0
** (J2000.0).
**
** Reference:
**
** Lieske,J.H., 1979. Astron.Astrophys.,73,282.
**
*/
void iauEpb2jd(double epb, double *djm0, double *djm)
/*
** - - - - - - - - - -
** i a u E p b 2 j d
** - - - - - - - - - -
**
** Besselian Epoch to Julian Date.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** epb double Besselian Epoch (e.g. 1957.3D0)
**
** Returned:
** djm0 double MJD zero-point: always 2400000.5
** djm double Modified Julian Date
**
** Note:
**
** The Julian Date is returned in two pieces, in the usual SOFA
** manner, which is designed to preserve time resolution. The
** Julian Date is available as a single number by adding djm0 and
** djm.
**
** Reference:
**
** Lieske, J.H., 1979, Astron.Astrophys. 73, 282.
**
*/
double iauEpj(double dj1, double dj2)
/*
** - - - - - - -
** i a u E p j
** - - - - - - -
**
** Julian Date to Julian Epoch.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** dj1,dj2 double Julian Date (see note)
**
** Returned (function value):
** double Julian Epoch
**
** Note:
**
** The Julian Date is supplied in two pieces, in the usual SOFA
** manner, which is designed to preserve time resolution. The
** Julian Date is available as a single number by adding dj1 and
** dj2. The maximum resolution is achieved if dj1 is 2451545D0
** (J2000.0).
**
** Reference:
**
** Lieske, J.H., 1979, Astron.Astrophys. 73, 282.
**
*/
void iauEpj2jd(double epj, double *djm0, double *djm)
/*
** - - - - - - - - - -
** i a u E p j 2 j d
** - - - - - - - - - -
**
** Julian Epoch to Julian Date.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** epj double Julian Epoch (e.g. 1996.8D0)
**
** Returned:
** djm0 double MJD zero-point: always 2400000.5
** djm double Modified Julian Date
**
** Note:
**
** The Julian Date is returned in two pieces, in the usual SOFA
** manner, which is designed to preserve time resolution. The
** Julian Date is available as a single number by adding djm0 and
** djm.
**
** Reference:
**
** Lieske, J.H., 1979, Astron.Astrophys. 73, 282.
**
*/
int iauEpv00(double date1, double date2,
double pvh[2][3], double pvb[2][3])
/*
** - - - - - - - - -
** i a u E p v 0 0
** - - - - - - - - -
**
** Earth position and velocity, heliocentric and barycentric, with
** respect to the Barycentric Celestial Reference System.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TDB date (Note 1)
**
** Returned:
** pvh double[2][3] heliocentric Earth position/velocity
** pvb double[2][3] barycentric Earth position/velocity
**
** Returned (function value):
** int status: 0 = OK
** +1 = warning: date outside
** the range 1900-2100 AD
**
** Notes:
**
** 1) The TDB date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TDB)=2450123.7 could be expressed in any of these ways, among
** others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in cases
** where the loss of several decimal digits of resolution is
** acceptable. The J2000 method is best matched to the way the
** argument is handled internally and will deliver the optimum
** resolution. The MJD method and the date & time methods are both
** good compromises between resolution and convenience. However,
** the accuracy of the result is more likely to be limited by the
** algorithm itself than the way the date has been expressed.
**
** n.b. TT can be used instead of TDB in most applications.
**
** 2) On return, the arrays pvh and pvb contain the following:
**
** pvh[0][0] x }
** pvh[0][1] y } heliocentric position, AU
** pvh[0][2] z }
**
** pvh[1][0] xdot }
** pvh[1][1] ydot } heliocentric velocity, AU/d
** pvh[1][2] zdot }
**
** pvb[0][0] x }
** pvb[0][1] y } barycentric position, AU
** pvb[0][2] z }
**
** pvb[1][0] xdot }
** pvb[1][1] ydot } barycentric velocity, AU/d
** pvb[1][2] zdot }
**
** The vectors are with respect to the Barycentric Celestial
** Reference System. The time unit is one day in TDB.
**
** 3) The function is a SIMPLIFIED SOLUTION from the planetary theory
** VSOP2000 (X. Moisson, P. Bretagnon, 2001, Celes. Mechanics &
** Dyn. Astron., 80, 3/4, 205-213) and is an adaptation of original
** Fortran code supplied by P. Bretagnon (private comm., 2000).
**
** 4) Comparisons over the time span 1900-2100 with this simplified
** solution and the JPL DE405 ephemeris give the following results:
**
** RMS max
** Heliocentric:
** position error 3.7 11.2 km
** velocity error 1.4 5.0 mm/s
**
** Barycentric:
** position error 4.6 13.4 km
** velocity error 1.4 4.9 mm/s
**
** Comparisons with the JPL DE406 ephemeris show that by 1800 and
** 2200 the position errors are approximately double their 1900-2100
** size. By 1500 and 2500 the deterioration is a factor of 10 and
** by 1000 and 3000 a factor of 60. The velocity accuracy falls off
** at about half that rate.
**
** 5) It is permissible to use the same array for pvh and pvb, which
** will receive the barycentric values.
**
*/
double iauEqeq94(double date1, double date2)
/*
** - - - - - - - - - -
** i a u E q e q 9 4
** - - - - - - - - - -
**
** Equation of the equinoxes, IAU 1994 model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** date1,date2 double TDB date (Note 1)
**
** Returned (function value):
** double equation of the equinoxes (Note 2)
**
** Notes:
**
** 1) The date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The result, which is in radians, operates in the following sense:
**
** Greenwich apparent ST = GMST + equation of the equinoxes
**
** Called:
** iauNut80 nutation, IAU 1980
** iauObl80 mean obliquity, IAU 1980
**
** References:
**
** IAU Resolution C7, Recommendation 3 (1994).
**
** Capitaine, N. & Gontier, A.-M., 1993, Astron. Astrophys., 275,
** 645-650.
**
*/
double iauEra00(double dj1, double dj2)
/*
** - - - - - - - - -
** i a u E r a 0 0
** - - - - - - - - -
**
** Earth rotation angle (IAU 2000 model).
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** dj1,dj2 double UT1 as a 2-part Julian Date (see note)
**
** Returned (function value):
** double Earth rotation angle (radians), range 0-2pi
**
** Notes:
**
** 1) The UT1 date dj1+dj2 is a Julian Date, apportioned in any
** convenient way between the arguments dj1 and dj2. For example,
** JD(UT1)=2450123.7 could be expressed in any of these ways,
** among others:
**
** dj1 dj2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 and MJD methods are good compromises
** between resolution and convenience. The date & time method is
** best matched to the algorithm used: maximum precision is
** delivered when the dj1 argument is for 0hrs UT1 on the day in
** question and the dj2 argument lies in the range 0 to 1, or vice
** versa.
**
** 2) The algorithm is adapted from Expression 22 of Capitaine et al.
** 2000. The time argument has been expressed in days directly,
** and, to retain precision, integer contributions have been
** eliminated. The same formulation is given in IERS Conventions
** (2003), Chap. 5, Eq. 14.
**
** Called:
** iauAnp normalize angle into range 0 to 2pi
**
** References:
**
** Capitaine N., Guinot B. and McCarthy D.D, 2000, Astron.
** Astrophys., 355, 398-405.
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
*/
double iauFad03(double t)
/*
** - - - - - - - - -
** i a u F a d 0 3
** - - - - - - - - -
**
** Fundamental argument, IERS Conventions (2003):
** mean elongation of the Moon from the Sun.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** t double TDB, Julian centuries since J2000.0 (Note 1)
**
** Returned (function value):
** double D, radians (Note 2)
**
** Notes:
**
** 1) Though t is strictly TDB, it is usually more convenient to use
** TT, which makes no significant difference.
**
** 2) The expression used is as adopted in IERS Conventions (2003) and
** is from Simon et al. (1994).
**
** References:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
**
*/
double iauFae03(double t)
/*
** - - - - - - - - -
** i a u F a e 0 3
** - - - - - - - - -
**
** Fundamental argument, IERS Conventions (2003):
** mean longitude of Earth.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** t double TDB, Julian centuries since J2000.0 (Note 1)
**
** Returned (function value):
** double mean longitude of Earth, radians (Note 2)
**
** Notes:
**
** 1) Though t is strictly TDB, it is usually more convenient to use
** TT, which makes no significant difference.
**
** 2) The expression used is as adopted in IERS Conventions (2003) and
** comes from Souchay et al. (1999) after Simon et al. (1994).
**
** References:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
**
** Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
** Astron.Astrophys.Supp.Ser. 135, 111
**
*/
double iauFaf03(double t)
/*
** - - - - - - - - -
** i a u F a f 0 3
** - - - - - - - - -
**
** Fundamental argument, IERS Conventions (2003):
** mean longitude of the Moon minus mean longitude of the ascending
** node.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** t double TDB, Julian centuries since J2000.0 (Note 1)
**
** Returned (function value):
** double F, radians (Note 2)
**
** Notes:
**
** 1) Though t is strictly TDB, it is usually more convenient to use
** TT, which makes no significant difference.
**
** 2) The expression used is as adopted in IERS Conventions (2003) and
** is from Simon et al. (1994).
**
** References:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
**
*/
double iauFaju03(double t)
/*
** - - - - - - - - - -
** i a u F a j u 0 3
** - - - - - - - - - -
**
** Fundamental argument, IERS Conventions (2003):
** mean longitude of Jupiter.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** t double TDB, Julian centuries since J2000.0 (Note 1)
**
** Returned (function value):
** double mean longitude of Jupiter, radians (Note 2)
**
** Notes:
**
** 1) Though t is strictly TDB, it is usually more convenient to use
** TT, which makes no significant difference.
**
** 2) The expression used is as adopted in IERS Conventions (2003) and
** comes from Souchay et al. (1999) after Simon et al. (1994).
**
** References:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
**
** Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
** Astron.Astrophys.Supp.Ser. 135, 111
**
*/
double iauFal03(double t)
/*
** - - - - - - - - -
** i a u F a l 0 3
** - - - - - - - - -
**
** Fundamental argument, IERS Conventions (2003):
** mean anomaly of the Moon.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** t double TDB, Julian centuries since J2000.0 (Note 1)
**
** Returned (function value):
** double l, radians (Note 2)
**
** Notes:
**
** 1) Though t is strictly TDB, it is usually more convenient to use
** TT, which makes no significant difference.
**
** 2) The expression used is as adopted in IERS Conventions (2003) and
** is from Simon et al. (1994).
**
** References:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
**
*/
double iauFalp03(double t)
/*
** - - - - - - - - - -
** i a u F a l p 0 3
** - - - - - - - - - -
**
** Fundamental argument, IERS Conventions (2003):
** mean anomaly of the Sun.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** t double TDB, Julian centuries since J2000.0 (Note 1)
**
** Returned (function value):
** double l', radians (Note 2)
**
** Notes:
**
** 1) Though t is strictly TDB, it is usually more convenient to use
** TT, which makes no significant difference.
**
** 2) The expression used is as adopted in IERS Conventions (2003) and
** is from Simon et al. (1994).
**
** References:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
**
*/
double iauFama03(double t)
/*
** - - - - - - - - - -
** i a u F a m a 0 3
** - - - - - - - - - -
**
** Fundamental argument, IERS Conventions (2003):
** mean longitude of Mars.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** t double TDB, Julian centuries since J2000.0 (Note 1)
**
** Returned (function value):
** double mean longitude of Mars, radians (Note 2)
**
** Notes:
**
** 1) Though t is strictly TDB, it is usually more convenient to use
** TT, which makes no significant difference.
**
** 2) The expression used is as adopted in IERS Conventions (2003) and
** comes from Souchay et al. (1999) after Simon et al. (1994).
**
** References:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
**
** Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
** Astron.Astrophys.Supp.Ser. 135, 111
**
*/
double iauFame03(double t)
/*
** - - - - - - - - - -
** i a u F a m e 0 3
** - - - - - - - - - -
**
** Fundamental argument, IERS Conventions (2003):
** mean longitude of Mercury.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** t double TDB, Julian centuries since J2000.0 (Note 1)
**
** Returned (function value):
** double mean longitude of Mercury, radians (Note 2)
**
** Notes:
**
** 1) Though t is strictly TDB, it is usually more convenient to use
** TT, which makes no significant difference.
**
** 2) The expression used is as adopted in IERS Conventions (2003) and
** comes from Souchay et al. (1999) after Simon et al. (1994).
**
** References:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
**
** Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
** Astron.Astrophys.Supp.Ser. 135, 111
**
*/
double iauFane03(double t)
/*
** - - - - - - - - - -
** i a u F a n e 0 3
** - - - - - - - - - -
**
** Fundamental argument, IERS Conventions (2003):
** mean longitude of Neptune.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** t double TDB, Julian centuries since J2000.0 (Note 1)
**
** Returned (function value):
** double mean longitude of Neptune, radians (Note 2)
**
** Notes:
**
** 1) Though t is strictly TDB, it is usually more convenient to use
** TT, which makes no significant difference.
**
** 2) The expression used is as adopted in IERS Conventions (2003) and
** is adapted from Simon et al. (1994).
**
** References:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
**
*/
double iauFaom03(double t)
/*
** - - - - - - - - - -
** i a u F a o m 0 3
** - - - - - - - - - -
**
** Fundamental argument, IERS Conventions (2003):
** mean longitude of the Moon's ascending node.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** t double TDB, Julian centuries since J2000.0 (Note 1)
**
** Returned (function value):
** double Omega, radians (Note 2)
**
** Notes:
**
** 1) Though t is strictly TDB, it is usually more convenient to use
** TT, which makes no significant difference.
**
** 2) The expression used is as adopted in IERS Conventions (2003) and
** is from Simon et al. (1994).
**
** References:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
**
*/
double iauFapa03(double t)
/*
** - - - - - - - - - -
** i a u F a p a 0 3
** - - - - - - - - - -
**
** Fundamental argument, IERS Conventions (2003):
** general accumulated precession in longitude.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** t double TDB, Julian centuries since J2000.0 (Note 1)
**
** Returned (function value):
** double general precession in longitude, radians (Note 2)
**
** Notes:
**
** 1) Though t is strictly TDB, it is usually more convenient to use
** TT, which makes no significant difference.
**
** 2) The expression used is as adopted in IERS Conventions (2003). It
** is taken from Kinoshita & Souchay (1990) and comes originally
** from Lieske et al. (1977).
**
** References:
**
** Kinoshita, H. and Souchay J. 1990, Celest.Mech. and Dyn.Astron.
** 48, 187
**
** Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977,
** Astron.Astrophys. 58, 1-16
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
*/
double iauFasa03(double t)
/*
** - - - - - - - - - -
** i a u F a s a 0 3
** - - - - - - - - - -
**
** Fundamental argument, IERS Conventions (2003):
** mean longitude of Saturn.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** t double TDB, Julian centuries since J2000.0 (Note 1)
**
** Returned (function value):
** double mean longitude of Saturn, radians (Note 2)
**
** Notes:
**
** 1) Though t is strictly TDB, it is usually more convenient to use
** TT, which makes no significant difference.
**
** 2) The expression used is as adopted in IERS Conventions (2003) and
** comes from Souchay et al. (1999) after Simon et al. (1994).
**
** References:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
**
** Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
** Astron.Astrophys.Supp.Ser. 135, 111
**
*/
double iauFaur03(double t)
/*
** - - - - - - - - - -
** i a u F a u r 0 3
** - - - - - - - - - -
**
** Fundamental argument, IERS Conventions (2003):
** mean longitude of Uranus.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** t double TDB, Julian centuries since J2000.0 (Note 1)
**
** Returned (function value):
** double mean longitude of Uranus, radians (Note 2)
**
** Notes:
**
** 1) Though t is strictly TDB, it is usually more convenient to use
** TT, which makes no significant difference.
**
** 2) The expression used is as adopted in IERS Conventions (2003) and
** is adapted from Simon et al. (1994).
**
** References:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
**
*/
double iauFave03(double t)
/*
** - - - - - - - - - -
** i a u F a v e 0 3
** - - - - - - - - - -
**
** Fundamental argument, IERS Conventions (2003):
** mean longitude of Venus.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** t double TDB, Julian centuries since J2000.0 (Note 1)
**
** Returned (function value):
** double mean longitude of Venus, radians (Note 2)
**
** Notes:
**
** 1) Though t is strictly TDB, it is usually more convenient to use
** TT, which makes no significant difference.
**
** 2) The expression used is as adopted in IERS Conventions (2003) and
** comes from Souchay et al. (1999) after Simon et al. (1994).
**
** References:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
**
** Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
** Astron.Astrophys.Supp.Ser. 135, 111
**
*/
void iauFk52h(double r5, double d5,
double dr5, double dd5, double px5, double rv5,
double *rh, double *dh,
double *drh, double *ddh, double *pxh, double *rvh)
/*
** - - - - - - - - -
** i a u F k 5 2 h
** - - - - - - - - -
**
** Transform FK5 (J2000.0) star data into the Hipparcos system.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given (all FK5, equinox J2000.0, epoch J2000.0):
** r5 double RA (radians)
** d5 double Dec (radians)
** dr5 double proper motion in RA (dRA/dt, rad/Jyear)
** dd5 double proper motion in Dec (dDec/dt, rad/Jyear)
** px5 double parallax (arcsec)
** rv5 double radial velocity (km/s, positive = receding)
**
** Returned (all Hipparcos, epoch J2000.0):
** rh double RA (radians)
** dh double Dec (radians)
** drh double proper motion in RA (dRA/dt, rad/Jyear)
** ddh double proper motion in Dec (dDec/dt, rad/Jyear)
** pxh double parallax (arcsec)
** rvh double radial velocity (km/s, positive = receding)
**
** Notes:
**
** 1) This function transforms FK5 star positions and proper motions
** into the system of the Hipparcos catalog.
**
** 2) The proper motions in RA are dRA/dt rather than
** cos(Dec)*dRA/dt, and are per year rather than per century.
**
** 3) The FK5 to Hipparcos transformation is modeled as a pure
** rotation and spin; zonal errors in the FK5 catalog are not
** taken into account.
**
** 4) See also iauH2fk5, iauFk5hz, iauHfk5z.
**
** Called:
** iauStarpv star catalog data to space motion pv-vector
** iauFk5hip FK5 to Hipparcos rotation and spin
** iauRxp product of r-matrix and p-vector
** iauPxp vector product of two p-vectors
** iauPpp p-vector plus p-vector
** iauPvstar space motion pv-vector to star catalog data
**
** Reference:
**
** F.Mignard & M.Froeschle, Astron. Astrophys. 354, 732-739 (2000).
**
*/
void iauFk5hip(double r5h[3][3], double s5h[3])
/*
** - - - - - - - - - -
** i a u F k 5 h i p
** - - - - - - - - - -
**
** FK5 to Hipparcos rotation and spin.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Returned:
** r5h double[3][3] r-matrix: FK5 rotation wrt Hipparcos (Note 2)
** s5h double[3] r-vector: FK5 spin wrt Hipparcos (Note 3)
**
** Notes:
**
** 1) This function models the FK5 to Hipparcos transformation as a
** pure rotation and spin; zonal errors in the FK5 catalogue are
** not taken into account.
**
** 2) The r-matrix r5h operates in the sense:
**
** P_Hipparcos = r5h x P_FK5
**
** where P_FK5 is a p-vector in the FK5 frame, and P_Hipparcos is
** the equivalent Hipparcos p-vector.
**
** 3) The r-vector s5h represents the time derivative of the FK5 to
** Hipparcos rotation. The units are radians per year (Julian,
** TDB).
**
** Called:
** iauRv2m r-vector to r-matrix
**
** Reference:
**
** F.Mignard & M.Froeschle, Astron. Astrophys. 354, 732-739 (2000).
**
*/
void iauFk5hz(double r5, double d5, double date1, double date2,
double *rh, double *dh)
/*
** - - - - - - - - -
** i a u F k 5 h z
** - - - - - - - - -
**
** Transform an FK5 (J2000.0) star position into the system of the
** Hipparcos catalogue, assuming zero Hipparcos proper motion.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** r5 double FK5 RA (radians), equinox J2000.0, at date
** d5 double FK5 Dec (radians), equinox J2000.0, at date
** date1,date2 double TDB date (Notes 1,2)
**
** Returned:
** rh double Hipparcos RA (radians)
** dh double Hipparcos Dec (radians)
**
** Notes:
**
** 1) This function converts a star position from the FK5 system to
** the Hipparcos system, in such a way that the Hipparcos proper
** motion is zero. Because such a star has, in general, a non-zero
** proper motion in the FK5 system, the function requires the date
** at which the position in the FK5 system was determined.
**
** 2) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 3) The FK5 to Hipparcos transformation is modeled as a pure
** rotation and spin; zonal errors in the FK5 catalogue are not
** taken into account.
**
** 4) The position returned by this function is in the Hipparcos
** reference system but at date date1+date2.
**
** 5) See also iauFk52h, iauH2fk5, iauHfk5z.
**
** Called:
** iauS2c spherical coordinates to unit vector
** iauFk5hip FK5 to Hipparcos rotation and spin
** iauSxp multiply p-vector by scalar
** iauRv2m r-vector to r-matrix
** iauTrxp product of transpose of r-matrix and p-vector
** iauPxp vector product of two p-vectors
** iauC2s p-vector to spherical
** iauAnp normalize angle into range 0 to 2pi
**
** Reference:
**
** F.Mignard & M.Froeschle, 2000, Astron.Astrophys. 354, 732-739.
**
*/
void iauFw2m(double gamb, double phib, double psi, double eps,
double r[3][3])
/*
** - - - - - - - -
** i a u F w 2 m
** - - - - - - - -
**
** Form rotation matrix given the Fukushima-Williams angles.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** gamb double F-W angle gamma_bar (radians)
