SUBROUTINE iau_FK425 ( R1950, D1950,
: DR1950, DD1950, P1950, V1950,
: R2000, D2000,
: DR2000, DD2000, P2000, V2000 )
*+
* - - - - - - - - - -
* i a u _ F K 4 2 5
* - - - - - - - - - -
*
* Convert B1950.0 FK4 star catalog data to J2000.0 FK5.
*
* This routine is part of the International Astronomical Union's
* SOFA (Standards of Fundamental Astronomy) software collection.
*
* Status: support routine.
*
* This routine converts a star's catalog data from the old FK4
* (Bessel-Newcomb) system to the later IAU 1976 FK5 (Fricke) system.
*
* Given: (all B1950.0, FK4)
* R1950,D1950 d B1950.0 RA,Dec (rad)
* DR1950,DD1950 d B1950.0 proper motions (rad/trop.yr)
* P1950 d parallax (arcsec)
* V1950 d radial velocity (km/s, +ve = moving away)
*
* Returned: (all J2000.0, FK5)
* R2000,D2000 d J2000.0 RA,Dec (rad)
* DR2000,DD2000 d J2000.0 proper motions (rad/Jul.yr)
* P2000 d parallax (arcsec)
* V2000 d radial velocity (km/s, +ve = moving away)
*
* Notes:
*
* 1) The proper motions in RA are dRA/dt rather than cos(Dec)*dRA/dt,
* and are per year rather than per century.
*
* 2) The conversion is somewhat complicated, for several reasons:
*
* . Change of standard epoch from B1950.0 to J2000.0.
*
* . An intermediate transition date of 1984 January 1.0 TT.
*
* . A change of precession model.
*
* . Change of time unit for proper motion (tropical to Julian).
*
* . FK4 positions include the E-terms of aberration, to simplify the
* hand computation of annual aberration. FK5 positions assume a
* rigorous aberration computation based on the Earth's barycentric
* velocity.
*
* . The E-terms also affect proper motions, and in particular cause
* objects at large distances to exhibit fictitious proper motions.
*
* The algorithm is based on Smith et al. (1989) and Yallop et al.
* (1989), which presented a matrix method due to Standish (1982) as
* developed by Aoki et al. (1983), using Kinoshita's development of
* Andoyer's post-Newcomb precession. The numerical constants from
* Seidelmann (1992) are used canonically.
*
* 3) Conversion from B1950.0 FK4 to J2000.0 FK5 only is provided for.
* Conversions for different epochs and equinoxes would require
* additional treatment for precession, proper motion and E-terms.
*
* 4) In the FK4 catalog the proper motions of stars within 10 degrees
* of the poles do not embody differential E-terms effects and
* should, strictly speaking, be handled in a different manner from
* stars outside these regions. However, given the general lack of
* homogeneity of the star data available for routine astrometry, the
* difficulties of handling positions that may have been determined
* from astrometric fields spanning the polar and non-polar regions,
* the likelihood that the differential E-terms effect was not taken
* into account when allowing for proper motion in past astrometry,
* and the undesirability of a discontinuity in the algorithm, the
* decision has been made in this SOFA algorithm to include the
* effects of differential E-terms on the proper motions for all
* stars, whether polar or not. At epoch J2000.0, and measuring "on
* the sky" rather than in terms of RA change, the errors resulting
* from this simplification are less than 1 milliarcsecond in
* position and 1 milliarcsecond per century in proper motion.
*
* Called:
* iau_ANP normalize angle into range 0 to 2pi
* iau_PV2S pv-vector to spherical coordinates
* iau_PDP scalar product of two p-vectors
* iau_PVMPV pv-vector minus pv_vector
* iau_PVPPV pv-vector plus pv_vector
* iau_S2PV spherical coordinates to pv-vector
* iau_SXP multiply p-vector by scalar
*
* References:
*
* Aoki, S. et al., 1983, "Conversion matrix of epoch B1950.0
* FK4-based positions of stars to epoch J2000.0 positions in
* accordance with the new IAU resolutions". Astron.Astrophys.
* 128, 263-267.
*
* Seidelmann, P.K. (ed), 1992, "Explanatory Supplement to the
* Astronomical Almanac", ISBN 0-935702-68-7.
*
* Smith, C.A. et al., 1989, "The transformation of astrometric
* catalog systems to the equinox J2000.0". Astron.J. 97, 265.
*
* Standish, E.M., 1982, "Conversion of positions and proper motions
* from B1950.0 to the IAU system at J2000.0". Astron.Astrophys.,
* 115, 1, 20-22.
*
* Yallop, B.D. et al., 1989, "Transformation of mean star places
* from FK4 B1950.0 to FK5 J2000.0 using matrices in 6-space".
