#include "sofa.h"
#include "sofam.h"
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", Astron.Astrophys., 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)
**
** This revision: 2021 May 11
**
** SOFA release 2021-05-12
**
** Copyright (C) 2021 IAU SOFA Board. See notes at end.
*/
{
/* Time since J2000.0, in Julian centuries */
double t;
/* Miscellaneous */
int i, j;
double a, s0, s1;
/* Fundamental arguments */
double fa[14];
/* Returned value. */
double eect;
/* ----------------------------------------- */
/* The series for the EE complementary terms */
/* ----------------------------------------- */
typedef struct {
int nfa[8]; /* coefficients of l,l',F,D,Om,LVe,LE,pA */
double s, c; /* sine and cosine coefficients */
} TERM;
/* Terms of order t^0 */
static const TERM e0[] = {
/* 1-10 */
{{ 0, 0, 0, 0, 1, 0, 0, 0}, 2640.96e-6, -0.39e-6 },
{{ 0, 0, 0, 0, 2, 0, 0, 0}, 63.52e-6, -0.02e-6 },
{{ 0, 0, 2, -2, 3, 0, 0, 0}, 11.75e-6, 0.01e-6 },
{{ 0, 0, 2, -2, 1, 0, 0, 0}, 11.21e-6, 0.01e-6 },
{{ 0, 0, 2, -2, 2, 0, 0, 0}, -4.55e-6, 0.00e-6 },
{{ 0, 0, 2, 0, 3, 0, 0, 0}, 2.02e-6, 0.00e-6 },
{{ 0, 0, 2, 0, 1, 0, 0, 0}, 1.98e-6, 0.00e-6 },
{{ 0, 0, 0, 0, 3, 0, 0, 0}, -1.72e-6, 0.00e-6 },
{{ 0, 1, 0, 0, 1, 0, 0, 0}, -1.41e-6, -0.01e-6 },
{{ 0, 1, 0, 0, -1, 0, 0, 0}, -1.26e-6, -0.01e-6 },
/* 11-20 */
{{ 1, 0, 0, 0, -1, 0, 0, 0}, -0.63e-6, 0.00e-6 },
{{ 1, 0, 0, 0, 1, 0, 0, 0}, -0.63e-6, 0.00e-6 },
{{ 0, 1, 2, -2, 3, 0, 0, 0}, 0.46e-6, 0.00e-6 },
{{ 0, 1, 2, -2, 1, 0, 0, 0}, 0.45e-6, 0.00e-6 },
{{ 0, 0, 4, -4, 4, 0, 0, 0}, 0.36e-6, 0.00e-6 },
{{ 0, 0, 1, -1, 1, -8, 12, 0}, -0.24e-6, -0.12e-6 },
{{ 0, 0, 2, 0, 0, 0, 0, 0}, 0.32e-6, 0.00e-6 },
{{ 0, 0, 2, 0, 2, 0, 0, 0}, 0.28e-6, 0.00e-6 },
{{ 1, 0, 2, 0, 3, 0, 0, 0}, 0.27e-6, 0.00e-6 },
{{ 1, 0, 2, 0, 1, 0, 0, 0}, 0.26e-6, 0.00e-6 },
/* 21-30 */
{{ 0, 0, 2, -2, 0, 0, 0, 0}, -0.21e-6, 0.00e-6 },
{{ 0, 1, -2, 2, -3, 0, 0, 0}, 0.19e-6, 0.00e-6 },
{{ 0, 1, -2, 2, -1, 0, 0, 0}, 0.18e-6, 0.00e-6 },
{{ 0, 0, 0, 0, 0, 8,-13, -1}, -0.10e-6, 0.05e-6 },
{{ 0, 0, 0, 2, 0, 0, 0, 0}, 0.15e-6, 0.00e-6 },
{{ 2, 0, -2, 0, -1, 0, 0, 0}, -0.14e-6, 0.00e-6 },
{{ 1, 0, 0, -2, 1, 0, 0, 0}, 0.14e-6, 0.00e-6 },
{{ 0, 1, 2, -2, 2, 0, 0, 0}, -0.14e-6, 0.00e-6 },
{{ 1, 0, 0, -2, -1, 0, 0, 0}, 0.14e-6, 0.00e-6 },
{{ 0, 0, 4, -2, 4, 0, 0, 0}, 0.13e-6, 0.00e-6 },
/* 31-33 */
{{ 0, 0, 2, -2, 4, 0, 0, 0}, -0.11e-6, 0.00e-6 },
{{ 1, 0, -2, 0, -3, 0, 0, 0}, 0.11e-6, 0.00e-6 },
{{ 1, 0, -2, 0, -1, 0, 0, 0}, 0.11e-6, 0.00e-6 }
};
/* Terms of order t^1 */
static const TERM e1[] = {
{{ 0, 0, 0, 0, 1, 0, 0, 0}, -0.87e-6, 0.00e-6 }
};
/* Number of terms in the series */
const int NE0 = (int) (sizeof e0 / sizeof (TERM));
const int NE1 = (int) (sizeof e1 / sizeof (TERM));
/* ------------------------------------------------------------------ */
/* Interval between fundamental epoch J2000.0 and current date (JC). */
t = ((date1 - DJ00) + date2) / DJC;
/* Fundamental Arguments (from IERS Conventions 2003) */
/* Mean anomaly of the Moon. */
fa[0] = iauFal03(t);
/* Mean anomaly of the Sun. */
fa[1] = iauFalp03(t);
/* Mean longitude of the Moon minus that of the ascending node. */
fa[2] = iauFaf03(t);
/* Mean elongation of the Moon from the Sun. */
fa[3] = iauFad03(t);
/* Mean longitude of the ascending node of the Moon. */
fa[4] = iauFaom03(t);
/* Mean longitude of Venus. */
fa[5] = iauFave03(t);
/* Mean longitude of Earth. */
fa[6] = iauFae03(t);
/* General precession in longitude. */
fa[7] = iauFapa03(t);
/* Evaluate the EE complementary terms. */
s0 = 0.0;
s1 = 0.0;
for (i = NE0-1; i >= 0; i--) {
a = 0.0;
for (j = 0; j < 8; j++) {
a += (double)(e0[i].nfa[j]) * fa[j];
}
s0 += e0[i].s * sin(a) + e0[i].c * cos(a);
}
for (i = NE1-1; i >= 0; i--) {
a = 0.0;
for (j = 0; j < 8; j++) {
a += (double)(e1[i].nfa[j]) * fa[j];
}
s1 += e1[i].s * sin(a) + e1[i].c * cos(a);
}
eect = (s0 + s1 * t ) * DAS2R;
return eect;
/* Finished. */
/*----------------------------------------------------------------------
**
** Copyright (C) 2021
** Standards Of Fundamental Astronomy Board
** of the International Astronomical Union.
**
** =====================
** SOFA Software License
** =====================
**
** NOTICE TO USER:
**
** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX 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 names of all routines in your derived work shall not
** include the prefix "iau" or "sofa" or trivial modifications
** thereof such as changes of case.
**
** 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. You shall not cause the SOFA software to be brought into
** disrepute, either by misuse, or use for inappropriate tasks, or
** by inappropriate modification.
**
** 5. 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.
**
** 6. 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.
*
** In any published work or commercial product which uses the SOFA
** software directly, acknowledgement (see www.iausofa.org) is
** appreciated.
**
** 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
**
**--------------------------------------------------------------------*/
}