** phib double F-W angle phi_bar (radians)
** psi double F-W angle psi (radians)
** eps double F-W angle epsilon (radians)
**
** Returned:
** r double[3][3] rotation matrix
**
** Notes:
**
** 1) Naming the following points:
**
** e = J2000.0 ecliptic pole,
** p = GCRS pole,
** E = ecliptic pole of date,
** and P = CIP,
**
** the four Fukushima-Williams angles are as follows:
**
** gamb = gamma = epE
** phib = phi = pE
** psi = psi = pEP
** eps = epsilon = EP
**
** 2) The matrix representing the combined effects of frame bias,
** precession and nutation is:
**
** NxPxB = R_1(-eps).R_3(-psi).R_1(phib).R_3(gamb)
**
** 3) Three different matrices can be constructed, depending on the
** supplied angles:
**
** o To obtain the nutation x precession x frame bias matrix,
** generate the four precession angles, generate the nutation
** components and add them to the psi_bar and epsilon_A angles,
** and call the present function.
**
** o To obtain the precession x frame bias matrix, generate the
** four precession angles and call the present function.
**
** o To obtain the frame bias matrix, generate the four precession
** angles for date J2000.0 and call the present function.
**
** The nutation-only and precession-only matrices can if necessary
** be obtained by combining these three appropriately.
**
** Called:
** iauIr initialize r-matrix to identity
** iauRz rotate around Z-axis
** iauRx rotate around X-axis
**
** Reference:
**
** Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351
**
*/
void iauFw2xy(double gamb, double phib, double psi, double eps,
double *x, double *y)
/*
** - - - - - - - - -
** i a u F w 2 x y
** - - - - - - - - -
**
** CIP X,Y given Fukushima-Williams bias-precession-nutation angles.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** gamb double F-W angle gamma_bar (radians)
** phib double F-W angle phi_bar (radians)
** psi double F-W angle psi (radians)
** eps double F-W angle epsilon (radians)
**
** Returned:
** x,y double CIP X,Y ("radians")
**
** Notes:
**
** 1) Naming the following points:
**
** e = J2000.0 ecliptic pole,
** p = GCRS pole
** E = ecliptic pole of date,
** and P = CIP,
**
** the four Fukushima-Williams angles are as follows:
**
** gamb = gamma = epE
** phib = phi = pE
** psi = psi = pEP
** eps = epsilon = EP
**
** 2) The matrix representing the combined effects of frame bias,
** precession and nutation is:
**
** NxPxB = R_1(-epsA).R_3(-psi).R_1(phib).R_3(gamb)
**
** X,Y are elements (3,1) and (3,2) of the matrix.
**
** Called:
** iauFw2m F-W angles to r-matrix
** iauBpn2xy extract CIP X,Y coordinates from NPB matrix
**
** Reference:
**
** Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351
**
*/
int iauGc2gd ( int n, double xyz[3],
double *elong, double *phi, double *height )
/*
** - - - - - - - - -
** i a u G c 2 g d
** - - - - - - - - -
**
** Transform geocentric coordinates to geodetic using the specified
** reference ellipsoid.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: canonical transformation.
**
** Given:
** n int ellipsoid identifier (Note 1)
** xyz double[3] geocentric vector (Note 2)
**
** Returned:
** elong double longitude (radians, east +ve)
** phi double latitude (geodetic, radians, Note 3)
** height double height above ellipsoid (geodetic, Notes 2,3)
**
** Returned (function value):
** int status:
** 0 = OK
** -1 = illegal identifier (Note 3)
** -2 = internal error (Note 3)
**
** Notes:
**
** 1) The identifier n is a number that specifies the choice of
** reference ellipsoid. The following are supported:
**
** n ellipsoid
**
** 1 WGS84
** 2 GRS80
** 3 WGS72
**
** The number n has no significance outside the SOFA software.
**
** 2) The geocentric vector (xyz, given) and height (height, returned)
** are in meters.
**
** 3) An error status -1 means that the identifier n is illegal. An
** error status -2 is theoretically impossible. In all error cases,
** phi and height are both set to -1e9.
**
** 4) The inverse transformation is performed in the function iauGd2gc.
**
** Called:
** iauEform Earth reference ellipsoids
** iauGc2gde geocentric to geodetic transformation, general
**
*/
int iauGc2gde ( double a, double f, double xyz[3],
double *elong, double *phi, double *height )
/*
** - - - - - - - - - -
** i a u G c 2 g d e
** - - - - - - - - - -
**
** Transform geocentric coordinates to geodetic for a reference
** ellipsoid of specified form.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** a double equatorial radius (Notes 2,4)
** f double flattening (Note 3)
** xyz double[3] geocentric vector (Note 4)
**
** Returned:
** elong double longitude (radians, east +ve)
** phi double latitude (geodetic, radians)
** height double height above ellipsoid (geodetic, Note 4)
**
** Returned (function value):
** int status:
** 0 = OK
** -1 = illegal f
** -2 = illegal a
**
** Notes:
**
** 1) This function is based on the GCONV2H Fortran subroutine by
** Toshio Fukushima (see reference).
**
** 2) The equatorial radius, a, can be in any units, but meters is
** the conventional choice.
**
** 3) The flattening, f, is (for the Earth) a value around 0.00335,
** i.e. around 1/298.
**
** 4) The equatorial radius, a, and the geocentric vector, xyz,
** must be given in the same units, and determine the units of
** the returned height, height.
**
** 5) If an error occurs (status < 0), elong, phi and height are
** unchanged.
**
** 6) The inverse transformation is performed in the function
** iauGd2gce.
**
** 7) The transformation for a standard ellipsoid (such as WGS84) can
** more conveniently be performed by calling iauGc2gd, which uses a
** numerical code (1 for WGS84) to identify the required A and F
** values.
**
** Reference:
**
** Fukushima, T., "Transformation from Cartesian to geodetic
** coordinates accelerated by Halley's method", J.Geodesy (2006)
** 79: 689-693
**
*/
int iauGd2gc ( int n, double elong, double phi, double height,
double xyz[3] )
/*
** - - - - - - - - -
** i a u G d 2 g c
** - - - - - - - - -
**
** Transform geodetic coordinates to geocentric using the specified
** reference ellipsoid.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: canonical transformation.
**
** Given:
** n int ellipsoid identifier (Note 1)
** elong double longitude (radians, east +ve)
** phi double latitude (geodetic, radians, Note 3)
** height double height above ellipsoid (geodetic, Notes 2,3)
**
** Returned:
** xyz double[3] geocentric vector (Note 2)
**
** Returned (function value):
** int status:
** 0 = OK
** -1 = illegal identifier (Note 3)
** -2 = illegal case (Note 3)
**
** Notes:
**
** 1) The identifier n is a number that specifies the choice of
** reference ellipsoid. The following are supported:
**
** n ellipsoid
**
** 1 WGS84
** 2 GRS80
** 3 WGS72
**
** The number n has no significance outside the SOFA software.
**
** 2) The height (height, given) and the geocentric vector (xyz,
** returned) are in meters.
**
** 3) No validation is performed on the arguments elong, phi and
** height. An error status -1 means that the identifier n is
** illegal. An error status -2 protects against cases that would
** lead to arithmetic exceptions. In all error cases, xyz is set
** to zeros.
**
** 4) The inverse transformation is performed in the function iauGc2gd.
**
** Called:
** iauEform Earth reference ellipsoids
** iauGd2gce geodetic to geocentric transformation, general
** iauZp zero p-vector
**
*/
int iauGd2gce ( double a, double f, double elong, double phi,
double height, double xyz[3] )
/*
** - - - - - - - - - -
** i a u G d 2 g c e
** - - - - - - - - - -
**
** Transform geodetic coordinates to geocentric for a reference
** ellipsoid of specified form.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** a double equatorial radius (Notes 1,4)
** f double flattening (Notes 2,4)
** elong double longitude (radians, east +ve)
** phi double latitude (geodetic, radians, Note 4)
** height double height above ellipsoid (geodetic, Notes 3,4)
**
** Returned:
** xyz double[3] geocentric vector (Note 3)
**
** Returned (function value):
** int status:
** 0 = OK
** -1 = illegal case (Note 4)
** Notes:
**
** 1) The equatorial radius, a, can be in any units, but meters is
** the conventional choice.
**
** 2) The flattening, f, is (for the Earth) a value around 0.00335,
** i.e. around 1/298.
**
** 3) The equatorial radius, a, and the height, height, must be
** given in the same units, and determine the units of the
** returned geocentric vector, xyz.
**
** 4) No validation is performed on individual arguments. The error
** status -1 protects against (unrealistic) cases that would lead
** to arithmetic exceptions. If an error occurs, xyz is unchanged.
**
** 5) The inverse transformation is performed in the function
** iauGc2gde.
**
** 6) The transformation for a standard ellipsoid (such as WGS84) can
** more conveniently be performed by calling iauGd2gc, which uses a
** numerical code (1 for WGS84) to identify the required a and f
** values.
**
** References:
**
** Green, R.M., Spherical Astronomy, Cambridge University Press,
** (1985) Section 4.5, p96.
**
** Explanatory Supplement to the Astronomical Almanac,
** P. Kenneth Seidelmann (ed), University Science Books (1992),
** Section 4.22, p202.
**
*/
double iauGmst00(double uta, double utb, double tta, double ttb)
/*
** - - - - - - - - - -
** i a u G m s t 0 0
** - - - - - - - - - -
**
** Greenwich mean sidereal time (model consistent with IAU 2000
** resolutions).
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** uta,utb double UT1 as a 2-part Julian Date (Notes 1,2)
** tta,ttb double TT as a 2-part Julian Date (Notes 1,2)
**
** Returned (function value):
** double Greenwich mean sidereal time (radians)
**
** Notes:
**
** 1) The UT1 and TT dates uta+utb and tta+ttb respectively, are both
** Julian Dates, apportioned in any convenient way between the
** argument pairs. For example, JD=2450123.7 could be expressed in
** any of these ways, among others:
**
** Part A Part B
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable (in the case of UT; the TT is not at all critical
** in this respect). The J2000 and MJD methods are good compromises
** between resolution and convenience. For UT, the date & time
** method is best matched to the algorithm that is used by the Earth
** Rotation Angle function, called internally: maximum precision is
** delivered when the uta argument is for 0hrs UT1 on the day in
** question and the utb argument lies in the range 0 to 1, or vice
** versa.
**
** 2) Both UT1 and TT are required, UT1 to predict the Earth rotation
** and TT to predict the effects of precession. If UT1 is used for
** both purposes, errors of order 100 microarcseconds result.
**
** 3) This GMST is compatible with the IAU 2000 resolutions and must be
** used only in conjunction with other IAU 2000 compatible
** components such as precession-nutation and equation of the
** equinoxes.
**
** 4) The result is returned in the range 0 to 2pi.
**
** 5) The algorithm is from Capitaine et al. (2003) and IERS
** Conventions 2003.
**
** Called:
** iauEra00 Earth rotation angle, IAU 2000
** iauAnp normalize angle into range 0 to 2pi
**
** References:
**
** Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
** implement the IAU 2000 definition of UT1", Astronomy &
** Astrophysics, 406, 1135-1149 (2003)
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
*/
double iauGmst06(double uta, double utb, double tta, double ttb)
/*
** - - - - - - - - - -
** i a u G m s t 0 6
** - - - - - - - - - -
**
** Greenwich mean sidereal time (consistent with IAU 2006 precession).
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** uta,utb double UT1 as a 2-part Julian Date (Notes 1,2)
** tta,ttb double TT as a 2-part Julian Date (Notes 1,2)
**
** Returned (function value):
** double Greenwich mean sidereal time (radians)
**
** Notes:
**
** 1) The UT1 and TT dates uta+utb and tta+ttb respectively, are both
** Julian Dates, apportioned in any convenient way between the
** argument pairs. For example, JD=2450123.7 could be expressed in
** any of these ways, among others:
**
** Part A Part B
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable (in the case of UT; the TT is not at all critical
** in this respect). The J2000 and MJD methods are good compromises
** between resolution and convenience. For UT, the date & time
** method is best matched to the algorithm that is used by the Earth
** rotation angle function, called internally: maximum precision is
** delivered when the uta argument is for 0hrs UT1 on the day in
** question and the utb argument lies in the range 0 to 1, or vice
** versa.
**
** 2) Both UT1 and TT are required, UT1 to predict the Earth rotation
** and TT to predict the effects of precession. If UT1 is used for
** both purposes, errors of order 100 microarcseconds result.
**
** 3) This GMST is compatible with the IAU 2006 precession and must not
** be used with other precession models.
**
** 4) The result is returned in the range 0 to 2pi.
**
** Called:
** iauEra00 Earth rotation angle, IAU 2000
** iauAnp normalize angle into range 0 to 2pi
**
** Reference:
**
** Capitaine, N., Wallace, P.T. & Chapront, J., 2005,
** Astron.Astrophys. 432, 355
**
*/
double iauGmst82(double dj1, double dj2)
/*
** - - - - - - - - - -
** i a u G m s t 8 2
** - - - - - - - - - -
**
** Universal Time to Greenwich mean sidereal time (IAU 1982 model).
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** dj1,dj2 double UT1 Julian Date (see note)
**
** Returned (function value):
** double Greenwich mean sidereal time (radians)
**
** Notes:
**
** 1) The UT1 date dj1+dj2 is a Julian Date, apportioned in any
** convenient way between the arguments dj1 and dj2. For example,
** JD(UT1)=2450123.7 could be expressed in any of these ways,
** among others:
**
** dj1 dj2
**
** 2450123.7D0 0D0 (JD method)
** 2451545D0 -1421.3D0 (J2000 method)
** 2400000.5D0 50123.2D0 (MJD method)
** 2450123.5D0 0.2D0 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 and MJD methods are good compromises
** between resolution and convenience. The date & time method is
** best matched to the algorithm used: maximum accuracy (or, at
** least, minimum noise) is delivered when the dj1 argument is for
** 0hrs UT1 on the day in question and the dj2 argument lies in the
** range 0 to 1, or vice versa.
**
** 2) The algorithm is based on the IAU 1982 expression. This is
** always described as giving the GMST at 0 hours UT1. In fact, it
** gives the difference between the GMST and the UT, the steady
** 4-minutes-per-day drawing-ahead of ST with respect to UT. When
** whole days are ignored, the expression happens to equal the GMST
** at 0 hours UT1 each day.
**
** 3) In this function, the entire UT1 (the sum of the two arguments
** dj1 and dj2) is used directly as the argument for the standard
** formula, the constant term of which is adjusted by 12 hours to
** take account of the noon phasing of Julian Date. The UT1 is then
** added, but omitting whole days to conserve accuracy.
**
** Called:
** iauAnp normalize angle into range 0 to 2pi
**
** References:
**
** Transactions of the International Astronomical Union,
** XVIII B, 67 (1983).
**
** Aoki et al., Astron. Astrophys. 105, 359-361 (1982).
**
*/
double iauGst00a(double uta, double utb, double tta, double ttb)
/*
** - - - - - - - - - -
** i a u G s t 0 0 a
** - - - - - - - - - -
**
** Greenwich apparent sidereal time (consistent with IAU 2000
** resolutions).
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** uta,utb double UT1 as a 2-part Julian Date (Notes 1,2)
** tta,ttb double TT as a 2-part Julian Date (Notes 1,2)
**
** Returned (function value):
** double Greenwich apparent sidereal time (radians)
**
** Notes:
**
** 1) The UT1 and TT dates uta+utb and tta+ttb respectively, are both
** Julian Dates, apportioned in any convenient way between the
** argument pairs. For example, JD=2450123.7 could be expressed in
** any of these ways, among others:
**
** Part A Part B
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable (in the case of UT; the TT is not at all critical
** in this respect). The J2000 and MJD methods are good compromises
** between resolution and convenience. For UT, the date & time
** method is best matched to the algorithm that is used by the Earth
** Rotation Angle function, called internally: maximum precision is
** delivered when the uta argument is for 0hrs UT1 on the day in
** question and the utb argument lies in the range 0 to 1, or vice
** versa.
**
** 2) Both UT1 and TT are required, UT1 to predict the Earth rotation
** and TT to predict the effects of precession-nutation. If UT1 is
** used for both purposes, errors of order 100 microarcseconds
** result.
**
** 3) This GAST is compatible with the IAU 2000 resolutions and must be
** used only in conjunction with other IAU 2000 compatible
** components such as precession-nutation.
**
** 4) The result is returned in the range 0 to 2pi.
**
** 5) The algorithm is from Capitaine et al. (2003) and IERS
** Conventions 2003.
**
** Called:
** iauGmst00 Greenwich mean sidereal time, IAU 2000
** iauEe00a equation of the equinoxes, IAU 2000A
** iauAnp normalize angle into range 0 to 2pi
**
** References:
**
** Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
** implement the IAU 2000 definition of UT1", Astronomy &
** Astrophysics, 406, 1135-1149 (2003)
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
*/
double iauGst00b(double uta, double utb)
/*
** - - - - - - - - - -
** i a u G s t 0 0 b
** - - - - - - - - - -
**
** Greenwich apparent sidereal time (consistent with IAU 2000
** resolutions but using the truncated nutation model IAU 2000B).
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** uta,utb double UT1 as a 2-part Julian Date (Notes 1,2)
**
** Returned (function value):
** double Greenwich apparent sidereal time (radians)
**
** Notes:
**
** 1) The UT1 date uta+utb is a Julian Date, apportioned in any
** convenient way between the argument pair. For example,
** JD=2450123.7 could be expressed in any of these ways, among
** others:
**
** uta utb
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in cases
** where the loss of several decimal digits of resolution is
** acceptable. The J2000 and MJD methods are good compromises
** between resolution and convenience. For UT, the date & time
** method is best matched to the algorithm that is used by the Earth
** Rotation Angle function, called internally: maximum precision is
** delivered when the uta argument is for 0hrs UT1 on the day in
** question and the utb argument lies in the range 0 to 1, or vice
** versa.
**
** 2) The result is compatible with the IAU 2000 resolutions, except
** that accuracy has been compromised for the sake of speed and
** convenience in two respects:
**
** . UT is used instead of TDB (or TT) to compute the precession
** component of GMST and the equation of the equinoxes. This
** results in errors of order 0.1 mas at present.
**
** . The IAU 2000B abridged nutation model (McCarthy & Luzum, 2001)
** is used, introducing errors of up to 1 mas.
**
** 3) This GAST is compatible with the IAU 2000 resolutions and must be
** used only in conjunction with other IAU 2000 compatible
** components such as precession-nutation.
**
** 4) The result is returned in the range 0 to 2pi.
**
** 5) The algorithm is from Capitaine et al. (2003) and IERS
** Conventions 2003.
**
** Called:
** iauGmst00 Greenwich mean sidereal time, IAU 2000
** iauEe00b equation of the equinoxes, IAU 2000B
** iauAnp normalize angle into range 0 to 2pi
**
** References:
**
** Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
** implement the IAU 2000 definition of UT1", Astronomy &
** Astrophysics, 406, 1135-1149 (2003)
**
** McCarthy, D.D. & Luzum, B.J., "An abridged model of the
** precession-nutation of the celestial pole", Celestial Mechanics &
** Dynamical Astronomy, 85, 37-49 (2003)
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
*/
double iauGst06(double uta, double utb, double tta, double ttb,
double rnpb[3][3])
/*
** - - - - - - - - -
** i a u G s t 0 6
** - - - - - - - - -
**
** Greenwich apparent sidereal time, IAU 2006, given the NPB matrix.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** uta,utb double UT1 as a 2-part Julian Date (Notes 1,2)
** tta,ttb double TT as a 2-part Julian Date (Notes 1,2)
** rnpb double[3][3] nutation x precession x bias matrix
**
** Returned (function value):
** double Greenwich apparent sidereal time (radians)
**
** Notes:
**
** 1) The UT1 and TT dates uta+utb and tta+ttb respectively, are both
** Julian Dates, apportioned in any convenient way between the
** argument pairs. For example, JD=2450123.7 could be expressed in
** any of these ways, among others:
**
** Part A Part B
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable (in the case of UT; the TT is not at all critical
** in this respect). The J2000 and MJD methods are good compromises
** between resolution and convenience. For UT, the date & time
** method is best matched to the algorithm that is used by the Earth
** rotation angle function, called internally: maximum precision is
** delivered when the uta argument is for 0hrs UT1 on the day in
** question and the utb argument lies in the range 0 to 1, or vice
** versa.
**
** 2) Both UT1 and TT are required, UT1 to predict the Earth rotation
** and TT to predict the effects of precession-nutation. If UT1 is
** used for both purposes, errors of order 100 microarcseconds
** result.
**
** 3) Although the function uses the IAU 2006 series for s+XY/2, it is
** otherwise independent of the precession-nutation model and can in
** practice be used with any equinox-based NPB matrix.
**
** 4) The result is returned in the range 0 to 2pi.
**
** Called:
** iauBpn2xy extract CIP X,Y coordinates from NPB matrix
** iauS06 the CIO locator s, given X,Y, IAU 2006
** iauAnp normalize angle into range 0 to 2pi
** iauEra00 Earth rotation angle, IAU 2000
** iauEors equation of the origins, given NPB matrix and s
**
** Reference:
**
** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
**
*/
double iauGst06a(double uta, double utb, double tta, double ttb)
/*
** - - - - - - - - - -
** i a u G s t 0 6 a
** - - - - - - - - - -
**
** Greenwich apparent sidereal time (consistent with IAU 2000 and 2006
** resolutions).
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** uta,utb double UT1 as a 2-part Julian Date (Notes 1,2)
** tta,ttb double TT as a 2-part Julian Date (Notes 1,2)
**
** Returned (function value):
** double Greenwich apparent sidereal time (radians)
**
** Notes:
**
** 1) The UT1 and TT dates uta+utb and tta+ttb respectively, are both
** Julian Dates, apportioned in any convenient way between the
** argument pairs. For example, JD=2450123.7 could be expressed in
** any of these ways, among others:
**
** Part A Part B
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable (in the case of UT; the TT is not at all critical
** in this respect). The J2000 and MJD methods are good compromises
** between resolution and convenience. For UT, the date & time
** method is best matched to the algorithm that is used by the Earth
** rotation angle function, called internally: maximum precision is
** delivered when the uta argument is for 0hrs UT1 on the day in
** question and the utb argument lies in the range 0 to 1, or vice
** versa.
**
** 2) Both UT1 and TT are required, UT1 to predict the Earth rotation
** and TT to predict the effects of precession-nutation. If UT1 is
** used for both purposes, errors of order 100 microarcseconds
** result.
**
** 3) This GAST is compatible with the IAU 2000/2006 resolutions and
** must be used only in conjunction with IAU 2006 precession and
** IAU 2000A nutation.
**
** 4) The result is returned in the range 0 to 2pi.
**
** Called:
** iauPnm06a classical NPB matrix, IAU 2006/2000A
** iauGst06 Greenwich apparent ST, IAU 2006, given NPB matrix
**
** Reference:
**
** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
**
*/
double iauGst94(double uta, double utb)
/*
** - - - - - - - - -
** i a u G s t 9 4
** - - - - - - - - -
**
** Greenwich apparent sidereal time (consistent with IAU 1982/94
** resolutions).
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** uta,utb double UT1 as a 2-part Julian Date (Notes 1,2)
