#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", 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) ** ** This revision: 2009 December 17 ** ** SOFA release 2010-12-01 ** ** Copyright (C) 2010 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; /*---------------------------------------------------------------------- ** ** 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 ** **--------------------------------------------------------------------*/ }