* Astron.J. 97, 274.
*
* This revision: 2018 January 11
*
* SOFA release 2021-05-12
*
* Copyright (C) 2021 IAU SOFA Board. See notes at end.
*
*-----------------------------------------------------------------------
IMPLICIT NONE
DOUBLE PRECISION R1950, D1950, DR1950, DD1950, P1950, V1950,
: R2000, D2000, DR2000, DD2000, P2000, V2000
* 2Pi
DOUBLE PRECISION D2PI
PARAMETER ( D2PI = 6.283185307179586476925287D0 )
* Radians per year to arcsec per century
DOUBLE PRECISION PMF
PARAMETER ( PMF = 100D0*60D0*60D0*360D0/D2PI )
* Small number to avoid arithmetic problems
DOUBLE PRECISION TINY
PARAMETER ( TINY = 1D-30 )
* Miscellaneous
DOUBLE PRECISION R, D, UR, UD, PX, RV, PXVF, W, RD
INTEGER L, K, J, I
* Pv-vectors
DOUBLE PRECISION R0(3,2), PV1(3,2), PV2(3,2), PV3(3,2)
* Functions
DOUBLE PRECISION iau_ANP
*
* CANONICAL CONSTANTS (Seidelmann 1992)
*
* Km per sec to AU per tropical century
* = 86400 * 36524.2198782 / 149597870.7
DOUBLE PRECISION VF
PARAMETER ( VF = 21.095D0 )
* Constant pv-vector (cf. Seidelmann 3.591-2, vectors A and Adot)
DOUBLE PRECISION A(3,2)
DATA A / -1.62557D-6, -0.31919D-6, -0.13843D-6,
: +1.245D-3, -1.580D-3, -0.659D-3 /
* 3x2 matrix of pv-vectors (cf. Seidelmann 3.591-4, matrix M)
DOUBLE PRECISION EM(3,2,3,2)
DATA EM /
: +0.9999256782D0, -0.0111820611D0, -0.0048579477D0,
: +0.00000242395018D0, -0.00000002710663D0, -0.00000001177656D0,
:
: +0.0111820610D0, +0.9999374784D0, -0.0000271765D0,
: +0.00000002710663D0, +0.00000242397878D0, -0.00000000006587D0,
:
: +0.0048579479D0, -0.0000271474D0, +0.9999881997D0,
: +0.00000001177656D0, -0.00000000006582D0, +0.00000242410173D0,
:
: -0.000551D0, -0.238565D0, +0.435739D0,
: +0.99994704D0, -0.01118251D0, -0.00485767D0,
:
: +0.238514D0, -0.002667D0, -0.008541D0,
: +0.01118251D0, +0.99995883D0, -0.00002718D0,
:
: -0.435623D0, +0.012254D0, +0.002117D0,
: +0.00485767D0, -0.00002714D0, +1.00000956D0
: /
* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
* The FK4 data (units radians and arcsec per tropical century).
R = R1950
D = D1950
UR = DR1950*PMF
UD = DD1950*PMF
PX = P1950
RV = V1950
* Express as a pv-vector.
PXVF = PX*VF
W = RV*PXVF
CALL iau_S2PV ( R, D, 1D0, UR, UD, W, R0 )
* Allow for E-terms (cf. Seidelmann 3.591-2).
CALL iau_PVMPV ( R0, A, PV1 )
CALL iau_PDP ( R0, A, W )
CALL iau_SXP ( W, R0, PV2 )
CALL iau_PDP ( R0, A(1,2), W )
CALL iau_SXP ( W, R0, PV2(1,2) )
CALL iau_PVPPV ( PV1, PV2, PV3 )
* Convert pv-vector to Fricke system (cf. Seidelmann 3.591-3).
DO 4 L = 1,2
DO 3 K=1,3
W = 0D0
DO 2 J=1,2
DO 1 I=1,3
W = W + EM(I,J,K,L)*PV3(I,J)
1 CONTINUE
2 CONTINUE
PV1(K,L) = W
3 CONTINUE
4 CONTINUE
* Revert to catalog form.
CALL iau_PV2S ( PV1, R, D, W, UR, UD, RD )
IF ( PX.GT.TINY ) THEN
RV = RD/PXVF
PX = PX/W
END IF
* Return the results.
R2000 = iau_ANP(R)
D2000 = D
DR2000 = UR/PMF
DD2000 = UD/PMF
V2000 = RV
P2000 = PX
* Finished.
*+----------------------------------------------------------------------
*
* Copyright (C) 2021
* Standards Of Fundamental Astronomy Board
* of the International Astronomical Union.
*
* =====================
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* =====================
*
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*-----------------------------------------------------------------------
END