**
** Returned (function value):
** double Greenwich apparent sidereal time (radians)
**
** Notes:
**
** 1) The UT1 date uta+utb is a Julian Date, apportioned in any
** convenient way between the argument pair. For example,
** JD=2450123.7 could be expressed in any of these ways, among
** others:
**
** uta utb
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in cases
** where the loss of several decimal digits of resolution is
** acceptable. The J2000 and MJD methods are good compromises
** between resolution and convenience. For UT, the date & time
** method is best matched to the algorithm that is used by the Earth
** Rotation Angle function, called internally: maximum precision is
** delivered when the uta argument is for 0hrs UT1 on the day in
** question and the utb argument lies in the range 0 to 1, or vice
** versa.
**
** 2) The result is compatible with the IAU 1982 and 1994 resolutions,
** except that accuracy has been compromised for the sake of
** convenience in that UT is used instead of TDB (or TT) to compute
** the equation of the equinoxes.
**
** 3) This GAST must be used only in conjunction with contemporaneous
** IAU standards such as 1976 precession, 1980 obliquity and 1982
** nutation. It is not compatible with the IAU 2000 resolutions.
**
** 4) The result is returned in the range 0 to 2pi.
**
** Called:
** iauGmst82 Greenwich mean sidereal time, IAU 1982
** iauEqeq94 equation of the equinoxes, IAU 1994
** iauAnp normalize angle into range 0 to 2pi
**
** References:
**
** Explanatory Supplement to the Astronomical Almanac,
** P. Kenneth Seidelmann (ed), University Science Books (1992)
**
** IAU Resolution C7, Recommendation 3 (1994)
**
*/
void iauH2fk5(double rh, double dh,
double drh, double ddh, double pxh, double rvh,
double *r5, double *d5,
double *dr5, double *dd5, double *px5, double *rv5)
/*
** - - - - - - - - -
** i a u H 2 f k 5
** - - - - - - - - -
**
** Transform Hipparcos star data into the FK5 (J2000.0) system.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given (all Hipparcos, epoch J2000.0):
** rh double RA (radians)
** dh double Dec (radians)
** drh double proper motion in RA (dRA/dt, rad/Jyear)
** ddh double proper motion in Dec (dDec/dt, rad/Jyear)
** pxh double parallax (arcsec)
** rvh double radial velocity (km/s, positive = receding)
**
** Returned (all FK5, equinox J2000.0, epoch J2000.0):
** r5 double RA (radians)
** d5 double Dec (radians)
** dr5 double proper motion in RA (dRA/dt, rad/Jyear)
** dd5 double proper motion in Dec (dDec/dt, rad/Jyear)
** px5 double parallax (arcsec)
** rv5 double radial velocity (km/s, positive = receding)
**
** Notes:
**
** 1) This function transforms Hipparcos star positions and proper
** motions into FK5 J2000.0.
**
** 2) The proper motions in RA are dRA/dt rather than
** cos(Dec)*dRA/dt, and are per year rather than per century.
**
** 3) The FK5 to Hipparcos transformation is modeled as a pure
** rotation and spin; zonal errors in the FK5 catalog are not
** taken into account.
**
** 4) See also iauFk52h, iauFk5hz, iauHfk5z.
**
** Called:
** iauStarpv star catalog data to space motion pv-vector
** iauFk5hip FK5 to Hipparcos rotation and spin
** iauRv2m r-vector to r-matrix
** iauRxp product of r-matrix and p-vector
** iauTrxp product of transpose of r-matrix and p-vector
** iauPxp vector product of two p-vectors
** iauPmp p-vector minus p-vector
** iauPvstar space motion pv-vector to star catalog data
**
** Reference:
**
** F.Mignard & M.Froeschle, Astron. Astrophys. 354, 732-739 (2000).
**
*/
void iauHfk5z(double rh, double dh, double date1, double date2,
double *r5, double *d5, double *dr5, double *dd5)
/*
** - - - - - - - - -
** i a u H f k 5 z
** - - - - - - - - -
**
** Transform a Hipparcos star position into FK5 J2000.0, assuming
** zero Hipparcos proper motion.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** rh double Hipparcos RA (radians)
** dh double Hipparcos Dec (radians)
** date1,date2 double TDB date (Note 1)
**
** Returned (all FK5, equinox J2000.0, date date1+date2):
** r5 double RA (radians)
** d5 double Dec (radians)
** dr5 double FK5 RA proper motion (rad/year, Note 4)
** dd5 double Dec proper motion (rad/year, Note 4)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
**
** 3) The FK5 to Hipparcos transformation is modeled as a pure rotation
** and spin; zonal errors in the FK5 catalogue are not taken into
** account.
**
** 4) It was the intention that Hipparcos should be a close
** approximation to an inertial frame, so that distant objects have
** zero proper motion; such objects have (in general) non-zero
** proper motion in FK5, and this function returns those fictitious
** proper motions.
**
** 5) The position returned by this function is in the FK5 J2000.0
** reference system but at date date1+date2.
**
** 6) See also iauFk52h, iauH2fk5, iauFk5zhz.
**
** Called:
** iauS2c spherical coordinates to unit vector
** iauFk5hip FK5 to Hipparcos rotation and spin
** iauRxp product of r-matrix and p-vector
** iauSxp multiply p-vector by scalar
** iauRxr product of two r-matrices
** iauTrxp product of transpose of r-matrix and p-vector
** iauPxp vector product of two p-vectors
** iauPv2s pv-vector to spherical
** iauAnp normalize angle into range 0 to 2pi
**
** Reference:
**
** F.Mignard & M.Froeschle, 2000, Astron.Astrophys. 354, 732-739.
**
*/
void iauIr(double r[3][3])
/*
** - - - - - -
** i a u I r
** - - - - - -
**
** Initialize an r-matrix to the identity matrix.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Returned:
** r double[3][3] r-matrix
**
** Called:
** iauZr zero r-matrix
**
*/
int iauJd2cal(double dj1, double dj2,
int *iy, int *im, int *id, double *fd)
/*
** - - - - - - - - - -
** i a u J d 2 c a l
** - - - - - - - - - -
**
** Julian Date to Gregorian year, month, day, and fraction of a day.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** dj1,dj2 double Julian Date (Notes 1, 2)
**
** Returned (arguments):
** iy int year
** im int month
** id int day
** fd double fraction of day
**
** Returned (function value):
** int status:
** 0 = OK
** -1 = unacceptable date (Note 3)
**
** Notes:
**
** 1) The earliest valid date is -68569.5 (-4900 March 1). The
** largest value accepted is 10^9.
**
** 2) The Julian Date is apportioned in any convenient way between
** the arguments dj1 and dj2. For example, JD=2450123.7 could
** be expressed in any of these ways, among others:
**
** dj1 dj2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** 3) In early eras the conversion is from the "proleptic Gregorian
** calendar"; no account is taken of the date(s) of adoption of
** the Gregorian calendar, nor is the AD/BC numbering convention
** observed.
**
** Reference:
**
** Explanatory Supplement to the Astronomical Almanac,
** P. Kenneth Seidelmann (ed), University Science Books (1992),
** Section 12.92 (p604).
**
*/
int iauJdcalf(int ndp, double dj1, double dj2, int iymdf[4])
/*
** - - - - - - - - - -
** i a u J d c a l f
** - - - - - - - - - -
**
** Julian Date to Gregorian Calendar, expressed in a form convenient
** for formatting messages: rounded to a specified precision.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** ndp int number of decimal places of days in fraction
** dj1,dj2 double dj1+dj2 = Julian Date (Note 1)
**
** Returned:
** iymdf int[4] year, month, day, fraction in Gregorian
** calendar
**
** Returned (function value):
** int status:
** -1 = date out of range
** 0 = OK
** +1 = NDP not 0-9 (interpreted as 0)
**
** Notes:
**
** 1) The Julian Date is apportioned in any convenient way between
** the arguments dj1 and dj2. For example, JD=2450123.7 could
** be expressed in any of these ways, among others:
**
** dj1 dj2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** 2) In early eras the conversion is from the "Proleptic Gregorian
** Calendar"; no account is taken of the date(s) of adoption of
** the Gregorian Calendar, nor is the AD/BC numbering convention
** observed.
**
** 3) Refer to the function iauJd2cal.
**
** 4) NDP should be 4 or less if internal overflows are to be
** avoided on machines which use 16-bit integers.
**
** Called:
** iauJd2cal JD to Gregorian calendar
**
** Reference:
**
** Explanatory Supplement to the Astronomical Almanac,
** P. Kenneth Seidelmann (ed), University Science Books (1992),
** Section 12.92 (p604).
**
*/
void iauNum00a(double date1, double date2, double rmatn[3][3])
/*
** - - - - - - - - - -
** i a u N u m 0 0 a
** - - - - - - - - - -
**
** Form the matrix of nutation for a given date, IAU 2000A model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** rmatn double[3][3] nutation matrix
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The matrix operates in the sense V(true) = rmatn * V(mean), where
** the p-vector V(true) is with respect to the true equatorial triad
** of date and the p-vector V(mean) is with respect to the mean
** equatorial triad of date.
**
** 3) A faster, but slightly less accurate result (about 1 mas), can be
** obtained by using instead the iauNum00b function.
**
** Called:
** iauPn00a bias/precession/nutation, IAU 2000A
**
** Reference:
**
** Explanatory Supplement to the Astronomical Almanac,
** P. Kenneth Seidelmann (ed), University Science Books (1992),
** Section 3.222-3 (p114).
**
*/
void iauNum00b(double date1, double date2, double rmatn[3][3])
/*
** - - - - - - - - - -
** i a u N u m 0 0 b
** - - - - - - - - - -
**
** Form the matrix of nutation for a given date, IAU 2000B model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** rmatn double[3][3] nutation matrix
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The matrix operates in the sense V(true) = rmatn * V(mean), where
** the p-vector V(true) is with respect to the true equatorial triad
** of date and the p-vector V(mean) is with respect to the mean
** equatorial triad of date.
**
** 3) The present function is faster, but slightly less accurate (about
** 1 mas), than the iauNum00a function.
**
** Called:
** iauPn00b bias/precession/nutation, IAU 2000B
**
** Reference:
**
** Explanatory Supplement to the Astronomical Almanac,
** P. Kenneth Seidelmann (ed), University Science Books (1992),
** Section 3.222-3 (p114).
**
*/
void iauNum06a(double date1, double date2, double rmatn[3][3])
/*
** - - - - - - - - - -
** i a u N u m 0 6 a
** - - - - - - - - - -
**
** Form the matrix of nutation for a given date, IAU 2006/2000A model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** rmatn double[3][3] nutation matrix
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The matrix operates in the sense V(true) = rmatn * V(mean), where
** the p-vector V(true) is with respect to the true equatorial triad
** of date and the p-vector V(mean) is with respect to the mean
** equatorial triad of date.
**
** Called:
** iauObl06 mean obliquity, IAU 2006
** iauNut06a nutation, IAU 2006/2000A
** iauNumat form nutation matrix
**
** Reference:
**
** Explanatory Supplement to the Astronomical Almanac,
** P. Kenneth Seidelmann (ed), University Science Books (1992),
** Section 3.222-3 (p114).
**
*/
void iauNumat(double epsa, double dpsi, double deps, double rmatn[3][3])
/*
** - - - - - - - - -
** i a u N u m a t
** - - - - - - - - -
**
** Form the matrix of nutation.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** epsa double mean obliquity of date (Note 1)
** dpsi,deps double nutation (Note 2)
**
** Returned:
** rmatn double[3][3] nutation matrix (Note 3)
**
** Notes:
**
**
** 1) The supplied mean obliquity epsa, must be consistent with the
** precession-nutation models from which dpsi and deps were obtained.
**
** 2) The caller is responsible for providing the nutation components;
** they are in longitude and obliquity, in radians and are with
** respect to the equinox and ecliptic of date.
**
** 3) The matrix operates in the sense V(true) = rmatn * V(mean),
** where the p-vector V(true) is with respect to the true
** equatorial triad of date and the p-vector V(mean) is with
** respect to the mean equatorial triad of date.
**
** Called:
** iauIr initialize r-matrix to identity
** iauRx rotate around X-axis
** iauRz rotate around Z-axis
**
** Reference:
**
** Explanatory Supplement to the Astronomical Almanac,
** P. Kenneth Seidelmann (ed), University Science Books (1992),
** Section 3.222-3 (p114).
**
*/
void iauNut00a(double date1, double date2, double *dpsi, double *deps)
/*
** - - - - - - - - - -
** i a u N u t 0 0 a
** - - - - - - - - - -
**
** Nutation, IAU 2000A model (MHB2000 luni-solar and planetary nutation
** with free core nutation omitted).
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** dpsi,deps double nutation, luni-solar + planetary (Note 2)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The nutation components in longitude and obliquity are in radians
** and with respect to the equinox and ecliptic of date. The
** obliquity at J2000.0 is assumed to be the Lieske et al. (1977)
** value of 84381.448 arcsec.
**
** Both the luni-solar and planetary nutations are included. The
** latter are due to direct planetary nutations and the
** perturbations of the lunar and terrestrial orbits.
**
** 3) The function computes the MHB2000 nutation series with the
** associated corrections for planetary nutations. It is an
** implementation of the nutation part of the IAU 2000A precession-
** nutation model, formally adopted by the IAU General Assembly in
** 2000, namely MHB2000 (Mathews et al. 2002), but with the free
** core nutation (FCN - see Note 4) omitted.
**
** 4) The full MHB2000 model also contains contributions to the
** nutations in longitude and obliquity due to the free-excitation
** of the free-core-nutation during the period 1979-2000. These FCN
** terms, which are time-dependent and unpredictable, are NOT
** included in the present function and, if required, must be
** independently computed. With the FCN corrections included, the
** present function delivers a pole which is at current epochs
** accurate to a few hundred microarcseconds. The omission of FCN
** introduces further errors of about that size.
**
** 5) The present function provides classical nutation. The MHB2000
** algorithm, from which it is adapted, deals also with (i) the
** offsets between the GCRS and mean poles and (ii) the adjustments
** in longitude and obliquity due to the changed precession rates.
** These additional functions, namely frame bias and precession
** adjustments, are supported by the SOFA functions iauBi00 and
** iauPr00.
**
** 6) The MHB2000 algorithm also provides "total" nutations, comprising
** the arithmetic sum of the frame bias, precession adjustments,
** luni-solar nutation and planetary nutation. These total
** nutations can be used in combination with an existing IAU 1976
** precession implementation, such as iauPmat76, to deliver GCRS-
** to-true predictions of sub-mas accuracy at current dates.
** However, there are three shortcomings in the MHB2000 model that
** must be taken into account if more accurate or definitive results
** are required (see Wallace 2002):
**
** (i) The MHB2000 total nutations are simply arithmetic sums,
** yet in reality the various components are successive Euler
** rotations. This slight lack of rigor leads to cross terms
** that exceed 1 mas after a century. The rigorous procedure
** is to form the GCRS-to-true rotation matrix by applying the
** bias, precession and nutation in that order.
**
** (ii) Although the precession adjustments are stated to be with
** respect to Lieske et al. (1977), the MHB2000 model does
** not specify which set of Euler angles are to be used and
** how the adjustments are to be applied. The most literal
** and straightforward procedure is to adopt the 4-rotation
** epsilon_0, psi_A, omega_A, xi_A option, and to add DPSIPR
** to psi_A and DEPSPR to both omega_A and eps_A.
**
** (iii) The MHB2000 model predates the determination by Chapront
** et al. (2002) of a 14.6 mas displacement between the
** J2000.0 mean equinox and the origin of the ICRS frame. It
** should, however, be noted that neglecting this displacement
** when calculating star coordinates does not lead to a
** 14.6 mas change in right ascension, only a small second-
** order distortion in the pattern of the precession-nutation
** effect.
**
** For these reasons, the SOFA functions do not generate the "total
** nutations" directly, though they can of course easily be
** generated by calling iauBi00, iauPr00 and the present function
** and adding the results.
**
** 7) The MHB2000 model contains 41 instances where the same frequency
** appears multiple times, of which 38 are duplicates and three are
** triplicates. To keep the present code close to the original MHB
** algorithm, this small inefficiency has not been corrected.
**
** Called:
** iauFal03 mean anomaly of the Moon
** iauFaf03 mean argument of the latitude of the Moon
** iauFaom03 mean longitude of the Moon's ascending node
** iauFame03 mean longitude of Mercury
** iauFave03 mean longitude of Venus
** iauFae03 mean longitude of Earth
** iauFama03 mean longitude of Mars
** iauFaju03 mean longitude of Jupiter
** iauFasa03 mean longitude of Saturn
** iauFaur03 mean longitude of Uranus
** iauFapa03 general accumulated precession in longitude
**
** References:
**
** Chapront, J., Chapront-Touze, M. & Francou, G. 2002,
** Astron.Astrophys. 387, 700
**
** Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977,
** Astron.Astrophys. 58, 1-16
**
** Mathews, P.M., Herring, T.A., Buffet, B.A. 2002, J.Geophys.Res.
** 107, B4. The MHB_2000 code itself was obtained on 9th September
** 2002 from ftp//maia.usno.navy.mil/conv2000/chapter5/IAU2000A.
**
** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
**
** Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
** Astron.Astrophys.Supp.Ser. 135, 111
**
** Wallace, P.T., "Software for Implementing the IAU 2000
** Resolutions", in IERS Workshop 5.1 (2002)
**
*/
void iauNut00b(double date1, double date2, double *dpsi, double *deps)
/*
** - - - - - - - - - -
** i a u N u t 0 0 b
** - - - - - - - - - -
**
** Nutation, IAU 2000B model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** dpsi,deps double nutation, luni-solar + planetary (Note 2)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The nutation components in longitude and obliquity are in radians
** and with respect to the equinox and ecliptic of date. The
** obliquity at J2000.0 is assumed to be the Lieske et al. (1977)
** value of 84381.448 arcsec. (The errors that result from using
** this function with the IAU 2006 value of 84381.406 arcsec can be
** neglected.)
**
** The nutation model consists only of luni-solar terms, but
** includes also a fixed offset which compensates for certain long-
** period planetary terms (Note 7).
**
** 3) This function is an implementation of the IAU 2000B abridged
** nutation model formally adopted by the IAU General Assembly in
** 2000. The function computes the MHB_2000_SHORT luni-solar
** nutation series (Luzum 2001), but without the associated
** corrections for the precession rate adjustments and the offset
** between the GCRS and J2000.0 mean poles.
**
** 4) The full IAU 2000A (MHB2000) nutation model contains nearly 1400
** terms. The IAU 2000B model (McCarthy & Luzum 2003) contains only
** 77 terms, plus additional simplifications, yet still delivers
** results of 1 mas accuracy at present epochs. This combination of
** accuracy and size makes the IAU 2000B abridged nutation model
** suitable for most practical applications.
**
** The function delivers a pole accurate to 1 mas from 1900 to 2100
** (usually better than 1 mas, very occasionally just outside
** 1 mas). The full IAU 2000A model, which is implemented in the
** function iauNut00a (q.v.), delivers considerably greater accuracy
** at current dates; however, to realize this improved accuracy,
** corrections for the essentially unpredictable free-core-nutation
** (FCN) must also be included.
**
** 5) The present function provides classical nutation. The
** MHB_2000_SHORT algorithm, from which it is adapted, deals also
** with (i) the offsets between the GCRS and mean poles and (ii) the
** adjustments in longitude and obliquity due to the changed
** precession rates. These additional functions, namely frame bias
** and precession adjustments, are supported by the SOFA functions
** iauBi00 and iauPr00.
**
** 6) The MHB_2000_SHORT algorithm also provides "total" nutations,
** comprising the arithmetic sum of the frame bias, precession
** adjustments, and nutation (luni-solar + planetary). These total
** nutations can be used in combination with an existing IAU 1976
** precession implementation, such as iauPmat76, to deliver GCRS-
** to-true predictions of mas accuracy at current epochs. However,
** for symmetry with the iauNut00a function (q.v. for the reasons),
** the SOFA functions do not generate the "total nutations"
** directly. Should they be required, they could of course easily
** be generated by calling iauBi00, iauPr00 and the present function
** and adding the results.
**
** 7) The IAU 2000B model includes "planetary bias" terms that are
** fixed in size but compensate for long-period nutations. The
** amplitudes quoted in McCarthy & Luzum (2003), namely
** Dpsi = -1.5835 mas and Depsilon = +1.6339 mas, are optimized for
** the "total nutations" method described in Note 6. The Luzum
** (2001) values used in this SOFA implementation, namely -0.135 mas
** and +0.388 mas, are optimized for the "rigorous" method, where
** frame bias, precession and nutation are applied separately and in
** that order. During the interval 1995-2050, the SOFA
** implementation delivers a maximum error of 1.001 mas (not
** including FCN).
**
** References:
**
** Lieske, J.H., Lederle, T., Fricke, W., Morando, B., "Expressions
** for the precession quantities based upon the IAU /1976/ system of
** astronomical constants", Astron.Astrophys. 58, 1-2, 1-16. (1977)
**
** Luzum, B., private communication, 2001 (Fortran code
** MHB_2000_SHORT)
**
** McCarthy, D.D. & Luzum, B.J., "An abridged model of the
** precession-nutation of the celestial pole", Cel.Mech.Dyn.Astron.
** 85, 37-49 (2003)
**
** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
** Francou, G., Laskar, J., Astron.Astrophys. 282, 663-683 (1994)
**
*/
void iauNut06a(double date1, double date2, double *dpsi, double *deps)
/*
** - - - - - - - - - -
** i a u N u t 0 6 a
** - - - - - - - - - -
**
** IAU 2000A nutation with adjustments to match the IAU 2006
** precession.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** dpsi,deps double nutation, luni-solar + planetary (Note 2)
**
** Status: canonical model.
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The nutation components in longitude and obliquity are in radians
** and with respect to the mean equinox and ecliptic of date,
** IAU 2006 precession model (Hilton et al. 2006, Capitaine et al.
** 2005).
**
** 3) The function first computes the IAU 2000A nutation, then applies
** adjustments for (i) the consequences of the change in obliquity
** from the IAU 1980 ecliptic to the IAU 2006 ecliptic and (ii) the
** secular variation in the Earth's dynamical flattening.
**
** 4) The present function provides classical nutation, complementing
** the IAU 2000 frame bias and IAU 2006 precession. It delivers a
** pole which is at current epochs accurate to a few tens of
** microarcseconds, apart from the free core nutation.
**
** Called:
** iauNut00a nutation, IAU 2000A
**
** References:
**
** Chapront, J., Chapront-Touze, M. & Francou, G. 2002,
** Astron.Astrophys. 387, 700
**
** Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977,
** Astron.Astrophys. 58, 1-16
**
** Mathews, P.M., Herring, T.A., Buffet, B.A. 2002, J.Geophys.Res.
** 107, B4. The MHB_2000 code itself was obtained on 9th September
** 2002 from ftp//maia.usno.navy.mil/conv2000/chapter5/IAU2000A.
**
** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
**
** Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
** Astron.Astrophys.Supp.Ser. 135, 111
**
** Wallace, P.T., "Software for Implementing the IAU 2000
** Resolutions", in IERS Workshop 5.1 (2002)
**
*/
void iauNut80(double date1, double date2, double *dpsi, double *deps)
/*
** - - - - - - - - -
** i a u N u t 8 0
** - - - - - - - - -
**
** Nutation, IAU 1980 model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** dpsi double nutation in longitude (radians)
** deps double nutation in obliquity (radians)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The nutation components are with respect to the ecliptic of
** date.
**
** Called:
** iauAnpm normalize angle into range +/- pi
**
** Reference:
**
** Explanatory Supplement to the Astronomical Almanac,
** P. Kenneth Seidelmann (ed), University Science Books (1992),
** Section 3.222 (p111).
**
*/
void iauNutm80(double date1, double date2, double rmatn[3][3])
/*
** - - - - - - - - - -
** i a u N u t m 8 0
** - - - - - - - - - -
**
** Form the matrix of nutation for a given date, IAU 1980 model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TDB date (Note 1)
**
** Returned:
** rmatn double[3][3] nutation matrix
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The matrix operates in the sense V(true) = rmatn * V(mean),
** where the p-vector V(true) is with respect to the true
** equatorial triad of date and the p-vector V(mean) is with
** respect to the mean equatorial triad of date.
**
** Called:
** iauNut80 nutation, IAU 1980
** iauObl80 mean obliquity, IAU 1980
** iauNumat form nutation matrix
**
*/
double iauObl06(double date1, double date2)
/*
** - - - - - - - - -
** i a u O b l 0 6
** - - - - - - - - -
**
** Mean obliquity of the ecliptic, IAU 2006 precession model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned (function value):
** double obliquity of the ecliptic (radians, Note 2)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The result is the angle between the ecliptic and mean equator of
** date date1+date2.
**
** Reference:
**
** Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351
**
*/
double iauObl80(double date1, double date2)
/*
** - - - - - - - - -
** i a u O b l 8 0
** - - - - - - - - -
**
** Mean obliquity of the ecliptic, IAU 1980 model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned (function value):
** double obliquity of the ecliptic (radians, Note 2)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The result is the angle between the ecliptic and mean equator of
