#include "erfa.h" double eraEect00(double date1, double date2) /* ** - - - - - - - - - - ** e r a E e c t 0 0 ** - - - - - - - - - - ** ** Equation of the equinoxes complementary terms, consistent with ** IAU 2000 resolutions. ** ** 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: ** eraFal03 mean anomaly of the Moon ** eraFalp03 mean anomaly of the Sun ** eraFaf03 mean argument of the latitude of the Moon ** eraFad03 mean elongation of the Moon from the Sun ** eraFaom03 mean longitude of the Moon's ascending node ** eraFave03 mean longitude of Venus ** eraFae03 mean longitude of Earth ** eraFapa03 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) ** ** Copyright (C) 2013-2015, NumFOCUS Foundation. ** Derived, with permission, from the SOFA library. See notes at end of file. */ { /* 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 - ERFA_DJ00) + date2) / ERFA_DJC; /* Fundamental Arguments (from IERS Conventions 2003) */ /* Mean anomaly of the Moon. */ fa[0] = eraFal03(t); /* Mean anomaly of the Sun. */ fa[1] = eraFalp03(t); /* Mean longitude of the Moon minus that of the ascending node. */ fa[2] = eraFaf03(t); /* Mean elongation of the Moon from the Sun. */ fa[3] = eraFad03(t); /* Mean longitude of the ascending node of the Moon. */ fa[4] = eraFaom03(t); /* Mean longitude of Venus. */ fa[5] = eraFave03(t); /* Mean longitude of Earth. */ fa[6] = eraFae03(t); /* General precession in longitude. */ fa[7] = eraFapa03(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 ) * ERFA_DAS2R; return eect; } /*---------------------------------------------------------------------- ** ** ** Copyright (C) 2013-2015, NumFOCUS Foundation. ** All rights reserved. ** ** This library is derived, with permission, from the International ** Astronomical Union's "Standards of Fundamental Astronomy" library, ** available from http://www.iausofa.org. ** ** The ERFA version is intended to retain identical functionality to ** the SOFA library, but made distinct through different function and ** file names, as set out in the SOFA license conditions. The SOFA ** original has a role as a reference standard for the IAU and IERS, ** and consequently redistribution is permitted only in its unaltered ** state. The ERFA version is not subject to this restriction and ** therefore can be included in distributions which do not support the ** concept of "read only" software. ** ** Although the intent is to replicate the SOFA API (other than ** replacement of prefix names) and results (with the exception of ** bugs; any that are discovered will be fixed), SOFA is not ** responsible for any errors found in this version of the library. ** ** If you wish to acknowledge the SOFA heritage, please acknowledge ** that you are using a library derived from SOFA, rather than SOFA ** itself. ** ** ** TERMS AND CONDITIONS ** ** Redistribution and use in source and binary forms, with or without ** modification, are permitted provided that the following conditions ** are met: ** ** 1 Redistributions of source code must retain the above copyright ** notice, this list of conditions and the following disclaimer. ** ** 2 Redistributions in binary form must reproduce the above copyright ** notice, this list of conditions and the following disclaimer in ** the documentation and/or other materials provided with the ** distribution. ** ** 3 Neither the name of the Standards Of Fundamental Astronomy Board, ** the International Astronomical Union nor the names of its ** contributors may be used to endorse or promote products derived ** from this software without specific prior written permission. ** ** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT ** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS ** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE ** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, ** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, ** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; ** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT ** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ** POSSIBILITY OF SUCH DAMAGE. ** */