** date date1+date2.
**
** Reference:
**
** Explanatory Supplement to the Astronomical Almanac,
** P. Kenneth Seidelmann (ed), University Science Books (1992),
** Expression 3.222-1 (p114).
**
*/
void iauP06e(double date1, double date2,
double *eps0, double *psia, double *oma, double *bpa,
double *bqa, double *pia, double *bpia,
double *epsa, double *chia, double *za, double *zetaa,
double *thetaa, double *pa,
double *gam, double *phi, double *psi)
/*
** - - - - - - - -
** i a u P 0 6 e
** - - - - - - - -
**
** Precession angles, IAU 2006, equinox based.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical models.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned (see Note 2):
** eps0 double epsilon_0
** psia double psi_A
** oma double omega_A
** bpa double P_A
** bqa double Q_A
** pia double pi_A
** bpia double Pi_A
** epsa double obliquity epsilon_A
** chia double chi_A
** za double z_A
** zetaa double zeta_A
** thetaa double theta_A
** pa double p_A
** gam double F-W angle gamma_J2000
** phi double F-W angle phi_J2000
** psi double F-W angle psi_J2000
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) This function returns the set of equinox based angles for the
** Capitaine et al. "P03" precession theory, adopted by the IAU in
** 2006. The angles are set out in Table 1 of Hilton et al. (2006):
**
** eps0 epsilon_0 obliquity at J2000.0
** psia psi_A luni-solar precession
** oma omega_A inclination of equator wrt J2000.0 ecliptic
** bpa P_A ecliptic pole x, J2000.0 ecliptic triad
** bqa Q_A ecliptic pole -y, J2000.0 ecliptic triad
** pia pi_A angle between moving and J2000.0 ecliptics
** bpia Pi_A longitude of ascending node of the ecliptic
** epsa epsilon_A obliquity of the ecliptic
** chia chi_A planetary precession
** za z_A equatorial precession: -3rd 323 Euler angle
** zetaa zeta_A equatorial precession: -1st 323 Euler angle
** thetaa theta_A equatorial precession: 2nd 323 Euler angle
** pa p_A general precession
** gam gamma_J2000 J2000.0 RA difference of ecliptic poles
** phi phi_J2000 J2000.0 codeclination of ecliptic pole
** psi psi_J2000 longitude difference of equator poles, J2000.0
**
** The returned values are all radians.
**
** 3) Hilton et al. (2006) Table 1 also contains angles that depend on
** models distinct from the P03 precession theory itself, namely the
** IAU 2000A frame bias and nutation. The quoted polynomials are
** used in other SOFA functions:
**
** . iauXy06 contains the polynomial parts of the X and Y series.
**
** . iauS06 contains the polynomial part of the s+XY/2 series.
**
** . iauPfw06 implements the series for the Fukushima-Williams
** angles that are with respect to the GCRS pole (i.e. the variants
** that include frame bias).
**
** 4) The IAU resolution stipulated that the choice of parameterization
** was left to the user, and so an IAU compliant precession
** implementation can be constructed using various combinations of
** the angles returned by the present function.
**
** 5) The parameterization used by SOFA is the Fukushima-Williams angles
** referred directly to the GCRS pole. These are the final four
** arguments returned by the present function, but are more
** efficiently calculated by calling the function iauPfw06. SOFA
** also supports the direct computation of the CIP GCRS X,Y by
** series, available by calling iauXy06.
**
** 6) The agreement between the different parameterizations is at the
** 1 microarcsecond level in the present era.
**
** 7) When constructing a precession formulation that refers to the GCRS
** pole rather than the dynamical pole, it may (depending on the
** choice of angles) be necessary to introduce the frame bias
** explicitly.
**
** 8) It is permissible to re-use the same variable in the returned
** arguments. The quantities are stored in the stated order.
**
** Reference:
**
** Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351
**
** Called:
** iauObl06 mean obliquity, IAU 2006
**
*/
void iauP2pv(double p[3], double pv[2][3])
/*
** - - - - - - - -
** i a u P 2 p v
** - - - - - - - -
**
** Extend a p-vector to a pv-vector by appending a zero velocity.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** p double[3] p-vector
**
** Returned:
** pv double[2][3] pv-vector
**
** Called:
** iauCp copy p-vector
** iauZp zero p-vector
**
*/
void iauP2s(double p[3], double *theta, double *phi, double *r)
/*
** - - - - - - -
** i a u P 2 s
** - - - - - - -
**
** P-vector to spherical polar coordinates.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** p double[3] p-vector
**
** Returned:
** theta double longitude angle (radians)
** phi double latitude angle (radians)
** r double radial distance
**
** Notes:
**
** 1) If P is null, zero theta, phi and r are returned.
**
** 2) At either pole, zero theta is returned.
**
** Called:
** iauC2s p-vector to spherical
** iauPm modulus of p-vector
**
*/
double iauPap(double a[3], double b[3])
/*
** - - - - - - -
** i a u P a p
** - - - - - - -
**
** Position-angle from two p-vectors.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** a double[3] direction of reference point
** b double[3] direction of point whose PA is required
**
** Returned (function value):
** double position angle of b with respect to a (radians)
**
** Notes:
**
** 1) The result is the position angle, in radians, of direction b with
** respect to direction a. It is in the range -pi to +pi. The
** sense is such that if b is a small distance "north" of a the
** position angle is approximately zero, and if b is a small
** distance "east" of a the position angle is approximately +pi/2.
**
** 2) The vectors a and b need not be of unit length.
**
** 3) Zero is returned if the two directions are the same or if either
** vector is null.
**
** 4) If vector a is at a pole, the result is ill-defined.
**
** Called:
** iauPn decompose p-vector into modulus and direction
** iauPm modulus of p-vector
** iauPxp vector product of two p-vectors
** iauPmp p-vector minus p-vector
** iauPdp scalar product of two p-vectors
**
*/
double iauPas(double al, double ap, double bl, double bp)
/*
** - - - - - - -
** i a u P a s
** - - - - - - -
**
** Position-angle from spherical coordinates.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** al double longitude of point A (e.g. RA) in radians
** ap double latitude of point A (e.g. Dec) in radians
** bl double longitude of point B
** bp double latitude of point B
**
** Returned (function value):
** double position angle of B with respect to A
**
** Notes:
**
** 1) The result is the bearing (position angle), in radians, of point
** B with respect to point A. It is in the range -pi to +pi. The
** sense is such that if B is a small distance "east" of point A,
** the bearing is approximately +pi/2.
**
** 2) Zero is returned if the two points are coincident.
**
*/
void iauPb06(double date1, double date2,
double *bzeta, double *bz, double *btheta)
/*
** - - - - - - - -
** i a u P b 0 6
** - - - - - - - -
**
** This function forms three Euler angles which implement general
** precession from epoch J2000.0, using the IAU 2006 model. Frame
** bias (the offset between ICRS and mean J2000.0) is included.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** bzeta double 1st rotation: radians cw around z
** bz double 3rd rotation: radians cw around z
** btheta double 2nd rotation: radians ccw around y
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The traditional accumulated precession angles zeta_A, z_A,
** theta_A cannot be obtained in the usual way, namely through
** polynomial expressions, because of the frame bias. The latter
** means that two of the angles undergo rapid changes near this
** date. They are instead the results of decomposing the
** precession-bias matrix obtained by using the Fukushima-Williams
** method, which does not suffer from the problem. The
** decomposition returns values which can be used in the
** conventional formulation and which include frame bias.
**
** 3) The three angles are returned in the conventional order, which
** is not the same as the order of the corresponding Euler
** rotations. The precession-bias matrix is
** R_3(-z) x R_2(+theta) x R_3(-zeta).
**
** 4) Should zeta_A, z_A, theta_A angles be required that do not
** contain frame bias, they are available by calling the SOFA
** function iauP06e.
**
** Called:
** iauPmat06 PB matrix, IAU 2006
** iauRz rotate around Z-axis
**
*/
double iauPdp(double a[3], double b[3])
/*
** - - - - - - -
** i a u P d p
** - - - - - - -
**
** p-vector inner (=scalar=dot) product.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** a double[3] first p-vector
** b double[3] second p-vector
**
** Returned (function value):
** double a . b
**
*/
void iauPfw06(double date1, double date2,
double *gamb, double *phib, double *psib, double *epsa)
/*
** - - - - - - - - -
** i a u P f w 0 6
** - - - - - - - - -
**
** Precession angles, IAU 2006 (Fukushima-Williams 4-angle formulation).
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** gamb double F-W angle gamma_bar (radians)
** phib double F-W angle phi_bar (radians)
** psib double F-W angle psi_bar (radians)
** epsa double F-W angle epsilon_A (radians)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) Naming the following points:
**
** e = J2000.0 ecliptic pole,
** p = GCRS pole,
** E = mean ecliptic pole of date,
** and P = mean pole of date,
**
** the four Fukushima-Williams angles are as follows:
**
** gamb = gamma_bar = epE
** phib = phi_bar = pE
** psib = psi_bar = pEP
** epsa = epsilon_A = EP
**
** 3) The matrix representing the combined effects of frame bias and
** precession is:
**
** PxB = R_1(-epsa).R_3(-psib).R_1(phib).R_3(gamb)
**
** 4) The matrix representing the combined effects of frame bias,
** precession and nutation is simply:
**
** NxPxB = R_1(-epsa-dE).R_3(-psib-dP).R_1(phib).R_3(gamb)
**
** where dP and dE are the nutation components with respect to the
** ecliptic of date.
**
** Reference:
**
** Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351
**
** Called:
** iauObl06 mean obliquity, IAU 2006
**
*/
int iauPlan94(double date1, double date2, int np, double pv[2][3])
/*
** - - - - - - - - - -
** i a u P l a n 9 4
** - - - - - - - - - -
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Approximate heliocentric position and velocity of a nominated major
** planet: Mercury, Venus, EMB, Mars, Jupiter, Saturn, Uranus or
** Neptune (but not the Earth itself).
**
** Given:
** date1 double TDB date part A (Note 1)
** date2 double TDB date part B (Note 1)
** np int planet (1=Mercury, 2=Venus, 3=EMB, 4=Mars,
** 5=Jupiter, 6=Saturn, 7=Uranus, 8=Neptune)
**
** Returned (argument):
** pv double[3][2] planet p,v (heliocentric, J2000.0, AU,AU/d)
**
** Returned (function value):
** int status: -1 = illegal NP (outside 1-8)
** 0 = OK
** +1 = warning: year outside 1000-3000
** +2 = warning: failed to converge
**
** Notes:
**
** 1) The date date1+date2 is in the TDB time scale (in practice TT can
** be used) and is a Julian Date, apportioned in any convenient way
** between the two arguments. For example, JD(TDB)=2450123.7 could
** be expressed in any of these ways, among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in cases
** where the loss of several decimal digits of resolution is
** acceptable. The J2000 method is best matched to the way the
** argument is handled internally and will deliver the optimum
** resolution. The MJD method and the date & time methods are both
** good compromises between resolution and convenience. The limited
** accuracy of the present algorithm is such that any of the methods
** is satisfactory.
**
** 2) If an np value outside the range 1-8 is supplied, an error status
** (function value -1) is returned and the pv vector set to zeroes.
**
** 3) For np=3 the result is for the Earth-Moon Barycenter. To obtain
** the heliocentric position and velocity of the Earth, use instead
** the SOFA function iauEpv00.
**
** 4) On successful return, the array pv contains the following:
**
** pv[0][0] x }
** pv[1][0] y } heliocentric position, AU
** pv[2][0] z }
**
** pv[0][1] xdot }
** pv[1][1] ydot } heliocentric velocity, AU/d
** pv[2][1] zdot }
**
** The reference frame is equatorial and is with respect to the
** mean equator and equinox of epoch J2000.0.
**
** 5) The algorithm is due to J.L. Simon, P. Bretagnon, J. Chapront,
** M. Chapront-Touze, G. Francou and J. Laskar (Bureau des
** Longitudes, Paris, France). From comparisons with JPL
** ephemeris DE102, they quote the following maximum errors
** over the interval 1800-2050:
**
** L (arcsec) B (arcsec) R (km)
**
** Mercury 4 1 300
** Venus 5 1 800
** EMB 6 1 1000
** Mars 17 1 7700
** Jupiter 71 5 76000
** Saturn 81 13 267000
** Uranus 86 7 712000
** Neptune 11 1 253000
**
** Over the interval 1000-3000, they report that the accuracy is no
** worse than 1.5 times that over 1800-2050. Outside 1000-3000 the
** accuracy declines.
**
** Comparisons of the present function with the JPL DE200 ephemeris
** give the following RMS errors over the interval 1960-2025:
**
** position (km) velocity (m/s)
**
** Mercury 334 0.437
** Venus 1060 0.855
** EMB 2010 0.815
** Mars 7690 1.98
** Jupiter 71700 7.70
** Saturn 199000 19.4
** Uranus 564000 16.4
** Neptune 158000 14.4
**
** Comparisons against DE200 over the interval 1800-2100 gave the
** following maximum absolute differences. (The results using
** DE406 were essentially the same.)
**
** L (arcsec) B (arcsec) R (km) Rdot (m/s)
**
** Mercury 7 1 500 0.7
** Venus 7 1 1100 0.9
** EMB 9 1 1300 1.0
** Mars 26 1 9000 2.5
** Jupiter 78 6 82000 8.2
** Saturn 87 14 263000 24.6
** Uranus 86 7 661000 27.4
** Neptune 11 2 248000 21.4
**
** 6) The present SOFA re-implementation of the original Simon et al.
** Fortran code differs from the original in the following respects:
**
** * C instead of Fortran.
**
** * The date is supplied in two parts.
**
** * The result is returned only in equatorial Cartesian form;
** the ecliptic longitude, latitude and radius vector are not
** returned.
**
** * The result is in the J2000.0 equatorial frame, not ecliptic.
**
** * More is done in-line: there are fewer calls to subroutines.
**
** * Different error/warning status values are used.
**
** * A different Kepler's-equation-solver is used (avoiding
** use of double precision complex).
**
** * Polynomials in t are nested to minimize rounding errors.
**
** * Explicit double constants are used to avoid mixed-mode
** expressions.
**
** None of the above changes affects the result significantly.
**
** 7) The returned status indicates the most serious condition
** encountered during execution of the function. Illegal np is
** considered the most serious, overriding failure to converge,
** which in turn takes precedence over the remote date warning.
**
** Called:
** iauAnp normalize angle into range 0 to 2pi
**
** Reference: Simon, J.L, Bretagnon, P., Chapront, J.,
** Chapront-Touze, M., Francou, G., and Laskar, J.,
** Astron. Astrophys. 282, 663 (1994).
**
*/
double iauPm(double p[3])
/*
** - - - - - -
** i a u P m
** - - - - - -
**
** Modulus of p-vector.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** p double[3] p-vector
**
** Returned (function value):
** double modulus
**
*/
void iauPmat00(double date1, double date2, double rbp[3][3])
/*
** - - - - - - - - - -
** i a u P m a t 0 0
** - - - - - - - - - -
**
** Precession matrix (including frame bias) from GCRS to a specified
** date, IAU 2000 model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** rbp double[3][3] bias-precession matrix (Note 2)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The matrix operates in the sense V(date) = rbp * V(GCRS), where
** the p-vector V(GCRS) is with respect to the Geocentric Celestial
** Reference System (IAU, 2000) and the p-vector V(date) is with
** respect to the mean equatorial triad of the given date.
**
** Called:
** iauBp00 frame bias and precession matrices, IAU 2000
**
** Reference:
**
** IAU: Trans. International Astronomical Union, Vol. XXIVB; Proc.
** 24th General Assembly, Manchester, UK. Resolutions B1.3, B1.6.
** (2000)
**
*/
void iauPmat06(double date1, double date2, double rbp[3][3])
/*
** - - - - - - - - - -
** i a u P m a t 0 6
** - - - - - - - - - -
**
** Precession matrix (including frame bias) from GCRS to a specified
** date, IAU 2006 model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** rbp double[3][3] bias-precession matrix (Note 2)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The matrix operates in the sense V(date) = rbp * V(GCRS), where
** the p-vector V(GCRS) is with respect to the Geocentric Celestial
** Reference System (IAU, 2000) and the p-vector V(date) is with
** respect to the mean equatorial triad of the given date.
**
** Called:
** iauPfw06 bias-precession F-W angles, IAU 2006
** iauFw2m F-W angles to r-matrix
**
** References:
**
** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
**
** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
**
*/
void iauPmat76(double date1, double date2, double rmatp[3][3])
/*
** - - - - - - - - - -
** i a u P m a t 7 6
** - - - - - - - - - -
**
** Precession matrix from J2000.0 to a specified date, IAU 1976 model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double ending date, TT (Note 1)
**
** Returned:
** rmatp double[3][3] precession matrix, J2000.0 -> date1+date2
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The matrix operates in the sense V(date) = RMATP * V(J2000),
** where the p-vector V(J2000) is with respect to the mean
** equatorial triad of epoch J2000.0 and the p-vector V(date)
** is with respect to the mean equatorial triad of the given
** date.
**
** 3) Though the matrix method itself is rigorous, the precession
** angles are expressed through canonical polynomials which are
** valid only for a limited time span. In addition, the IAU 1976
** precession rate is known to be imperfect. The absolute accuracy
** of the present formulation is better than 0.1 arcsec from
** 1960AD to 2040AD, better than 1 arcsec from 1640AD to 2360AD,
** and remains below 3 arcsec for the whole of the period
** 500BC to 3000AD. The errors exceed 10 arcsec outside the
** range 1200BC to 3900AD, exceed 100 arcsec outside 4200BC to
** 5600AD and exceed 1000 arcsec outside 6800BC to 8200AD.
**
** Called:
** iauPrec76 accumulated precession angles, IAU 1976
** iauIr initialize r-matrix to identity
** iauRz rotate around Z-axis
** iauRy rotate around Y-axis
** iauCr copy r-matrix
**
** References:
**
** Lieske, J.H., 1979, Astron.Astrophys. 73, 282.
** equations (6) & (7), p283.
**
** Kaplan,G.H., 1981. USNO circular no. 163, pA2.
**
*/
void iauPmp(double a[3], double b[3], double amb[3])
/*
** - - - - - - -
** i a u P m p
** - - - - - - -
**
** P-vector subtraction.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** a double[3] first p-vector
** b double[3] second p-vector
**
** Returned:
** amb double[3] a - b
**
** Note:
** It is permissible to re-use the same array for any of the
** arguments.
**
*/
void iauPn(double p[3], double *r, double u[3])
/*
** - - - - - -
** i a u P n
** - - - - - -
**
** Convert a p-vector into modulus and unit vector.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** p double[3] p-vector
**
** Returned:
** r double modulus
** u double[3] unit vector
**
** Notes:
**
** 1) If p is null, the result is null. Otherwise the result is a unit
** vector.
**
** 2) It is permissible to re-use the same array for any of the
** arguments.
**
** Called:
** iauPm modulus of p-vector
** iauZp zero p-vector
** iauSxp multiply p-vector by scalar
**
*/
void iauPn00(double date1, double date2, double dpsi, double deps,
double *epsa,
double rb[3][3], double rp[3][3], double rbp[3][3],
double rn[3][3], double rbpn[3][3])
/*
** - - - - - - - -
** i a u P n 0 0
** - - - - - - - -
**
** Precession-nutation, IAU 2000 model: a multi-purpose function,
** supporting classical (equinox-based) use directly and CIO-based
** use indirectly.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
** dpsi,deps double nutation (Note 2)
**
** Returned:
** epsa double mean obliquity (Note 3)
** rb double[3][3] frame bias matrix (Note 4)
** rp double[3][3] precession matrix (Note 5)
** rbp double[3][3] bias-precession matrix (Note 6)
** rn double[3][3] nutation matrix (Note 7)
** rbpn double[3][3] GCRS-to-true matrix (Note 8)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The caller is responsible for providing the nutation components;
** they are in longitude and obliquity, in radians and are with
** respect to the equinox and ecliptic of date. For high-accuracy
** applications, free core nutation should be included as well as
** any other relevant corrections to the position of the CIP.
**
** 3) The returned mean obliquity is consistent with the IAU 2000
** precession-nutation models.
**
** 4) The matrix rb transforms vectors from GCRS to J2000.0 mean
** equator and equinox by applying frame bias.
**
** 5) The matrix rp transforms vectors from J2000.0 mean equator and
** equinox to mean equator and equinox of date by applying
** precession.
**
** 6) The matrix rbp transforms vectors from GCRS to mean equator and
** equinox of date by applying frame bias then precession. It is
** the product rp x rb.
**
** 7) The matrix rn transforms vectors from mean equator and equinox of
** date to true equator and equinox of date by applying the nutation
** (luni-solar + planetary).
**
** 8) The matrix rbpn transforms vectors from GCRS to true equator and
** equinox of date. It is the product rn x rbp, applying frame
** bias, precession and nutation in that order.
**
** 9) It is permissible to re-use the same array in the returned
** arguments. The arrays are filled in the order given.
**
** Called:
** iauPr00 IAU 2000 precession adjustments
** iauObl80 mean obliquity, IAU 1980
** iauBp00 frame bias and precession matrices, IAU 2000
** iauCr copy r-matrix
** iauNumat form nutation matrix
** iauRxr product of two r-matrices
**
** Reference:
**
** Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
** "Expressions for the Celestial Intermediate Pole and Celestial
** Ephemeris Origin consistent with the IAU 2000A precession-
** nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
**
** n.b. The celestial ephemeris origin (CEO) was renamed "celestial
** intermediate origin" (CIO) by IAU 2006 Resolution 2.
**
*/
void iauPn00a(double date1, double date2,
double *dpsi, double *deps, double *epsa,
double rb[3][3], double rp[3][3], double rbp[3][3],
double rn[3][3], double rbpn[3][3])
/*
** - - - - - - - - -
** i a u P n 0 0 a
** - - - - - - - - -
**
** Precession-nutation, IAU 2000A model: a multi-purpose function,
** supporting classical (equinox-based) use directly and CIO-based
** use indirectly.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** dpsi,deps double nutation (Note 2)
** epsa double mean obliquity (Note 3)
** rb double[3][3] frame bias matrix (Note 4)
** rp double[3][3] precession matrix (Note 5)
** rbp double[3][3] bias-precession matrix (Note 6)
** rn double[3][3] nutation matrix (Note 7)
** rbpn double[3][3] GCRS-to-true matrix (Notes 8,9)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The nutation components (luni-solar + planetary, IAU 2000A) in
** longitude and obliquity are in radians and with respect to the
** equinox and ecliptic of date. Free core nutation is omitted;
** for the utmost accuracy, use the iauPn00 function, where the
** nutation components are caller-specified. For faster but
** slightly less accurate results, use the iauPn00b function.
**
** 3) The mean obliquity is consistent with the IAU 2000 precession.
**
** 4) The matrix rb transforms vectors from GCRS to J2000.0 mean
** equator and equinox by applying frame bias.
**
** 5) The matrix rp transforms vectors from J2000.0 mean equator and
** equinox to mean equator and equinox of date by applying
** precession.
**
** 6) The matrix rbp transforms vectors from GCRS to mean equator and
** equinox of date by applying frame bias then precession. It is
** the product rp x rb.
**
** 7) The matrix rn transforms vectors from mean equator and equinox
** of date to true equator and equinox of date by applying the
** nutation (luni-solar + planetary).
**
** 8) The matrix rbpn transforms vectors from GCRS to true equator and
** equinox of date. It is the product rn x rbp, applying frame
** bias, precession and nutation in that order.
**
** 9) The X,Y,Z coordinates of the IAU 2000B Celestial Intermediate
** Pole are elements (3,1-3) of the matrix rbpn.
**
** 10) It is permissible to re-use the same array in the returned
** arguments. The arrays are filled in the order given.
**
** Called:
** iauNut00a nutation, IAU 2000A
** iauPn00 bias/precession/nutation results, IAU 2000
**
** Reference:
**
** Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
** "Expressions for the Celestial Intermediate Pole and Celestial
** Ephemeris Origin consistent with the IAU 2000A precession-
** nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
**
** n.b. The celestial ephemeris origin (CEO) was renamed "celestial
** intermediate origin" (CIO) by IAU 2006 Resolution 2.
**
*/
void iauPn00b(double date1, double date2,
double *dpsi, double *deps, double *epsa,
double rb[3][3], double rp[3][3], double rbp[3][3],
double rn[3][3], double rbpn[3][3])
/*
** - - - - - - - - -
** i a u P n 0 0 b
** - - - - - - - - -
**
** Precession-nutation, IAU 2000B model: a multi-purpose function,
** supporting classical (equinox-based) use directly and CIO-based
** use indirectly.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** dpsi,deps double nutation (Note 2)
** epsa double mean obliquity (Note 3)
** rb double[3][3] frame bias matrix (Note 4)
** rp double[3][3] precession matrix (Note 5)
** rbp double[3][3] bias-precession matrix (Note 6)
** rn double[3][3] nutation matrix (Note 7)
** rbpn double[3][3] GCRS-to-true matrix (Notes 8,9)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The nutation components (luni-solar + planetary, IAU 2000B) in
** longitude and obliquity are in radians and with respect to the
** equinox and ecliptic of date. For more accurate results, but
** at the cost of increased computation, use the iauPn00a function.
** For the utmost accuracy, use the iauPn00 function, where the
** nutation components are caller-specified.
**
** 3) The mean obliquity is consistent with the IAU 2000 precession.
**
** 4) The matrix rb transforms vectors from GCRS to J2000.0 mean
** equator and equinox by applying frame bias.
**
** 5) The matrix rp transforms vectors from J2000.0 mean equator and
** equinox to mean equator and equinox of date by applying
** precession.
**
** 6) The matrix rbp transforms vectors from GCRS to mean equator and
** equinox of date by applying frame bias then precession. It is
** the product rp x rb.
**
** 7) The matrix rn transforms vectors from mean equator and equinox
** of date to true equator and equinox of date by applying the
** nutation (luni-solar + planetary).
**
** 8) The matrix rbpn transforms vectors from GCRS to true equator and
** equinox of date. It is the product rn x rbp, applying frame
** bias, precession and nutation in that order.
**
** 9) The X,Y,Z coordinates of the IAU 2000B Celestial Intermediate
** Pole are elements (3,1-3) of the matrix rbpn.
**
** 10) It is permissible to re-use the same array in the returned
** arguments. The arrays are filled in the stated order.
**
** Called:
** iauNut00b nutation, IAU 2000B
** iauPn00 bias/precession/nutation results, IAU 2000
**
** Reference:
**
** Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
** "Expressions for the Celestial Intermediate Pole and Celestial
** Ephemeris Origin consistent with the IAU 2000A precession-
** nutation model", Astron.Astrophys. 400, 1145-1154 (2003).
**
** n.b. The celestial ephemeris origin (CEO) was renamed "celestial
** intermediate origin" (CIO) by IAU 2006 Resolution 2.
**
*/
void iauPn06(double date1, double date2, double dpsi, double deps,
double *epsa,
double rb[3][3], double rp[3][3], double rbp[3][3],
double rn[3][3], double rbpn[3][3])
/*
** - - - - - - - -
** i a u P n 0 6
** - - - - - - - -
**
** Precession-nutation, IAU 2006 model: a multi-purpose function,
** supporting classical (equinox-based) use directly and CIO-based use
** indirectly.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
** dpsi,deps double nutation (Note 2)
**
** Returned:
** epsa double mean obliquity (Note 3)
** rb double[3][3] frame bias matrix (Note 4)
** rp double[3][3] precession matrix (Note 5)
** rbp double[3][3] bias-precession matrix (Note 6)
** rn double[3][3] nutation matrix (Note 7)
** rbpn double[3][3] GCRS-to-true matrix (Note 8)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The caller is responsible for providing the nutation components;
** they are in longitude and obliquity, in radians and are with
** respect to the equinox and ecliptic of date. For high-accuracy
** applications, free core nutation should be included as well as
** any other relevant corrections to the position of the CIP.
**
** 3) The returned mean obliquity is consistent with the IAU 2006
** precession.
**
** 4) The matrix rb transforms vectors from GCRS to J2000.0 mean
** equator and equinox by applying frame bias.
**
** 5) The matrix rp transforms vectors from J2000.0 mean equator and
** equinox to mean equator and equinox of date by applying
** precession.
**
** 6) The matrix rbp transforms vectors from GCRS to mean equator and
** equinox of date by applying frame bias then precession. It is
** the product rp x rb.
**
** 7) The matrix rn transforms vectors from mean equator and equinox
** of date to true equator and equinox of date by applying the
** nutation (luni-solar + planetary).
**
** 8) The matrix rbpn transforms vectors from GCRS to true equator and
** equinox of date. It is the product rn x rbp, applying frame
** bias, precession and nutation in that order.
**
** 9) The X,Y,Z coordinates of the IAU 2000B Celestial Intermediate
** Pole are elements (3,1-3) of the matrix rbpn.
**
** 10) It is permissible to re-use the same array in the returned
** arguments. The arrays are filled in the stated order.
**
** Called:
** iauPfw06 bias-precession F-W angles, IAU 2006
** iauFw2m F-W angles to r-matrix
** iauCr copy r-matrix
** iauTr transpose r-matrix
** iauRxr product of two r-matrices
**
** References:
**
** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
**
** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
**
*/
void iauPn06a(double date1, double date2,
double *dpsi, double *deps, double *epsa,
double rb[3][3], double rp[3][3], double rbp[3][3],
double rn[3][3], double rbpn[3][3])
/*
** - - - - - - - - -
** i a u P n 0 6 a
** - - - - - - - - -
**
** Precession-nutation, IAU 2006/2000A models: a multi-purpose function,
** supporting classical (equinox-based) use directly and CIO-based use
** indirectly.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** dpsi,deps double nutation (Note 2)
** epsa double mean obliquity (Note 3)
** rb double[3][3] frame bias matrix (Note 4)
** rp double[3][3] precession matrix (Note 5)
** rbp double[3][3] bias-precession matrix (Note 6)
** rn double[3][3] nutation matrix (Note 7)
** rbpn double[3][3] GCRS-to-true matrix (Notes 8,9)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The nutation components (luni-solar + planetary, IAU 2000A) in
** longitude and obliquity are in radians and with respect to the
** equinox and ecliptic of date. Free core nutation is omitted;
** for the utmost accuracy, use the iauPn06 function, where the
** nutation components are caller-specified.
**
** 3) The mean obliquity is consistent with the IAU 2006 precession.
**
** 4) The matrix rb transforms vectors from GCRS to mean J2000.0 by
** applying frame bias.
**
** 5) The matrix rp transforms vectors from mean J2000.0 to mean of
** date by applying precession.
**
** 6) The matrix rbp transforms vectors from GCRS to mean of date by
** applying frame bias then precession. It is the product rp x rb.
**
** 7) The matrix rn transforms vectors from mean of date to true of
** date by applying the nutation (luni-solar + planetary).
**
** 8) The matrix rbpn transforms vectors from GCRS to true of date
** (CIP/equinox). It is the product rn x rbp, applying frame bias,
** precession and nutation in that order.
**
** 9) The X,Y,Z coordinates of the IAU 2006/2000A Celestial
** Intermediate Pole are elements (1,1-3) of the matrix rbpn.
**
** 10) It is permissible to re-use the same array in the returned
** arguments. The arrays are filled in the stated order.
**
** Called:
** iauNut06a nutation, IAU 2006/2000A
** iauPn06 bias/precession/nutation results, IAU 2006
**
** Reference:
**
** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
**
*/
void iauPnm00a(double date1, double date2, double rbpn[3][3])
/*
** - - - - - - - - - -
** i a u P n m 0 0 a
** - - - - - - - - - -
**
** Form the matrix of precession-nutation for a given date (including
** frame bias), equinox-based, IAU 2000A model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** rbpn double[3][3] classical NPB matrix (Note 2)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The matrix operates in the sense V(date) = rbpn * V(GCRS), where
** the p-vector V(date) is with respect to the true equatorial triad
** of date date1+date2 and the p-vector V(GCRS) is with respect to
** the Geocentric Celestial Reference System (IAU, 2000).
**
** 3) A faster, but slightly less accurate result (about 1 mas), can be
** obtained by using instead the iauPnm00b function.
**
** Called:
** iauPn00a bias/precession/nutation, IAU 2000A
**
** Reference:
**
** IAU: Trans. International Astronomical Union, Vol. XXIVB; Proc.
** 24th General Assembly, Manchester, UK. Resolutions B1.3, B1.6.
** (2000)
**
*/
void iauPnm00b(double date1, double date2, double rbpn[3][3])
/*
** - - - - - - - - - -
** i a u P n m 0 0 b
** - - - - - - - - - -
**
** Form the matrix of precession-nutation for a given date (including
** frame bias), equinox-based, IAU 2000B model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** rbpn double[3][3] bias-precession-nutation matrix (Note 2)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The matrix operates in the sense V(date) = rbpn * V(GCRS), where
** the p-vector V(date) is with respect to the true equatorial triad
** of date date1+date2 and the p-vector V(GCRS) is with respect to
** the Geocentric Celestial Reference System (IAU, 2000).
**
** 3) The present function is faster, but slightly less accurate (about
** 1 mas), than the iauPnm00a function.
**
** Called:
** iauPn00b bias/precession/nutation, IAU 2000B
**
** Reference:
**
** IAU: Trans. International Astronomical Union, Vol. XXIVB; Proc.
** 24th General Assembly, Manchester, UK. Resolutions B1.3, B1.6.
** (2000)
**
*/
void iauPnm06a(double date1, double date2, double rnpb[3][3])
/*
** - - - - - - - - - -
** i a u P n m 0 6 a
** - - - - - - - - - -
**
** Form the matrix of precession-nutation for a given date (including
** frame bias), IAU 2006 precession and IAU 2000A nutation models.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** rnpb double[3][3] bias-precession-nutation matrix (Note 2)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The matrix operates in the sense V(date) = rnpb * V(GCRS), where
** the p-vector V(date) is with respect to the true equatorial triad
** of date date1+date2 and the p-vector V(GCRS) is with respect to
** the Geocentric Celestial Reference System (IAU, 2000).
**
** Called:
** iauPfw06 bias-precession F-W angles, IAU 2006
** iauNut06a nutation, IAU 2006/2000A
** iauFw2m F-W angles to r-matrix
**
** Reference:
**
** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855.
**
*/
void iauPnm80(double date1, double date2, double rmatpn[3][3])
/*
** - - - - - - - - -
** i a u P n m 8 0
** - - - - - - - - -
**
** Form the matrix of precession/nutation for a given date, IAU 1976
** precession model, IAU 1980 nutation model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TDB date (Note 1)
**
** Returned:
** rmatpn double[3][3] combined precession/nutation matrix
**
** Notes:
**
** 1) The TDB date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TDB)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The matrix operates in the sense V(date) = rmatpn * V(J2000),
** where the p-vector V(date) is with respect to the true equatorial
** triad of date date1+date2 and the p-vector V(J2000) is with
** respect to the mean equatorial triad of epoch J2000.0.
**
** Called:
** iauPmat76 precession matrix, IAU 1976
** iauNutm80 nutation matrix, IAU 1980
** iauRxr product of two r-matrices
**
** Reference:
**
** Explanatory Supplement to the Astronomical Almanac,
** P. Kenneth Seidelmann (ed), University Science Books (1992),
** Section 3.3 (p145).
**
*/
void iauPom00(double xp, double yp, double sp, double rpom[3][3])
/*
** - - - - - - - - - -
** i a u P o m 0 0
** - - - - - - - - - -
**
** Form the matrix of polar motion for a given date, IAU 2000.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** xp,yp double coordinates of the pole (radians, Note 1)
** sp double the TIO locator s' (radians, Note 2)
**
** Returned:
** rpom double[3][3] polar-motion matrix (Note 3)
**
** Notes:
**
** 1) The arguments xp and yp are the coordinates (in radians) of the
** Celestial Intermediate Pole with respect to the International
** Terrestrial Reference System (see IERS Conventions 2003),
** measured along the meridians to 0 and 90 deg west respectively.
**
** 2) The argument sp is the TIO locator s', in radians, which
** positions the Terrestrial Intermediate Origin on the equator. It
** is obtained from polar motion observations by numerical
** integration, and so is in essence unpredictable. However, it is
** dominated by a secular drift of about 47 microarcseconds per
** century, and so can be taken into account by using s' = -47*t,
** where t is centuries since J2000.0. The function iauSp00
** implements this approximation.
**
** 3) The matrix operates in the sense V(TRS) = rpom * V(CIP), meaning
** that it is the final rotation when computing the pointing
** direction to a celestial source.
**
** Called:
** iauIr initialize r-matrix to identity
** iauRz rotate around Z-axis
** iauRy rotate around Y-axis
** iauRx rotate around X-axis
**
** Reference:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
*/
void iauPpp(double a[3], double b[3], double apb[3])
/*
** - - - - - - -
** i a u P p p
** - - - - - - -
**
** P-vector addition.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** a double[3] first p-vector
** b double[3] second p-vector
**
** Returned:
** apb double[3] a + b
**
** Note:
** It is permissible to re-use the same array for any of the
** arguments.
**
*/
void iauPpsp(double a[3], double s, double b[3], double apsb[3])
/*
** - - - - - - - -
** i a u P p s p
** - - - - - - - -
**
** P-vector plus scaled p-vector.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** a double[3] first p-vector
** s double scalar (multiplier for b)
** b double[3] second p-vector
**
** Returned:
** apsb double[3] a + s*b
**
** Note:
** It is permissible for any of a, b and apsb to be the same array.
**
** Called:
** iauSxp multiply p-vector by scalar
** iauPpp p-vector plus p-vector
**
*/
void iauPr00(double date1, double date2, double *dpsipr, double *depspr)
/*
** - - - - - - - -
** i a u P r 0 0
** - - - - - - - -
**
** Precession-rate part of the IAU 2000 precession-nutation models
** (part of MHB2000).
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** dpsipr,depspr double precession corrections (Notes 2,3)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The precession adjustments are expressed as "nutation
** components", corrections in longitude and obliquity with respect
** to the J2000.0 equinox and ecliptic.
**
** 3) Although the precession adjustments are stated to be with respect
** to Lieske et al. (1977), the MHB2000 model does not specify which
** set of Euler angles are to be used and how the adjustments are to
** be applied. The most literal and straightforward procedure is to
** adopt the 4-rotation epsilon_0, psi_A, omega_A, xi_A option, and
** to add dpsipr to psi_A and depspr to both omega_A and eps_A.
**
** 4) This is an implementation of one aspect of the IAU 2000A nutation
** model, formally adopted by the IAU General Assembly in 2000,
** namely MHB2000 (Mathews et al. 2002).
**
** References:
**
** Lieske, J.H., Lederle, T., Fricke, W. & Morando, B., "Expressions
** for the precession quantities based upon the IAU (1976) System of
** Astronomical Constants", Astron.Astrophys., 58, 1-16 (1977)
**
** Mathews, P.M., Herring, T.A., Buffet, B.A., "Modeling of nutation
** and precession New nutation series for nonrigid Earth and
** insights into the Earth's interior", J.Geophys.Res., 107, B4,
** 2002. The MHB2000 code itself was obtained on 9th September 2002
** from ftp://maia.usno.navy.mil/conv2000/chapter5/IAU2000A.
**
** Wallace, P.T., "Software for Implementing the IAU 2000
** Resolutions", in IERS Workshop 5.1 (2002).
**
*/
void iauPrec76(double ep01, double ep02, double ep11, double ep12,
double *zeta, double *z, double *theta)
/*
** - - - - - - - - - -
** i a u P r e c 7 6
** - - - - - - - - - -
**
** IAU 1976 precession model.
**
** This function forms the three Euler angles which implement general
** precession between two epochs, using the IAU 1976 model (as for
** the FK5 catalog).
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** ep01,ep02 double TDB starting epoch (Note 1)
** ep11,ep12 double TDB ending epoch (Note 1)
**
** Returned:
** zeta double 1st rotation: radians cw around z
** z double 3rd rotation: radians cw around z
** theta double 2nd rotation: radians ccw around y
**
** Notes:
**
** 1) The epochs ep01+ep02 and ep11+ep12 are Julian Dates, apportioned
** in any convenient way between the arguments epn1 and epn2. For
** example, JD(TDB)=2450123.7 could be expressed in any of these
** ways, among others:
**
** epn1 epn2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in cases
** where the loss of several decimal digits of resolution is
** acceptable. The J2000 method is best matched to the way the
** argument is handled internally and will deliver the optimum
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
** The two epochs may be expressed using different methods, but at
** the risk of losing some resolution.
**
** 2) The accumulated precession angles zeta, z, theta are expressed
** through canonical polynomials which are valid only for a limited
** time span. In addition, the IAU 1976 precession rate is known to
** be imperfect. The absolute accuracy of the present formulation
** is better than 0.1 arcsec from 1960AD to 2040AD, better than
** 1 arcsec from 1640AD to 2360AD, and remains below 3 arcsec for
** the whole of the period 500BC to 3000AD. The errors exceed
** 10 arcsec outside the range 1200BC to 3900AD, exceed 100 arcsec
** outside 4200BC to 5600AD and exceed 1000 arcsec outside 6800BC to
** 8200AD.
**
** 3) The three angles are returned in the conventional order, which
** is not the same as the order of the corresponding Euler
** rotations. The precession matrix is
** R_3(-z) x R_2(+theta) x R_3(-zeta).
**
** Reference:
**
** Lieske, J.H., 1979, Astron.Astrophys. 73, 282, equations
** (6) & (7), p283.
**
*/
void iauPv2p(double pv[2][3], double p[3])
/*
** - - - - - - - -
** i a u P v 2 p
** - - - - - - - -
**
** Discard velocity component of a pv-vector.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** pv double[2][3] pv-vector
**
** Returned:
** p double[3] p-vector
**
** Called:
** iauCp copy p-vector
**
*/
void iauPv2s(double pv[2][3],
double *theta, double *phi, double *r,
double *td, double *pd, double *rd)
/*
** - - - - - - - -
** i a u P v 2 s
** - - - - - - - -
**
** Convert position/velocity from Cartesian to spherical coordinates.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** pv double[2][3] pv-vector
**
** Returned:
** theta double longitude angle (radians)
** phi double latitude angle (radians)
** r double radial distance
** td double rate of change of theta
** pd double rate of change of phi
** rd double rate of change of r
**
** Notes:
**
** 1) If the position part of pv is null, theta, phi, td and pd
** are indeterminate. This is handled by extrapolating the
** position through unit time by using the velocity part of
** pv. This moves the origin without changing the direction
** of the velocity component. If the position and velocity
** components of pv are both null, zeroes are returned for all
** six results.
**
** 2) If the position is a pole, theta, td and pd are indeterminate.
** In such cases zeroes are returned for all three.
**
*/
void iauPvdpv(double a[2][3], double b[2][3], double adb[2])
/*
** - - - - - - - - -
** i a u P v d p v
** - - - - - - - - -
**
** Inner (=scalar=dot) product of two pv-vectors.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** a double[2][3] first pv-vector
** b double[2][3] second pv-vector
**
** Returned:
** adb double[2] a . b (see note)
**
** Note:
**
** If the position and velocity components of the two pv-vectors are
** ( ap, av ) and ( bp, bv ), the result, a . b, is the pair of
** numbers ( ap . bp , ap . bv + av . bp ). The two numbers are the
** dot-product of the two p-vectors and its derivative.
**
** Called:
** iauPdp scalar product of two p-vectors
**
*/
void iauPvm(double pv[2][3], double *r, double *s)
/*
** - - - - - - -
** i a u P v m
** - - - - - - -
**
** Modulus of pv-vector.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** pv double[2][3] pv-vector
**
** Returned:
** r double modulus of position component
** s double modulus of velocity component
**
** Called:
** iauPm modulus of p-vector
**
*/
void iauPvmpv(double a[2][3], double b[2][3], double amb[2][3])
/*
** - - - - - - - - -
** i a u P v m p v
** - - - - - - - - -
**
** Subtract one pv-vector from another.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** a double[2][3] first pv-vector
** b double[2][3] second pv-vector
**
** Returned:
** amb double[2][3] a - b
**
** Note:
** It is permissible to re-use the same array for any of the
** arguments.
**
** Called:
** iauPmp p-vector minus p-vector
**
*/
void iauPvppv(double a[2][3], double b[2][3], double apb[2][3])
/*
** - - - - - - - - -
** i a u P v p p v
** - - - - - - - - -
**
** Add one pv-vector to another.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** a double[2][3] first pv-vector
** b double[2][3] second pv-vector
**
** Returned:
** apb double[2][3] a + b
**
** Note:
** It is permissible to re-use the same array for any of the
** arguments.
**
** Called:
** iauPpp p-vector plus p-vector
**
*/
int iauPvstar(double pv[2][3], double *ra, double *dec,
double *pmr, double *pmd, double *px, double *rv)
/*
** - - - - - - - - - -
** i a u P v s t a r
** - - - - - - - - - -
**
** Convert star position+velocity vector to catalog coordinates.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given (Note 1):
** pv double[2][3] pv-vector (AU, AU/day)
**
** Returned (Note 2):
** ra double right ascension (radians)
** dec double declination (radians)
** pmr double RA proper motion (radians/year)
** pmd double Dec proper motion (radians/year)
** px double parallax (arcsec)
** rv double radial velocity (km/s, positive = receding)
**
** Returned (function value):
** int status:
** 0 = OK
** -1 = superluminal speed (Note 5)
** -2 = null position vector
**
** Notes:
**
** 1) The specified pv-vector is the coordinate direction (and its rate
** of change) for the date at which the light leaving the star
** reached the solar-system barycenter.
**
** 2) The star data returned by this function are "observables" for an
** imaginary observer at the solar-system barycenter. Proper motion
** and radial velocity are, strictly, in terms of barycentric
** coordinate time, TCB. For most practical applications, it is
** permissible to neglect the distinction between TCB and ordinary
** "proper" time on Earth (TT/TAI). The result will, as a rule, be
** limited by the intrinsic accuracy of the proper-motion and
** radial-velocity data; moreover, the supplied pv-vector is likely
** to be merely an intermediate result (for example generated by the
** function iauStarpv), so that a change of time unit will cancel
** out overall.
**
** In accordance with normal star-catalog conventions, the object's
** right ascension and declination are freed from the effects of
** secular aberration. The frame, which is aligned to the catalog
** equator and equinox, is Lorentzian and centered on the SSB.
**
** Summarizing, the specified pv-vector is for most stars almost
** identical to the result of applying the standard geometrical
** "space motion" transformation to the catalog data. The
** differences, which are the subject of the Stumpff paper cited
** below, are:
**
** (i) In stars with significant radial velocity and proper motion,
** the constantly changing light-time distorts the apparent proper
** motion. Note that this is a classical, not a relativistic,
** effect.
**
** (ii) The transformation complies with special relativity.
**
** 3) Care is needed with units. The star coordinates are in radians
** and the proper motions in radians per Julian year, but the
** parallax is in arcseconds; the radial velocity is in km/s, but
** the pv-vector result is in AU and AU/day.
**
** 4) The proper motions are the rate of change of the right ascension
** and declination at the catalog epoch and are in radians per Julian
** year. The RA proper motion is in terms of coordinate angle, not
** true angle, and will thus be numerically larger at high
** declinations.
**
** 5) Straight-line motion at constant speed in the inertial frame is
** assumed. If the speed is greater than or equal to the speed of
** light, the function aborts with an error status.
**
** 6) The inverse transformation is performed by the function iauStarpv.
**
** Called:
** iauPn decompose p-vector into modulus and direction
** iauPdp scalar product of two p-vectors
** iauSxp multiply p-vector by scalar
** iauPmp p-vector minus p-vector
** iauPm modulus of p-vector
** iauPpp p-vector plus p-vector
** iauPv2s pv-vector to spherical
** iauAnp normalize angle into range 0 to 2pi
**
** Reference:
**
** Stumpff, P., 1985, Astron.Astrophys. 144, 232-240.
**
*/
void iauPvu(double dt, double pv[2][3], double upv[2][3])
/*
** - - - - - - -
** i a u P v u
** - - - - - - -
**
** Update a pv-vector.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** dt double time interval
** pv double[2][3] pv-vector
**
** Returned:
** upv double[2][3] p updated, v unchanged
**
** Notes:
**
** 1) "Update" means "refer the position component of the vector
** to a new date dt time units from the existing date".
**
** 2) The time units of dt must match those of the velocity.
**
** 3) It is permissible for pv and upv to be the same array.
**
** Called:
** iauPpsp p-vector plus scaled p-vector
** iauCp copy p-vector
**
*/
void iauPvup(double dt, double pv[2][3], double p[3])
/*
** - - - - - - - -
** i a u P v u p
** - - - - - - - -
**
** Update a pv-vector, discarding the velocity component.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** dt double time interval
** pv double[2][3] pv-vector
**
** Returned:
** p double[3] p-vector
**
** Notes:
**
** 1) "Update" means "refer the position component of the vector to a
** new date dt time units from the existing date".
**
** 2) The time units of dt must match those of the velocity.
**
*/
void iauPvxpv(double a[2][3], double b[2][3], double axb[2][3])
/*
** - - - - - - - - -
** i a u P v x p v
** - - - - - - - - -
**
** Outer (=vector=cross) product of two pv-vectors.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** a double[2][3] first pv-vector
** b double[2][3] second pv-vector
**
** Returned:
** axb double[2][3] a x b
**
** Notes:
**
** 1) If the position and velocity components of the two pv-vectors are
** ( ap, av ) and ( bp, bv ), the result, a x b, is the pair of
** vectors ( ap x bp, ap x bv + av x bp ). The two vectors are the
** cross-product of the two p-vectors and its derivative.
**
** 2) It is permissible to re-use the same array for any of the
** arguments.
**
** Called:
** iauCpv copy pv-vector
** iauPxp vector product of two p-vectors
** iauPpp p-vector plus p-vector
**
*/
void iauPxp(double a[3], double b[3], double axb[3])
/*
** - - - - - - -
** i a u P x p
** - - - - - - -
**
** p-vector outer (=vector=cross) product.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** a double[3] first p-vector
** b double[3] second p-vector
**
** Returned:
** axb double[3] a x b
**
** Note:
** It is permissible to re-use the same array for any of the
** arguments.
**
*/
void iauRm2v(double r[3][3], double w[3])
/*
** - - - - - - - -
** i a u R m 2 v
** - - - - - - - -
**
** Express an r-matrix as an r-vector.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** r double[3][3] rotation matrix
**
** Returned:
** w double[3] rotation vector (Note 1)
**
** Notes:
**
** 1) A rotation matrix describes a rotation through some angle about
** some arbitrary axis called the Euler axis. The "rotation vector"
** returned by this function has the same direction as the Euler axis,
** and its magnitude is the angle in radians. (The magnitude and
** direction can be separated by means of the function iauPn.)
**
** 2) If r is null, so is the result. If r is not a rotation matrix
** the result is undefined; r must be proper (i.e. have a positive
** determinant) and real orthogonal (inverse = transpose).
**
** 3) The reference frame rotates clockwise as seen looking along
** the rotation vector from the origin.
**
*/
void iauRv2m(double w[3], double r[3][3])
/*
** - - - - - - - -
** i a u R v 2 m
** - - - - - - - -
**
** Form the r-matrix corresponding to a given r-vector.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** w double[3] rotation vector (Note 1)
**
** Returned:
** r double[3][3] rotation matrix
**
** Notes:
**
** 1) A rotation matrix describes a rotation through some angle about
** some arbitrary axis called the Euler axis. The "rotation vector"
** supplied to This function has the same direction as the Euler
** axis, and its magnitude is the angle in radians.
**
** 2) If w is null, the unit matrix is returned.
**
** 3) The reference frame rotates clockwise as seen looking along the
** rotation vector from the origin.
**
*/
void iauRx(double phi, double r[3][3])
/*
** - - - - - -
** i a u R x
** - - - - - -
**
** Rotate an r-matrix about the x-axis.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** phi double angle (radians)
**
** Given and returned:
** r double[3][3] r-matrix
**
** Sign convention: The matrix can be used to rotate the reference
** frame of a vector. Calling this function with positive phi
** incorporates in the matrix an additional rotation, about the x-axis,
** anticlockwise as seen looking towards the origin from positive x.
**
** Called:
** iauIr initialize r-matrix to identity
** iauRxr product of two r-matrices
** iauCr copy r-matrix
**
*/
void iauRxp(double r[3][3], double p[3], double rp[3])
/*
** - - - - - - -
** i a u R x p
** - - - - - - -
**
** Multiply a p-vector by an r-matrix.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** r double[3][3] r-matrix
** p double[3] p-vector
**
** Returned:
** rp double[3] r * p
**
** Note:
** It is permissible for p and rp to be the same array.
**
** Called:
** iauCp copy p-vector
**
*/
void iauRxpv(double r[3][3], double pv[2][3], double rpv[2][3])
/*
** - - - - - - - -
** i a u R x p v
** - - - - - - - -
**
** Multiply a pv-vector by an r-matrix.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** r double[3][3] r-matrix
** pv double[2][3] pv-vector
**
** Returned:
** rpv double[2][3] r * pv
**
** Note:
** It is permissible for pv and rpv to be the same array.
**
** Called:
** iauRxp product of r-matrix and p-vector
**
*/
void iauRxr(double a[3][3], double b[3][3], double atb[3][3])
/*
** - - - - - - -
** i a u R x r
** - - - - - - -
**
** Multiply two r-matrices.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** a double[3][3] first r-matrix
** b double[3][3] second r-matrix
**
** Returned:
** atb double[3][3] a * b
**
** Note:
** It is permissible to re-use the same array for any of the
** arguments.
**
** Called:
** iauCr copy r-matrix
**
*/
void iauRy(double theta, double r[3][3])
/*
** - - - - - -
** i a u R y
** - - - - - -
**
** Rotate an r-matrix about the y-axis.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** theta double angle (radians)
**
** Given and returned:
** r double[3][3] r-matrix
**
** Sign convention: The matrix can be used to rotate the reference
** frame of a vector. Calling This function with positive theta
** incorporates in the matrix an additional rotation, about the y-axis,
** anticlockwise as seen looking towards the origin from positive y.
**
** Called:
** iauIr initialize r-matrix to identity
** iauRxr product of two r-matrices
** iauCr copy r-matrix
**
*/
void iauRz(double psi, double r[3][3])
/*
** - - - - - -
** i a u R z
** - - - - - -
**
** Rotate an r-matrix about the z-axis.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** psi double angle (radians)
**
** Given and returned:
** r double[3][3] r-matrix, rotated
**
** Sign convention: The matrix can be used to rotate the reference
** frame of a vector. Calling This function with positive psi
** incorporates in the matrix an additional rotation, about the z-axis,
** anticlockwise as seen looking towards the origin from positive z.
**
** Called:
** iauIr initialize r-matrix to identity
** iauRxr product of two r-matrices
** iauCr copy r-matrix
**
*/
double iauS00(double date1, double date2, double x, double y)
/*
** - - - - - - -
** i a u S 0 0
** - - - - - - -
**
** The CIO locator s, positioning the Celestial Intermediate Origin on
** the equator of the Celestial Intermediate Pole, given the CIP's X,Y
** coordinates. Compatible with IAU 2000A precession-nutation.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
** x,y double CIP coordinates (Note 3)
**
** Returned (function value):
** double the CIO locator s in radians (Note 2)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The CIO locator s is the difference between the right ascensions
** of the same point in two systems: the two systems are the GCRS
** and the CIP,CIO, and the point is the ascending node of the
** CIP equator. The quantity s remains below 0.1 arcsecond
** throughout 1900-2100.
**
** 3) The series used to compute s is in fact for s+XY/2, where X and Y
** are the x and y components of the CIP unit vector; this series
** is more compact than a direct series for s would be. This
** function requires X,Y to be supplied by the caller, who is
** responsible for providing values that are consistent with the
** supplied date.
**
** 4) The model is consistent with the IAU 2000A precession-nutation.
**
** Called:
** iauFal03 mean anomaly of the Moon
** iauFalp03 mean anomaly of the Sun
** iauFaf03 mean argument of the latitude of the Moon
** iauFad03 mean elongation of the Moon from the Sun
** iauFaom03 mean longitude of the Moon's ascending node
** iauFave03 mean longitude of Venus
** iauFae03 mean longitude of Earth
** iauFapa03 general accumulated precession in longitude
**
** References:
**
** Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
** "Expressions for the Celestial Intermediate Pole and Celestial
** Ephemeris Origin consistent with the IAU 2000A precession-
** nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
**
** n.b. The celestial ephemeris origin (CEO) was renamed "celestial
** intermediate origin" (CIO) by IAU 2006 Resolution 2.
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
*/
double iauS00a(double date1, double date2)
/*
** - - - - - - - -
** i a u S 0 0 a
** - - - - - - - -
**
** The CIO locator s, positioning the Celestial Intermediate Origin on
** the equator of the Celestial Intermediate Pole, using the IAU 2000A
** precession-nutation model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned (function value):
** double the CIO locator s in radians (Note 2)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The CIO locator s is the difference between the right ascensions
** of the same point in two systems. The two systems are the GCRS
** and the CIP,CIO, and the point is the ascending node of the
** CIP equator. The CIO locator s remains a small fraction of
** 1 arcsecond throughout 1900-2100.
**
** 3) The series used to compute s is in fact for s+XY/2, where X and Y
** are the x and y components of the CIP unit vector; this series
** is more compact than a direct series for s would be. The present
** function uses the full IAU 2000A nutation model when predicting
** the CIP position. Faster results, with no significant loss of
** accuracy, can be obtained via the function iauS00b, which uses
** instead the IAU 2000B truncated model.
**
** Called:
** iauPnm00a classical NPB matrix, IAU 2000A
** iauBnp2xy extract CIP X,Y from the BPN matrix
** iauS00 the CIO locator s, given X,Y, IAU 2000A
**
** References:
**
** Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
** "Expressions for the Celestial Intermediate Pole and Celestial
** Ephemeris Origin consistent with the IAU 2000A precession-
** nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
**
** n.b. The celestial ephemeris origin (CEO) was renamed "celestial
** intermediate origin" (CIO) by IAU 2006 Resolution 2.
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
*/
double iauS00b(double date1, double date2)
/*
** - - - - - - - -
** i a u S 0 0 b
** - - - - - - - -
**
** The CIO locator s, positioning the Celestial Intermediate Origin on
** the equator of the Celestial Intermediate Pole, using the IAU 2000B
** precession-nutation model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned (function value):
** double the CIO locator s in radians (Note 2)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The CIO locator s is the difference between the right ascensions
** of the same point in two systems. The two systems are the GCRS
** and the CIP,CIO, and the point is the ascending node of the
** CIP equator. The CIO locator s remains a small fraction of
** 1 arcsecond throughout 1900-2100.
**
** 3) The series used to compute s is in fact for s+XY/2, where X and Y
** are the x and y components of the CIP unit vector; this series
** is more compact than a direct series for s would be. The present
** function uses the IAU 2000B truncated nutation model when
** predicting the CIP position. The function iauS00a uses instead
** the full IAU 2000A model, but with no significant increase in
** accuracy and at some cost in speed.
**
** Called:
** iauPnm00b classical NPB matrix, IAU 2000B
** iauBnp2xy extract CIP X,Y from the BPN matrix
** iauS00 the CIO locator s, given X,Y, IAU 2000A
**
** References:
**
** Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
** "Expressions for the Celestial Intermediate Pole and Celestial
** Ephemeris Origin consistent with the IAU 2000A precession-
** nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
**
** n.b. The celestial ephemeris origin (CEO) was renamed "celestial
** intermediate origin" (CIO) by IAU 2006 Resolution 2.
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
*/
double iauS06(double date1, double date2, double x, double y)
/*
** - - - - - - -
** i a u S 0 6
** - - - - - - -
**
** The CIO locator s, positioning the Celestial Intermediate Origin on
** the equator of the Celestial Intermediate Pole, given the CIP's X,Y
** coordinates. Compatible with IAU 2006/2000A precession-nutation.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
** x,y double CIP coordinates (Note 3)
**
** Returned (function value):
** double the CIO locator s in radians (Note 2)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The CIO locator s is the difference between the right ascensions
** of the same point in two systems: the two systems are the GCRS
** and the CIP,CIO, and the point is the ascending node of the
** CIP equator. The quantity s remains below 0.1 arcsecond
** throughout 1900-2100.
**
** 3) The series used to compute s is in fact for s+XY/2, where X and Y
** are the x and y components of the CIP unit vector; this series
** is more compact than a direct series for s would be. This
** function requires X,Y to be supplied by the caller, who is
** responsible for providing values that are consistent with the
** supplied date.
**
** 4) The model is consistent with the "P03" precession (Capitaine et
** al. 2003), adopted by IAU 2006 Resolution 1, 2006, and the
** IAU 2000A nutation (with P03 adjustments).
**
** Called:
** iauFal03 mean anomaly of the Moon
** iauFalp03 mean anomaly of the Sun
** iauFaf03 mean argument of the latitude of the Moon
** iauFad03 mean elongation of the Moon from the Sun
** iauFaom03 mean longitude of the Moon's ascending node
** iauFave03 mean longitude of Venus
** iauFae03 mean longitude of Earth
** iauFapa03 general accumulated precession in longitude
**
** References:
**
** Capitaine, N., Wallace, P.T. & Chapront, J., 2003, Astron.
** Astrophys. 432, 355
**
** McCarthy, D.D., Petit, G. (eds.) 2004, IERS Conventions (2003),
** IERS Technical Note No. 32, BKG
**
*/
double iauS06a(double date1, double date2)
/*
** - - - - - - - -
** i a u S 0 6 a
** - - - - - - - -
**
** The CIO locator s, positioning the Celestial Intermediate Origin on
** the equator of the Celestial Intermediate Pole, using the IAU 2006
** precession and IAU 2000A nutation models.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned (function value):
** double the CIO locator s in radians (Note 2)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The CIO locator s is the difference between the right ascensions
** of the same point in two systems. The two systems are the GCRS
** and the CIP,CIO, and the point is the ascending node of the
** CIP equator. The CIO locator s remains a small fraction of
** 1 arcsecond throughout 1900-2100.
**
** 3) The series used to compute s is in fact for s+XY/2, where X and Y
** are the x and y components of the CIP unit vector; this series is
** more compact than a direct series for s would be. The present
** function uses the full IAU 2000A nutation model when predicting
** the CIP position.
**
** Called:
** iauPnm06a classical NPB matrix, IAU 2006/2000A
** iauBpn2xy extract CIP X,Y coordinates from NPB matrix
** iauS06 the CIO locator s, given X,Y, IAU 2006
**
** References:
**
** Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
** "Expressions for the Celestial Intermediate Pole and Celestial
** Ephemeris Origin consistent with the IAU 2000A precession-
** nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
**
** n.b. The celestial ephemeris origin (CEO) was renamed "celestial
** intermediate origin" (CIO) by IAU 2006 Resolution 2.
**
** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
**
** McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003),
** IERS Technical Note No. 32, BKG
**
** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
**
*/
void iauS2c(double theta, double phi, double c[3])
/*
** - - - - - - -
** i a u S 2 c
** - - - - - - -
**
** Convert spherical coordinates to Cartesian.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** theta double longitude angle (radians)
** phi double latitude angle (radians)
**
** Returned:
** c double[3] direction cosines
**
*/
void iauS2p(double theta, double phi, double r, double p[3])
/*
** - - - - - - -
** i a u S 2 p
** - - - - - - -
**
** Convert spherical polar coordinates to p-vector.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** theta double longitude angle (radians)
** phi double latitude angle (radians)
** r double radial distance
**
** Returned:
** p double[3] Cartesian coordinates
**
** Called:
** iauS2c spherical coordinates to unit vector
** iauSxp multiply p-vector by scalar
**
*/
void iauS2pv(double theta, double phi, double r,
double td, double pd, double rd,
double pv[2][3])
/*
** - - - - - - - -
** i a u S 2 p v
** - - - - - - - -
**
** Convert position/velocity from spherical to Cartesian coordinates.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** theta double longitude angle (radians)
** phi double latitude angle (radians)
** r double radial distance
** td double rate of change of theta
** pd double rate of change of phi
** rd double rate of change of r
**
** Returned:
** pv double[2][3] pv-vector
**
*/
void iauS2xpv(double s1, double s2, double pv[2][3], double spv[2][3])
/*
** - - - - - - - - -
** i a u S 2 x p v
** - - - - - - - - -
**
** Multiply a pv-vector by two scalars.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** s1 double scalar to multiply position component by
** s2 double scalar to multiply velocity component by
** pv double[2][3] pv-vector
**
** Returned:
** spv double[2][3] pv-vector: p scaled by s1, v scaled by s2
**
** Note:
** It is permissible for pv and spv to be the same array.
**
** Called:
** iauSxp multiply p-vector by scalar
**
*/
double iauSepp(double a[3], double b[3])
/*
** - - - - - - - -
** i a u S e p p
** - - - - - - - -
**
** Angular separation between two p-vectors.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** a double[3] first p-vector (not necessarily unit length)
** b double[3] second p-vector (not necessarily unit length)
**
** Returned (function value):
** double angular separation (radians, always positive)
**
** Notes:
**
** 1) If either vector is null, a zero result is returned.
**
** 2) The angular separation is most simply formulated in terms of
** scalar product. However, this gives poor accuracy for angles
** near zero and pi. The present algorithm uses both cross product
** and dot product, to deliver full accuracy whatever the size of
** the angle.
**
** Called:
** iauPxp vector product of two p-vectors
** iauPm modulus of p-vector
** iauPdp scalar product of two p-vectors
**
*/
double iauSeps(double al, double ap, double bl, double bp)
/*
** - - - - - - - -
** i a u S e p s
** - - - - - - - -
**
** Angular separation between two sets of spherical coordinates.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** al double first longitude (radians)
** ap double first latitude (radians)
** bl double second longitude (radians)
** bp double second latitude (radians)
**
** Returned (function value):
** double angular separation (radians)
**
** Called:
** iauS2c spherical coordinates to unit vector
** iauSepp angular separation between two p-vectors
**
*/
double iauSp00(double date1, double date2)
/*
** - - - - - - - -
** i a u S p 0 0
** - - - - - - - -
**
** The TIO locator s', positioning the Terrestrial Intermediate Origin
** on the equator of the Celestial Intermediate Pole.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned (function value):
** double the TIO locator s' in radians (Note 2)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The TIO locator s' is obtained from polar motion observations by
** numerical integration, and so is in essence unpredictable.
** However, it is dominated by a secular drift of about
** 47 microarcseconds per century, which is the approximation
** evaluated by the present function.
**
** Reference:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
*/
int iauStarpm(double ra1, double dec1,
double pmr1, double pmd1, double px1, double rv1,
double ep1a, double ep1b, double ep2a, double ep2b,
double *ra2, double *dec2,
double *pmr2, double *pmd2, double *px2, double *rv2)
/*
** - - - - - - - - - -
** i a u S t a r p m
** - - - - - - - - - -
**
** Star proper motion: update star catalog data for space motion.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** ra1 double right ascension (radians), before
** dec1 double declination (radians), before
** pmr1 double RA proper motion (radians/year), before
** pmd1 double Dec proper motion (radians/year), before
** px1 double parallax (arcseconds), before
** rv1 double radial velocity (km/s, +ve = receding), before
** ep1a double "before" epoch, part A (Note 1)
** ep1b double "before" epoch, part B (Note 1)
** ep2a double "after" epoch, part A (Note 1)
** ep2b double "after" epoch, part B (Note 1)
**
** Returned:
** ra2 double right ascension (radians), after
** dec2 double declination (radians), after
** pmr2 double RA proper motion (radians/year), after
** pmd2 double Dec proper motion (radians/year), after
** px2 double parallax (arcseconds), after
** rv2 double radial velocity (km/s, +ve = receding), after
**
** Returned (function value):
** int status:
** -1 = system error (should not occur)
** 0 = no warnings or errors
** 1 = distance overridden (Note 6)
** 2 = excessive velocity (Note 7)
** 4 = solution didn't converge (Note 8)
** else = binary logical OR of the above warnings
**
** Notes:
**
** 1) The starting and ending TDB dates ep1a+ep1b and ep2a+ep2b are
** Julian Dates, apportioned in any convenient way between the two
** parts (A and B). For example, JD(TDB)=2450123.7 could be
** expressed in any of these ways, among others:
**
** epna epnb
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) In accordance with normal star-catalog conventions, the object's
** right ascension and declination are freed from the effects of
** secular aberration. The frame, which is aligned to the catalog
** equator and equinox, is Lorentzian and centered on the SSB.
**
** The proper motions are the rate of change of the right ascension
** and declination at the catalog epoch and are in radians per TDB
** Julian year.
**
** The parallax and radial velocity are in the same frame.
**
** 3) Care is needed with units. The star coordinates are in radians
** and the proper motions in radians per Julian year, but the
** parallax is in arcseconds.
**
** 4) The RA proper motion is in terms of coordinate angle, not true
** angle. If the catalog uses arcseconds for both RA and Dec proper
** motions, the RA proper motion will need to be divided by cos(Dec)
** before use.
**
** 5) Straight-line motion at constant speed, in the inertial frame,
** is assumed.
**
** 6) An extremely small (or zero or negative) parallax is interpreted
** to mean that the object is on the "celestial sphere", the radius
** of which is an arbitrary (large) value (see the iauStarpv
** function for the value used). When the distance is overridden in
** this way, the status, initially zero, has 1 added to it.
**
** 7) If the space velocity is a significant fraction of c (see the
** constant VMAX in the function iauStarpv), it is arbitrarily set
** to zero. When this action occurs, 2 is added to the status.
**
** 8) The relativistic adjustment carried out in the iauStarpv function
** involves an iterative calculation. If the process fails to
** converge within a set number of iterations, 4 is added to the
** status.
**
** Called:
** iauStarpv star catalog data to space motion pv-vector
** iauPvu update a pv-vector
** iauPdp scalar product of two p-vectors
** iauPvstar space motion pv-vector to star catalog data
**
*/
int iauStarpv(double ra, double dec,
double pmr, double pmd, double px, double rv,
double pv[2][3])
/*
** - - - - - - - - - -
** i a u S t a r p v
** - - - - - - - - - -
**
** Convert star catalog coordinates to position+velocity vector.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given (Note 1):
** ra double right ascension (radians)
** dec double declination (radians)
** pmr double RA proper motion (radians/year)
** pmd double Dec proper motion (radians/year)
** px double parallax (arcseconds)
** rv double radial velocity (km/s, positive = receding)
**
** Returned (Note 2):
** pv double[2][3] pv-vector (AU, AU/day)
**
** Returned (function value):
** int status:
** 0 = no warnings
** 1 = distance overridden (Note 6)
** 2 = excessive speed (Note 7)
** 4 = solution didn't converge (Note 8)
** else = binary logical OR of the above
**
** Notes:
**
** 1) The star data accepted by this function are "observables" for an
** imaginary observer at the solar-system barycenter. Proper motion
** and radial velocity are, strictly, in terms of barycentric
** coordinate time, TCB. For most practical applications, it is
** permissible to neglect the distinction between TCB and ordinary
** "proper" time on Earth (TT/TAI). The result will, as a rule, be
** limited by the intrinsic accuracy of the proper-motion and
** radial-velocity data; moreover, the pv-vector is likely to be
** merely an intermediate result, so that a change of time unit
** would cancel out overall.
**
** In accordance with normal star-catalog conventions, the object's
** right ascension and declination are freed from the effects of
** secular aberration. The frame, which is aligned to the catalog
** equator and equinox, is Lorentzian and centered on the SSB.
**
** 2) The resulting position and velocity pv-vector is with respect to
** the same frame and, like the catalog coordinates, is freed from
** the effects of secular aberration. Should the "coordinate
** direction", where the object was located at the catalog epoch, be
** required, it may be obtained by calculating the magnitude of the
** position vector pv[0][0-2] dividing by the speed of light in
** AU/day to give the light-time, and then multiplying the space
** velocity pv[1][0-2] by this light-time and adding the result to
** pv[0][0-2].
**
** Summarizing, the pv-vector returned is for most stars almost
** identical to the result of applying the standard geometrical
** "space motion" transformation. The differences, which are the
** subject of the Stumpff paper referenced below, are:
**
** (i) In stars with significant radial velocity and proper motion,
** the constantly changing light-time distorts the apparent proper
** motion. Note that this is a classical, not a relativistic,
** effect.
**
** (ii) The transformation complies with special relativity.
**
** 3) Care is needed with units. The star coordinates are in radians
** and the proper motions in radians per Julian year, but the
** parallax is in arcseconds; the radial velocity is in km/s, but
** the pv-vector result is in AU and AU/day.
**
** 4) The RA proper motion is in terms of coordinate angle, not true
** angle. If the catalog uses arcseconds for both RA and Dec proper
** motions, the RA proper motion will need to be divided by cos(Dec)
** before use.
**
** 5) Straight-line motion at constant speed, in the inertial frame,
** is assumed.
**
** 6) An extremely small (or zero or negative) parallax is interpreted
** to mean that the object is on the "celestial sphere", the radius
** of which is an arbitrary (large) value (see the constant PXMIN).
** When the distance is overridden in this way, the status,
** initially zero, has 1 added to it.
**
** 7) If the space velocity is a significant fraction of c (see the
** constant VMAX), it is arbitrarily set to zero. When this action
** occurs, 2 is added to the status.
**
** 8) The relativistic adjustment involves an iterative calculation.
** If the process fails to converge within a set number (IMAX) of
** iterations, 4 is added to the status.
**
** 9) The inverse transformation is performed by the function
** iauPvstar.
**
** Called:
** iauS2pv spherical coordinates to pv-vector
** iauPm modulus of p-vector
** iauZp zero p-vector
** iauPn decompose p-vector into modulus and direction
** iauPdp scalar product of two p-vectors
** iauSxp multiply p-vector by scalar
** iauPmp p-vector minus p-vector
** iauPpp p-vector plus p-vector
**
** Reference:
**
** Stumpff, P., 1985, Astron.Astrophys. 144, 232-240.
**
*/
void iauSxp(double s, double p[3], double sp[3])
/*
** - - - - - - -
** i a u S x p
** - - - - - - -
**
** Multiply a p-vector by a scalar.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** s double scalar
** p double[3] p-vector
**
** Returned:
** sp double[3] s * p
**
** Note:
** It is permissible for p and sp to be the same array.
**
*/
void iauSxpv(double s, double pv[2][3], double spv[2][3])
/*
** - - - - - - - -
** i a u S x p v
** - - - - - - - -
**
** Multiply a pv-vector by a scalar.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** s double scalar
** pv double[2][3] pv-vector
**
** Returned:
** spv double[2][3] s * pv
**
** Note:
** It is permissible for pv and psv to be the same array
**
** Called:
** iauS2xpv multiply pv-vector by two scalars
**
*/
int iauTaitt(double tai1, double tai2, double *tt1, double *tt2)
/*
** - - - - - - - - -
** i a u T a i t t
** - - - - - - - - -
**
** Time scale transformation: International Atomic Time, TAI, to
** Terrestrial Time, TT.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: canonical.
**
** Given:
** tai1,tai2 double TAI as a 2-part Julian Date
**
** Returned:
** tt1,tt2 double TT as a 2-part Julian Date
**
** Returned (function value):
** int status: 0 = OK
**
** Note:
**
** tai1+tai2 is Julian Date, apportioned in any convenient way
** between the two arguments, for example where tai1 is the Julian
** Day Number and tai2 is the fraction of a day. The returned
** tt1,tt2 follow suit.
**
** References:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** Explanatory Supplement to the Astronomical Almanac,
** P. Kenneth Seidelmann (ed), University Science Books (1992)
**
*/
int iauTaiut1(double tai1, double tai2, double dta,
double *ut11, double *ut12)
/*
** - - - - - - - - - -
** i a u T a i u t 1
** - - - - - - - - - -
**
** Time scale transformation: International Atomic Time, TAI, to
** Universal Time, UT1.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: canonical.
**
** Given:
** tai1,tai2 double TAI as a 2-part Julian Date
** dta double UT1-TAI in seconds
**
** Returned:
** ut11,ut12 double UT1 as a 2-part Julian Date
**
** Returned (function value):
** int status: 0 = OK
**
** Notes:
**
** 1 tai1+tai2 is Julian Date, apportioned in any convenient way
** between the two arguments, for example where tai1 is the Julian
** Day Number and tai2 is the fraction of a day. The returned
** UT11,UT12 follow suit.
**
** 2 The argument dta, i.e. UT1-TAI, is an observed quantity, and is
** available from IERS tabulations.
**
** Reference:
**
** Explanatory Supplement to the Astronomical Almanac,
** P. Kenneth Seidelmann (ed), University Science Books (1992)
**
*/
int iauTaiutc(double tai1, double tai2, double *utc1, double *utc2)
/*
** - - - - - - - - - -
** i a u T a i u t c
** - - - - - - - - - -
**
** Time scale transformation: International Atomic Time, TAI, to
** Coordinated Universal Time, UTC.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: canonical.
**
** Given:
** tai1,tai2 double TAI as a 2-part Julian Date (Note 1)
**
** Returned:
** utc1,utc2 double UTC as a 2-part quasi Julian Date (Notes 1-3)
**
** Returned (function value):
** int status: +1 = dubious year (Note 4)
** 0 = OK
** -1 = unacceptable date
**
** Notes:
**
** 1 tai1+tai2 is Julian Date, apportioned in any convenient way
** between the two arguments, for example where tai1 is the Julian
** Day Number and tai2 is the fraction of a day. The returned utc1
** and utc2 form an analogous pair, except that a special convention
** is used, to deal with the problem of leap seconds - see the next
** note.
**
** 2) JD cannot unambiguously represent UTC during a leap second unless
** special measures are taken. The convention in the present
** function is that the JD day represents UTC days whether the
** length is 86399, 86400 or 86401 SI seconds.
**
** 3) The function iauD2dtf can be used to transform the UTC quasi-JD
** into calendar date and clock time, including UTC leap second
** handling.
**
** 4) The warning status "dubious year" flags UTCs that predate the
** introduction of the time scale and that are too far in the future
** to be trusted. See iauDat for further details.
**
** Called:
** iauJd2cal JD to Gregorian calendar
** iauDat delta(AT) = TAI-UTC
** iauCal2jd Gregorian calendar to JD
**
** References:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** Explanatory Supplement to the Astronomical Almanac,
** P. Kenneth Seidelmann (ed), University Science Books (1992)
**
*/
int iauTcbtdb(double tcb1, double tcb2, double *tdb1, double *tdb2)
/*
** - - - - - - - - - -
** i a u T c b t d b
** - - - - - - - - - -
**
** Time scale transformation: Barycentric Coordinate Time, TCB, to
** Barycentric Dynamical Time, TDB.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: canonical.
**
** Given:
** tcb1,tcb2 double TCB as a 2-part Julian Date
**
** Returned:
** tdb1,tdb2 double TDB as a 2-part Julian Date
**
** Returned (function value):
** int status: 0 = OK
**
** Notes:
**
** 1 tcb1+tcb2 is Julian Date, apportioned in any convenient way
** between the two arguments, for example where tcb1 is the Julian
** Day Number and tcb2 is the fraction of a day. The returned
** tdb1,tdb2 follow suit.
**
** 2 The 2006 IAU General Assembly introduced a conventional linear
** transformation between TDB and TCB. This transformation
** compensates for the drift between TCB and terrestrial time TT,
** and keeps TDB approximately centered on TT. Because the
** relationship between TT and TCB depends on the adopted solar
** system ephemeris, the degree of alignment between TDB and TT over
** long intervals will vary according to which ephemeris is used.
** Former definitions of TDB attempted to avoid this problem by
** stipulating that TDB and TT should differ only by periodic
** effects. This is a good description of the nature of the
** relationship but eluded precise mathematical formulation. The
** conventional linear relationship adopted in 2006 sidestepped
** these difficulties whilst delivering a TDB that in practice was
** consistent with values before that date.
**
** 3 TDB is essentially the same as Teph, the time argument for the
** JPL solar system ephemerides.
**
** Reference:
**
** IAU 2006 Resolution B3
**
*/
int iauTcgtt(double tcg1, double tcg2, double *tt1, double *tt2)
/*
** - - - - - - - - -
** i a u T c g t t
** - - - - - - - - -
**
** Time scale transformation: Geocentric Coordinate Time, TCG, to
** Terrestrial Time, TT.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: canonical.
**
** Given:
** tcg1,tcg2 double TCG as a 2-part Julian Date
**
** Returned:
** tt1,tt2 double TT as a 2-part Julian Date
**
** Returned (function value):
** int status: 0 = OK
**
** Note:
**
** tcg1+tcg2 is Julian Date, apportioned in any convenient way
** between the two arguments, for example where tcg1 is the Julian
** Day Number and tcg22 is the fraction of a day. The returned
** tt1,tt2 follow suit.
**
** References:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),.
** IERS Technical Note No. 32, BKG (2004)
**
** IAU 2000 Resolution B1.9
**
*/
int iauTdbtcb(double tdb1, double tdb2, double *tcb1, double *tcb2)
/*
** - - - - - - - - - -
** i a u T d b t c b
** - - - - - - - - - -
**
** Time scale transformation: Barycentric Dynamical Time, TDB, to
** Barycentric Coordinate Time, TCB.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: canonical.
**
** Given:
** tdb1,tdb2 double TDB as a 2-part Julian Date
**
** Returned:
** tcb1,tcb2 double TCB as a 2-part Julian Date
**
** Returned (function value):
** int status: 0 = OK
**
** Notes:
**
** 1 tdb1+tdb2 is Julian Date, apportioned in any convenient way
** between the two arguments, for example where tdb1 is the Julian
** Day Number and tdb2 is the fraction of a day. The returned
** tcb1,tcb2 follow suit.
**
** 2 The 2006 IAU General Assembly introduced a conventional linear
** transformation between TDB and TCB. This transformation
** compensates for the drift between TCB and terrestrial time TT,
** and keeps TDB approximately centered on TT. Because the
** relationship between TT and TCB depends on the adopted solar
** system ephemeris, the degree of alignment between TDB and TT over
** long intervals will vary according to which ephemeris is used.
** Former definitions of TDB attempted to avoid this problem by
** stipulating that TDB and TT should differ only by periodic
** effects. This is a good description of the nature of the
** relationship but eluded precise mathematical formulation. The
** conventional linear relationship adopted in 2006 sidestepped
** these difficulties whilst delivering a TDB that in practice was
** consistent with values before that date.
**
** 3 TDB is essentially the same as Teph, the time argument for the
** JPL solar system ephemerides.
**
** Reference:
**
** IAU 2006 Resolution B3
**
*/
int iauTdbtt(double tdb1, double tdb2, double dtr,
double *tt1, double *tt2 )
/*
** - - - - - - - - -
** i a u T d b t t
** - - - - - - - - -
**
** Time scale transformation: Barycentric Dynamical Time, TDB, to
** Terrestrial Time, TT.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: canonical.
**
** Given:
** dtb1,tdb2 double TDB as a 2-part Julian Date
** dtr double TDB-TT in seconds
**
** Returned:
** tt1,tt2 double TT as a 2-part Julian Date
**
** Returned (function value):
** int status: 0 = OK
**
** Notes:
**
** 1 tdb1+tdb2 is Julian Date, apportioned in any convenient way
** between the two arguments, for example where tdb1 is the Julian
** Day Number and tdb2 is the fraction of a day. The returned
** tt1,tt2 follow suit.
**
** 2 The argument dtr represents the quasi-periodic component of the
** GR transformation between TT and TCB. It is dependent upon the
** adopted solar-system ephemeris, and can be obtained by numerical
** integration, by interrogating a precomputed time ephemeris or by
** evaluating a model such as that implemented in the SOFA function
** iauDtdb. The quantity is dominated by an annual term of 1.7 ms
** amplitude.
**
** 3 TDB is essentially the same as Teph, the time argument for the
** JPL solar system ephemerides.
**
** References:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** IAU 2006 Resolution 3
**
*/
int iauTf2a(int s, int ihour, int imin, double sec, double *rad)
/*
** - - - - - - - -
** i a u T f 2 a
** - - - - - - - -
**
** Convert hours, minutes, seconds to radians.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** s int sign: '-' = negative, otherwise positive
** ihour int hours
** imin int minutes
** sec double seconds
**
** Returned:
** days double angle in radians
**
** Returned (function value):
** int status: 0 = OK
** 1 = ihour outside range 0-23
** 2 = imin outside range 0-59
** 3 = sec outside range 0-59.999...
**
** Notes:
**
** 1) The result is computed even if any of the range checks fail.
**
** 2) Negative ihour, imin and/or sec produce a warning status, but
** the absolute value is used in the conversion.
**
*/
int iauTf2d(int s, int ihour, int imin, double sec, double *days)
/*
** - - - - - - - -
** i a u T f 2 d
** - - - - - - - -
**
** Convert hours, minutes, seconds to days.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** s int sign: '-' = negative, otherwise positive
** ihour int hours
** imin int minutes
** sec double seconds
**
** Returned:
** days double interval in days
**
** Returned (function value):
** int status: 0 = OK
** 1 = ihour outside range 0-23
** 2 = imin outside range 0-59
** 3 = sec outside range 0-59.999...
**
** Notes:
**
** 1) The result is computed even if any of the range checks fail.
**
** 2) Negative ihour, imin and/or sec produce a warning status, but
** the absolute value is used in the conversion.
**
*/
void iauTr(double r[3][3], double rt[3][3])
/*
** - - - - - -
** i a u T r
** - - - - - -
**
** Transpose an r-matrix.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** r double[3][3] r-matrix
**
** Returned:
** rt double[3][3] transpose
**
** Note:
** It is permissible for r and rt to be the same array.
**
** Called:
** iauCr copy r-matrix
**
*/
void iauTrxp(double r[3][3], double p[3], double trp[3])
/*
** - - - - - - - -
** i a u T r x p
** - - - - - - - -
**
** Multiply a p-vector by the transpose of an r-matrix.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** r double[3][3] r-matrix
** p double[3] p-vector
**
** Returned:
** trp double[3] r * p
**
** Note:
** It is permissible for p and trp to be the same array.
**
** Called:
** iauTr transpose r-matrix
** iauRxp product of r-matrix and p-vector
**
*/
void iauTrxpv(double r[3][3], double pv[2][3], double trpv[2][3])
/*
** - - - - - - - - -
** i a u T r x p v
** - - - - - - - - -
**
** Multiply a pv-vector by the transpose of an r-matrix.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** r double[3][3] r-matrix
** pv double[2][3] pv-vector
**
** Returned:
** trpv double[2][3] r * pv
**
** Note:
** It is permissible for pv and trpv to be the same array.
**
** Called:
** iauTr transpose r-matrix
** iauRxpv product of r-matrix and pv-vector
**
*/
int iauTttai(double tt1, double tt2, double *tai1, double *tai2)
/*
** - - - - - - - - -
** i a u T t t a i
** - - - - - - - - -
**
** Time scale transformation: Terrestrial Time, TT, to International
** Atomic Time, TAI.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: canonical.
**
** Given:
** tt1,tt2 double TT as a 2-part Julian Date
**
** Returned:
** tai1,tai2 double TAI as a 2-part Julian Date
**
** Returned (function value):
** int status: 0 = OK
**
** Note:
**
** tt1+tt2 is Julian Date, apportioned in any convenient way between
** the two arguments, for example where tt1 is the Julian Day Number
** and tt2 is the fraction of a day. The returned tai1,tai2 follow
** suit.
**
** References:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** Explanatory Supplement to the Astronomical Almanac,
** P. Kenneth Seidelmann (ed), University Science Books (1992)
**
*/
int iauTttcg(double tt1, double tt2, double *tcg1, double *tcg2)
/*
** - - - - - - - - -
** i a u T t t c g
** - - - - - - - - -
**
** Time scale transformation: Terrestrial Time, TT, to Geocentric
** Coordinate Time, TCG.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: canonical.
**
** Given:
** tt1,tt2 double TT as a 2-part Julian Date
**
** Returned:
** tcg1,tcg2 double TCG as a 2-part Julian Date
**
** Returned (function value):
** int status: 0 = OK
**
** Note:
**
** tt1+tt2 is Julian Date, apportioned in any convenient way between
** the two arguments, for example where tt1 is the Julian Day Number
** and tt2 is the fraction of a day. The returned tcg1,tcg2 follow
** suit.
**
** References:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** IAU 2000 Resolution B1.9
**
*/
int iauTttdb(double tt1, double tt2, double dtr,
double *tdb1, double *tdb2)
/*
** - - - - - - - - -
** i a u T t t d b
** - - - - - - - - -
**
** Time scale transformation: Terrestrial Time, TT, to Barycentric
** Dynamical Time, TDB.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: canonical.
**
** Given:
** tt1,tt2 double TT as a 2-part Julian Date
** dtr double TDB-TT in seconds
**
** Returned:
** tdb1,tdb2 double TDB as a 2-part Julian Date
**
** Returned (function value):
** int status: 0 = OK
**
** Notes:
**
** 1 tt1+tt2 is Julian Date, apportioned in any convenient way between
** the two arguments, for example where tt1 is the Julian Day Number
** and tt2 is the fraction of a day. The returned tdb1,tdb2 follow
** suit.
**
** 2 The argument dtr represents the quasi-periodic component of the
** GR transformation between TT and TCB. It is dependent upon the
** adopted solar-system ephemeris, and can be obtained by numerical
** integration, by interrogating a precomputed time ephemeris or by
** evaluating a model such as that implemented in the SOFA function
** iauDtdb. The quantity is dominated by an annual term of 1.7 ms
** amplitude.
**
** 3 TDB is essentially the same as Teph, the time argument for the JPL
** solar system ephemerides.
**
** References:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** IAU 2006 Resolution 3
**
*/
int iauTtut1(double tt1, double tt2, double dt,
double *ut11, double *ut12)
/*
** - - - - - - - - -
** i a u T t u t 1
** - - - - - - - - -
**
** Time scale transformation: Terrestrial Time, TT, to Universal Time,
** UT1.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: canonical.
**
** Given:
** tt1,tt2 double TT as a 2-part Julian Date
** dt double TT-UT1 in seconds
**
** Returned:
** ut11,ut12 double UT1 as a 2-part Julian Date
**
** Returned (function value):
** int status: 0 = OK
**
** Notes:
**
** 1 tt1+tt2 is Julian Date, apportioned in any convenient way between
** the two arguments, for example where tt1 is the Julian Day Number
** and tt2 is the fraction of a day. The returned ut11,ut12 follow
** suit.
**
** 2 The argument dt is classical Delta T.
**
** Reference:
**
** Explanatory Supplement to the Astronomical Almanac,
** P. Kenneth Seidelmann (ed), University Science Books (1992)
**
*/
int iauUt1tai(double ut11, double ut12, double dta,
double *tai1, double *tai2)
/*
** - - - - - - - - - -
** i a u U t 1 t a i
** - - - - - - - - - -
**
** Time scale transformation: Universal Time, UT1, to International
** Atomic Time, TAI.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: canonical.
**
** Given:
** ut11,ut12 double UT1 as a 2-part Julian Date
** dta double UT1-TAI in seconds
**
** Returned:
** tai1,tai2 double TAI as a 2-part Julian Date
**
** Returned (function value):
** int status: 0 = OK
**
** Notes:
**
** 1 ut11+ut12 is Julian Date, apportioned in any convenient way
** between the two arguments, for example where ut11 is the Julian
** Day Number and ut12 is the fraction of a day. The returned
** TAI1,TAI2 follow suit.
**
** 2 The argument dta, i.e. UT1-TAI, is an observed quantity, and is
** available from IERS tabulations.
**
** Reference:
**
** Explanatory Supplement to the Astronomical Almanac,
** P. Kenneth Seidelmann (ed), University Science Books (1992)
**
*/
int iauUt1tt(double ut11, double ut12, double dt,
double *tt1, double *tt2)
/*
** - - - - - - - - -
** i a u U t 1 t t
** - - - - - - - - -
**
** Time scale transformation: Universal Time, UT1, to Terrestrial
** Time, TT.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: canonical.
**
** Given:
** ut11,ut12 double UT1 as a 2-part Julian Date
** dt double TT-UT1 in seconds
**
** Returned:
** tt1,tt2 double TAI as a 2-part Julian Date
**
** Returned (function value):
** int status: 0 = OK
**
** Notes:
**
** 1 ut11+ut12 is Julian Date, apportioned in any convenient way
** between the two arguments, for example where ut11 is the Julian
** Day Number and ut12 is the fraction of a day. The returned
** tt1,tt2 follow suit.
**
** 2 The argument dt is classical Delta T.
**
** Reference:
**
** Explanatory Supplement to the Astronomical Almanac,
** P. Kenneth Seidelmann (ed), University Science Books (1992)
**
*/
int iauUt1utc(double ut11, double ut12, double dut1,
double *utc1, double *utc2)
/*
** - - - - - - - - - -
** i a u U t 1 u t c
** - - - - - - - - - -
**
** Time scale transformation: Universal Time, UT1, to Coordinated
** Universal Time, UTC.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: canonical.
**
** Given:
** ut11,ut12 double UT1 as a 2-part Julian Date (Note 1)
** dut1 double Delta UT1: UT1-UTC in seconds (Note 2)
**
** Returned:
** utc1,utc2 double UTC as a 2-part quasi Julian Date (Notes 3,4)
**
** Returned (function value):
** int status: +1 = dubious year (Note 5)
** 0 = OK
** -1 = unacceptable date
**
** Notes:
**
** 1 ut11+ut12 is Julian Date, apportioned in any convenient way
** between the two arguments, for example where ut11 is the Julian
** Day Number and ut12 is the fraction of a day. The returned utc1
** and utc2 form an analogous pair, except that a special convention
** is used, to deal with the problem of leap seconds - see Note 3.
**
** 2) Delta UT1 can be obtained from tabulations provided by the
** International Earth Rotation and Reference Systems Service. The
** value changes abruptly by 1s at a leap second; however, close to
** a leap second the algorithm used here is tolerant of the "wrong"
** choice of value being made.
**
** 3) JD cannot unambiguously represent UTC during a leap second unless
** special measures are taken. The convention in the present
** function is that the returned quasi JD day UTC1+UTC2 represents
** UTC days whether the length is 86399, 86400 or 86401 SI seconds.
**
** 4) The function iauD2dtf can be used to transform the UTC quasi-JD
** into calendar date and clock time, including UTC leap second
** handling.
**
** 5) The warning status "dubious year" flags UTCs that predate the
** introduction of the time scale and that are too far in the future
** to be trusted. See iauDat for further details.
**
** Called:
** iauJd2cal JD to Gregorian calendar
** iauDat delta(AT) = TAI-UTC
** iauCal2jd Gregorian calendar to JD
**
** References:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** Explanatory Supplement to the Astronomical Almanac,
** P. Kenneth Seidelmann (ed), University Science Books (1992)
**
*/
int iauUtctai(double utc1, double utc2, double *tai1, double *tai2)
/*
** - - - - - - - - - -
** i a u U t c t a i
** - - - - - - - - - -
**
** Time scale transformation: Coordinated Universal Time, UTC, to
** International Atomic Time, TAI.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: canonical.
**
** Given:
** utc1,utc2 double UTC as a 2-part quasi Julian Date (Notes 1-4)
**
** Returned:
** tai1,tai2 double TAI as a 2-part Julian Date (Note 5)
**
** Returned (function value):
** int status: +1 = dubious year (Note 3)
** 0 = OK
** -1 = unacceptable date
**
** Notes:
**
** 1) utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any
** convenient way between the two arguments, for example where utc1
** is the Julian Day Number and utc2 is the fraction of a day.
**
** 2) JD cannot unambiguously represent UTC during a leap second unless
** special measures are taken. The convention in the present
** function is that the JD day represents UTC days whether the
** length is 86399, 86400 or 86401 SI seconds.
**
** 3) The warning status "dubious year" flags UTCs that predate the
** introduction of the time scale and that are too far in the future
** to be trusted. See iauDat for further details.
**
** 4) The function iauDtf2d converts from calendar date and time of day
** into 2-part Julian Date, and in the case of UTC implements the
** leap-second-ambiguity convention described above.
**
** 5) The returned TAI1,TAI2 are such that their sum is the TAI Julian
** Date.
**
** Called:
** iauJd2cal JD to Gregorian calendar
** iauDat delta(AT) = TAI-UTC
** iauCal2jd Gregorian calendar to JD
**
** References:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** Explanatory Supplement to the Astronomical Almanac,
** P. Kenneth Seidelmann (ed), University Science Books (1992)
**
*/
int iauUtcut1(double utc1, double utc2, double dut1,
double *ut11, double *ut12)
/*
** - - - - - - - - - -
** i a u U t c u t 1
** - - - - - - - - - -
**
** Time scale transformation: Coordinated Universal Time, UTC, to
** Universal Time, UT1.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: canonical.
**
** Given:
** utc1,utc2 double UTC as a 2-part quasi Julian Date (Notes 1-4)
** dut1 double Delta UT1 = UT1-UTC in seconds (Note 5)
**
** Returned:
** ut11,ut12 double UT1 as a 2-part Julian Date (Note 6)
**
** Returned (function value):
** int status: +1 = dubious year (Note 7)
** 0 = OK
** -1 = unacceptable date
**
** Notes:
**
** 1) utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any
** convenient way between the two arguments, for example where utc1
** is the Julian Day Number and utc2 is the fraction of a day.
**
** 2) JD cannot unambiguously represent UTC during a leap second unless
** special measures are taken. The convention in the present
** function is that the JD day represents UTC days whether the
** length is 86399, 86400 or 86401 SI seconds.
**
** 3) The warning status "dubious year" flags UTCs that predate the
** introduction of the time scale and that are too far in the future
** to be trusted. See iauDat for further details.
**
** 4) The function iauDtf2d converts from calendar date and time of
** day into 2-part Julian Date, and in the case of UTC implements
** the leap-second-ambiguity convention described above.
**
** 5) Delta UT1 can be obtained from tabulations provided by the
** International Earth Rotation and Reference Systems Service. It
** It is the caller's responsibility to supply a DUT argument
** containing the UT1-UTC value that matches the given UTC.
**
** 6) The returned ut11,ut12 are such that their sum is the UT1 Julian
** Date.
**
** 7) The warning status "dubious year" flags UTCs that predate the
** introduction of the time scale and that are too far in the future
** to be trusted. See iauDat for further details.
**
** References:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** Explanatory Supplement to the Astronomical Almanac,
** P. Kenneth Seidelmann (ed), University Science Books (1992)
**
** Called:
** iauJd2cal JD to Gregorian calendar
** iauDat delta(AT) = TAI-UTC
** iauUtctai UTC to TAI
** iauTaiut1 TAI to UT1
**
*/
void iauXy06(double date1, double date2, double *x, double *y)
/*
** - - - - - - - -
** i a u X y 0 6
** - - - - - - - -
**
** X,Y coordinates of celestial intermediate pole from series based
** on IAU 2006 precession and IAU 2000A nutation.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** x,y double CIP X,Y coordinates (Note 2)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The X,Y coordinates are those of the unit vector towards the
** celestial intermediate pole. They represent the combined effects
** of frame bias, precession and nutation.
**
** 3) The fundamental arguments used are as adopted in IERS Conventions
** (2003) and are from Simon et al. (1994) and Souchay et al.
** (1999).
**
** 4) This is an alternative to the angles-based method, via the SOFA
** function iauFw2xy and as used in iauXys06a for example. The two
** methods agree at the 1 microarcsecond level (at present), a
** negligible amount compared with the intrinsic accuracy of the
** models. However, it would be unwise to mix the two methods
** (angles-based and series-based) in a single application.
**
** Called:
** iauFal03 mean anomaly of the Moon
** iauFalp03 mean anomaly of the Sun
** iauFaf03 mean argument of the latitude of the Moon
** iauFad03 mean elongation of the Moon from the Sun
** iauFaom03 mean longitude of the Moon's ascending node
** iauFame03 mean longitude of Mercury
** iauFave03 mean longitude of Venus
** iauFae03 mean longitude of Earth
** iauFama03 mean longitude of Mars
** iauFaju03 mean longitude of Jupiter
** iauFasa03 mean longitude of Saturn
** iauFaur03 mean longitude of Uranus
** iauFane03 mean longitude of Neptune
** iauFapa03 general accumulated precession in longitude
**
** References:
**
** Capitaine, N., Wallace, P.T. & Chapront, J., 2003,
** Astron.Astrophys., 412, 567
**
** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
**
** McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003),
** IERS Technical Note No. 32, BKG
**
** Simon, J.L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
** Francou, G. & Laskar, J., Astron.Astrophys., 1994, 282, 663
**
** Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M., 1999,
** Astron.Astrophys.Supp.Ser. 135, 111
**
** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
**
*/
void iauXys00a(double date1, double date2,
double *x, double *y, double *s)
/*
** - - - - - - - - - -
** i a u X y s 0 0 a
** - - - - - - - - - -
**
** For a given TT date, compute the X,Y coordinates of the Celestial
** Intermediate Pole and the CIO locator s, using the IAU 2000A
** precession-nutation model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** x,y double Celestial Intermediate Pole (Note 2)
** s double the CIO locator s (Note 2)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The Celestial Intermediate Pole coordinates are the x,y
** components of the unit vector in the Geocentric Celestial
** Reference System.
**
** 3) The CIO locator s (in radians) positions the Celestial
** Intermediate Origin on the equator of the CIP.
**
** 4) A faster, but slightly less accurate result (about 1 mas for
** X,Y), can be obtained by using instead the iauXys00b function.
**
** Called:
** iauPnm00a classical NPB matrix, IAU 2000A
** iauBpn2xy extract CIP X,Y coordinates from NPB matrix
** iauS00 the CIO locator s, given X,Y, IAU 2000A
**
** Reference:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
*/
void iauXys00b(double date1, double date2,
double *x, double *y, double *s)
/*
** - - - - - - - - - -
** i a u X y s 0 0 b
** - - - - - - - - - -
**
** For a given TT date, compute the X,Y coordinates of the Celestial
** Intermediate Pole and the CIO locator s, using the IAU 2000B
** precession-nutation model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** x,y double Celestial Intermediate Pole (Note 2)
** s double the CIO locator s (Note 2)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The Celestial Intermediate Pole coordinates are the x,y
** components of the unit vector in the Geocentric Celestial
** Reference System.
**
** 3) The CIO locator s (in radians) positions the Celestial
** Intermediate Origin on the equator of the CIP.
**
** 4) The present function is faster, but slightly less accurate (about
** 1 mas in X,Y), than the iauXys00a function.
**
** Called:
** iauPnm00b classical NPB matrix, IAU 2000B
** iauBpn2xy extract CIP X,Y coordinates from NPB matrix
** iauS00 the CIO locator s, given X,Y, IAU 2000A
**
** Reference:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
*/
void iauXys06a(double date1, double date2,
double *x, double *y, double *s)
/*
** - - - - - - - - - -
** i a u X y s 0 6 a
** - - - - - - - - - -
**
** For a given TT date, compute the X,Y coordinates of the Celestial
** Intermediate Pole and the CIO locator s, using the IAU 2006
** precession and IAU 2000A nutation models.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** x,y double Celestial Intermediate Pole (Note 2)
** s double the CIO locator s (Note 2)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The Celestial Intermediate Pole coordinates are the x,y components
** of the unit vector in the Geocentric Celestial Reference System.
**
** 3) The CIO locator s (in radians) positions the Celestial
** Intermediate Origin on the equator of the CIP.
**
** 4) Series-based solutions for generating X and Y are also available:
** see Capitaine & Wallace (2006) and iauXy06.
**
** Called:
** iauPnm06a classical NPB matrix, IAU 2006/2000A
** iauBpn2xy extract CIP X,Y coordinates from NPB matrix
** iauS06 the CIO locator s, given X,Y, IAU 2006
**
** References:
**
** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
**
** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
**
*/
void iauZp(double p[3])
/*
** - - - - - -
** i a u Z p
** - - - - - -
**
** Zero a p-vector.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Returned:
** p double[3] p-vector
**
*/
void iauZpv(double pv[2][3])
/*
** - - - - - - -
** i a u Z p v
** - - - - - - -
**
** Zero a pv-vector.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Returned:
** pv double[2][3] pv-vector
**
** Called:
** iauZp zero p-vector
**
*/
void iauZr(double r[3][3])
/*
** - - - - - -
** i a u Z r
** - - - - - -
**
** Initialize an r-matrix to the null matrix.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Returned:
** r double[3][3] r-matrix
**
*/
copyr.lis 2010 September 10
COPYRIGHT NOTICE
Text equivalent to the following appears at the end of every SOFA
routine. (There are small formatting differences between the Fortran
and C versions.)
*+----------------------------------------------------------------------
*
* Copyright (C) 2010
* Standards Of Fundamental Astronomy Board
* of the International Astronomical Union.
*
* =====================
* SOFA Software License
* =====================
*
* NOTICE TO USER:
*
* BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING TERMS AND CONDITIONS
* WHICH APPLY TO ITS USE.
*
* 1. The Software is owned by the IAU SOFA Board ("SOFA").
*
* 2. Permission is granted to anyone to use the SOFA software for any
* purpose, including commercial applications, free of charge and
* without payment of royalties, subject to the conditions and
* restrictions listed below.
*
* 3. You (the user) may copy and distribute SOFA source code to others,
* and use and adapt its code and algorithms in your own software,
* on a world-wide, royalty-free basis. That portion of your
* distribution that does not consist of intact and unchanged copies
* of SOFA source code files is a "derived work" that must comply
* with the following requirements:
*
* a) Your work shall be marked or carry a statement that it
* (i) uses routines and computations derived by you from
* software provided by SOFA under license to you; and
* (ii) does not itself constitute software provided by and/or
* endorsed by SOFA.
*
* b) The source code of your derived work must contain descriptions
* of how the derived work is based upon, contains and/or differs
* from the original SOFA software.
*
* c) The name(s) of all routine(s) in your derived work shall not
* include the prefix "iau".
*
* d) The origin of the SOFA components of your derived work must
* not be misrepresented; you must not claim that you wrote the
* original software, nor file a patent application for SOFA
* software or algorithms embedded in the SOFA software.
*
* e) These requirements must be reproduced intact in any source
* distribution and shall apply to anyone to whom you have
* granted a further right to modify the source code of your
* derived work.
*
* Note that, as originally distributed, the SOFA software is
* intended to be a definitive implementation of the IAU standards,
* and consequently third-party modifications are discouraged. All
* variations, no matter how minor, must be explicitly marked as
* such, as explained above.
*
* 4. In any published work or commercial products which includes
* results achieved by using the SOFA software, you shall
* acknowledge that the SOFA software was used in obtaining those
* results.
*
* 5. You shall not cause the SOFA software to be brought into
* disrepute, either by misuse, or use for inappropriate tasks, or
* by inappropriate modification.
*
* 6. The SOFA software is provided "as is" and SOFA makes no warranty
* as to its use or performance. SOFA does not and cannot warrant
* the performance or results which the user may obtain by using the
* SOFA software. SOFA makes no warranties, express or implied, as
* to non-infringement of third party rights, merchantability, or
* fitness for any particular purpose. In no event will SOFA be
* liable to the user for any consequential, incidental, or special
* damages, including any lost profits or lost savings, even if a
* SOFA representative has been advised of such damages, or for any
* claim by any third party.
*
* 7. The provision of any version of the SOFA software under the terms
* and conditions specified herein does not imply that future
* versions will also be made available under the same terms and
* conditions.
*
* Correspondence concerning SOFA software should be addressed as
* follows:
*
* By email: sofa@ukho.gov.uk
* By post: IAU SOFA Center
* HM Nautical Almanac Office
* UK Hydrographic Office
* Admiralty Way, Taunton
* Somerset, TA1 2DN
* United Kingdom
*
*-----------------------------------------------------------------------
consts.lis 2008 September 30
SOFA Fortran constants
----------------------
These must be used exactly as presented below.
* Pi
DOUBLE PRECISION DPI
PARAMETER ( DPI = 3.141592653589793238462643D0 )
* 2Pi
DOUBLE PRECISION D2PI
PARAMETER ( D2PI = 6.283185307179586476925287D0 )
* Radians to hours
DOUBLE PRECISION DR2H
PARAMETER ( DR2H = 3.819718634205488058453210D0 )
* Radians to seconds
DOUBLE PRECISION DR2S
PARAMETER ( DR2S = 13750.98708313975701043156D0 )
* Radians to degrees
DOUBLE PRECISION DR2D
PARAMETER ( DR2D = 57.29577951308232087679815D0 )
* Radians to arc seconds
DOUBLE PRECISION DR2AS
PARAMETER ( DR2AS = 206264.8062470963551564734D0 )
* Hours to radians
DOUBLE PRECISION DH2R
PARAMETER ( DH2R = 0.2617993877991494365385536D0 )
* Seconds to radians
DOUBLE PRECISION DS2R
PARAMETER ( DS2R = 7.272205216643039903848712D-5 )
* Degrees to radians
DOUBLE PRECISION DD2R
PARAMETER ( DD2R = 1.745329251994329576923691D-2 )
* Arc seconds to radians
DOUBLE PRECISION DAS2R
PARAMETER ( DAS2R = 4.848136811095359935899141D-6 )
SOFA C constants
----------------
The constants used by the C version of SOFA are defined in the header
file sofam.h.
#ifndef SOFAMHDEF
#define SOFAMHDEF
/*
** - - - - - - - -
** s o f a m . h
** - - - - - - - -
**
** Macros used by SOFA library.
**
** This file is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** This revision: 2010 May 16
**
** SOFA release YYYY-MM-DD
**
** Copyright (C) 2010 IAU SOFA Board. See notes at end.
*/
#include "sofa.h"
/* Seconds of time per radian */
#define DS2R (7.272205216643039903848712e-5)
/* Pi */
#define DPI (3.141592653589793238462643)
/* 2Pi */
#define D2PI (6.283185307179586476925287)
/* Degrees to radians */
#define DD2R (1.745329251994329576923691e-2)
/* Radians to arcseconds */
#define DR2AS (206264.8062470963551564734)
/* Arcseconds to radians */
#define DAS2R (4.848136811095359935899141e-6)
/* Arcseconds in a full circle */
#define TURNAS (1296000.0)
/* Milliarcseconds to radians */
#define DMAS2R (DAS2R / 1e3)
/* Length of tropical year B1900 (days) */
#define DTY (365.242198781)
/* Seconds per day. */
#define DAYSEC (86400.0)
/* Days per Julian year */
#define DJY (365.25)
/* Days per Julian century */
#define DJC (36525.0)
/* Days per Julian millennium */
#define DJM (365250.0)
/* Reference epoch (J2000.0), Julian Date */
#define DJ00 (2451545.0)
/* Julian Date of Modified Julian Date zero */
#define DJM0 (2400000.5)
/* Reference epoch (J2000.0), Modified Julian Date */
#define DJM00 (51544.5)
/* 1977 Jan 1.0 as MJD */
#define DJM77 (43144.0)
/* TT minus TAI (s) */
#define TTMTAI (32.184)
/* AU (m) */
#define DAU (149597870e3)
/* Speed of light (AU per day) */
#define DC (DAYSEC / 499.004782)
/* L_G = 1 - d(TT)/d(TCG) */
#define ELG (6.969290134e-10)
/* L_B = 1 - d(TDB)/d(TCB), and TDB (s) at TAI 1977/1/1.0 */
#define ELB (1.550519768e-8)
#define TDB0 (-6.55e-5)
/* dint(A) - truncate to nearest whole number towards zero (double) */
#define dint(A) ((A)<0.0?ceil(A):floor(A))
/* dnint(A) - round to nearest whole number (double) */
#define dnint(A) ((A)<0.0?ceil((A)-0.5):floor((A)+0.5))
/* dsign(A,B) - magnitude of A with sign of B (double) */
#define dsign(A,B) ((B)<0.0?-(A):(A))
#endif
/*----------------------------------------------------------------------
**
** Copyright (C) 2010
** Standards Of Fundamental Astronomy Board
** of the International Astronomical Union.
**
** =====================
** SOFA Software License
** =====================
**
** NOTICE TO USER:
**
** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING TERMS AND CONDITIONS
** WHICH APPLY TO ITS USE.
**
** 1. The Software is owned by the IAU SOFA Board ("SOFA").
**
** 2. Permission is granted to anyone to use the SOFA software for any
** purpose, including commercial applications, free of charge and
** without payment of royalties, subject to the conditions and
** restrictions listed below.
**
** 3. You (the user) may copy and distribute SOFA source code to others,
** and use and adapt its code and algorithms in your own software,
** on a world-wide, royalty-free basis. That portion of your
** distribution that does not consist of intact and unchanged copies
** of SOFA source code files is a "derived work" that must comply
** with the following requirements:
**
** a) Your work shall be marked or carry a statement that it
** (i) uses routines and computations derived by you from
** software provided by SOFA under license to you; and
** (ii) does not itself constitute software provided by and/or
** endorsed by SOFA.
**
** b) The source code of your derived work must contain descriptions
** of how the derived work is based upon, contains and/or differs
** from the original SOFA software.
**
** c) The name(s) of all routine(s) in your derived work shall not
** include the prefix "iau".
**
** d) The origin of the SOFA components of your derived work must
** not be misrepresented; you must not claim that you wrote the
** original software, nor file a patent application for SOFA
** software or algorithms embedded in the SOFA software.
**
** e) These requirements must be reproduced intact in any source
** distribution and shall apply to anyone to whom you have
** granted a further right to modify the source code of your
** derived work.
**
** Note that, as originally distributed, the SOFA software is
** intended to be a definitive implementation of the IAU standards,
** and consequently third-party modifications are discouraged. All
** variations, no matter how minor, must be explicitly marked as
** such, as explained above.
**
** 4. In any published work or commercial products which includes
** results achieved by using the SOFA software, you shall
** acknowledge that the SOFA software was used in obtaining those
** results.
**
** 5. You shall not cause the SOFA software to be brought into
** disrepute, either by misuse, or use for inappropriate tasks, or
** by inappropriate modification.
**
** 6. The SOFA software is provided "as is" and SOFA makes no warranty
** as to its use or performance. SOFA does not and cannot warrant
** the performance or results which the user may obtain by using the
** SOFA software. SOFA makes no warranties, express or implied, as
** to non-infringement of third party rights, merchantability, or
** fitness for any particular purpose. In no event will SOFA be
** liable to the user for any consequential, incidental, or special
** damages, including any lost profits or lost savings, even if a
** SOFA representative has been advised of such damages, or for any
** claim by any third party.
**
** 7. The provision of any version of the SOFA software under the terms
** and conditions specified herein does not imply that future
** versions will also be made available under the same terms and
** conditions.
**
** Correspondence concerning SOFA software should be addressed as
** follows:
**
** By email: sofa@ukho.gov.uk
** By post: IAU SOFA Center
** HM Nautical Almanac Office
** UK Hydrographic Office
** Admiralty Way, Taunton
** Somerset, TA1 2DN
** United Kingdom
**
**--------------------------------------------------------------------*/
board.lis 2010 November 23
IAU STANDARDS OF FUNDAMENTAL ASTRONOMY BOARD
Current Membership
John Bangert United States Naval Observatory
Steven Bell Her Majesty's Nautical Almanac Office
Mark Calabretta Australia Telescope National Facility
Nicole Capitaine Paris Observatory
William Folkner Jet Propulsion Laboratory
George Hobbs Australia Telescope National Facility
Catherine Hohenkerk Her Majesty's Nautical Almanac Office (Chair)
Wen-Jing Jin Shanghai Observatory
Brian Luzum United States Naval Observatory (IERS)
Zinovy Malkin Pulkovo Observatory, St Petersburg
Jeffrey Percival University of Wisconsin
Patrick Wallace Rutherford Appleton Laboratory
Past Members
Wim Brouw University of Groningen
Anne-Marie Gontier Paris Observatory
George Kaplan United States Naval Observatory
Dennis McCarthy United States Naval Observatory
Skip Newhall Jet Propulsion Laboratory
The e-mail for the Board chair is Catherine.Hohenkerk@ukho.gov.uk