DOUBLE PRECISION FUNCTION iau_EECT00 ( DATE1, DATE2 ) *+ * - - - - - - - - - - - * i a u _ E E C T 0 0 * - - - - - - - - - - - * * Equation of the equinoxes complementary terms, consistent with * IAU 2000 resolutions. * * This routine is part of the International Astronomical Union's * SOFA (Standards of Fundamental Astronomy) software collection. * * Status: canonical model. * * Given: * DATE1,DATE2 d TT as a 2-part Julian Date (Note 1) * * Returned: * iau_EECT00 d 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 * * 2450123.7D0 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 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 routine computes CT in the above expression, * compatible with IAU 2000 resolutions (Capitaine et al., 2002, and * IERS Conventions 2003). * * Called: * iau_FAL03 mean anomaly of the Moon * iau_FALP03 mean anomaly of the Sun * iau_FAF03 mean argument of the latitude of the Moon * iau_FAD03 mean elongation of the Moon from the Sun * iau_FAOM03 mean longitude of the Moon's ascending node * iau_FAVE03 mean longitude of Venus * iau_FAE03 mean longitude of Earth * iau_FAPA03 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: 2017 October 23 * * SOFA release 2023-10-11 * * Copyright (C) 2023 IAU SOFA Board. See notes at end. * *----------------------------------------------------------------------- IMPLICIT NONE DOUBLE PRECISION DATE1, DATE2 * Arcseconds to radians DOUBLE PRECISION DAS2R PARAMETER ( DAS2R = 4.848136811095359935899141D-6 ) * Reference epoch (J2000.0), JD DOUBLE PRECISION DJ00 PARAMETER ( DJ00 = 2451545D0 ) * Days per Julian century DOUBLE PRECISION DJC PARAMETER ( DJC = 36525D0 ) * Time since J2000.0, in Julian centuries DOUBLE PRECISION T * Miscellaneous INTEGER I, J DOUBLE PRECISION A, S0, S1 DOUBLE PRECISION iau_FAL03, iau_FALP03, iau_FAF03, : iau_FAD03, iau_FAOM03, iau_FAVE03, iau_FAE03, : iau_FAPA03 * Fundamental arguments DOUBLE PRECISION FA(14) * ----------------------------------------- * The series for the EE complementary terms * ----------------------------------------- * Number of terms in the series INTEGER NE0, NE1 PARAMETER ( NE0=33, NE1=1 ) * Coefficients of l,l',F,D,Om,LVe,LE,pA INTEGER KE0 ( 8, NE0 ), : KE1 ( 8, NE1 ) * Sine and cosine coefficients DOUBLE PRECISION SE0 ( 2, NE0 ), : SE1 ( 2, NE1 ) * Argument coefficients for t^0 DATA ( ( KE0(I,J), I=1,8), J=1,10 ) / : 0, 0, 0, 0, 1, 0, 0, 0, : 0, 0, 0, 0, 2, 0, 0, 0, : 0, 0, 2, -2, 3, 0, 0, 0, : 0, 0, 2, -2, 1, 0, 0, 0, : 0, 0, 2, -2, 2, 0, 0, 0, : 0, 0, 2, 0, 3, 0, 0, 0, : 0, 0, 2, 0, 1, 0, 0, 0, : 0, 0, 0, 0, 3, 0, 0, 0, : 0, 1, 0, 0, 1, 0, 0, 0, : 0, 1, 0, 0, -1, 0, 0, 0 / DATA ( ( KE0(I,J), I=1,8), J=11,20 ) / : 1, 0, 0, 0, -1, 0, 0, 0, : 1, 0, 0, 0, 1, 0, 0, 0, : 0, 1, 2, -2, 3, 0, 0, 0, : 0, 1, 2, -2, 1, 0, 0, 0, : 0, 0, 4, -4, 4, 0, 0, 0, : 0, 0, 1, -1, 1, -8, 12, 0, : 0, 0, 2, 0, 0, 0, 0, 0, : 0, 0, 2, 0, 2, 0, 0, 0, : 1, 0, 2, 0, 3, 0, 0, 0, : 1, 0, 2, 0, 1, 0, 0, 0 / DATA ( ( KE0(I,J), I=1,8), J=21,30 ) / : 0, 0, 2, -2, 0, 0, 0, 0, : 0, 1, -2, 2, -3, 0, 0, 0, : 0, 1, -2, 2, -1, 0, 0, 0, : 0, 0, 0, 0, 0, 8,-13, -1, : 0, 0, 0, 2, 0, 0, 0, 0, : 2, 0, -2, 0, -1, 0, 0, 0, : 1, 0, 0, -2, 1, 0, 0, 0, : 0, 1, 2, -2, 2, 0, 0, 0, : 1, 0, 0, -2, -1, 0, 0, 0, : 0, 0, 4, -2, 4, 0, 0, 0 / DATA ( ( KE0(I,J), I=1,8), J=31,NE0 ) / : 0, 0, 2, -2, 4, 0, 0, 0, : 1, 0, -2, 0, -3, 0, 0, 0, : 1, 0, -2, 0, -1, 0, 0, 0 / * Argument coefficients for t^1 DATA ( ( KE1(I,J), I=1,8), J=1,NE1 ) / : 0, 0, 0, 0, 1, 0, 0, 0 / * Sine and cosine coefficients for t^0 DATA ( ( SE0(I,J), I=1,2), J = 1, 10 ) / : +2640.96D-6, -0.39D-6, : +63.52D-6, -0.02D-6, : +11.75D-6, +0.01D-6, : +11.21D-6, +0.01D-6, : -4.55D-6, +0.00D-6, : +2.02D-6, +0.00D-6, : +1.98D-6, +0.00D-6, : -1.72D-6, +0.00D-6, : -1.41D-6, -0.01D-6, : -1.26D-6, -0.01D-6 / DATA ( ( SE0(I,J), I=1,2), J = 11, 20 ) / : -0.63D-6, +0.00D-6, : -0.63D-6, +0.00D-6, : +0.46D-6, +0.00D-6, : +0.45D-6, +0.00D-6, : +0.36D-6, +0.00D-6, : -0.24D-6, -0.12D-6, : +0.32D-6, +0.00D-6, : +0.28D-6, +0.00D-6, : +0.27D-6, +0.00D-6, : +0.26D-6, +0.00D-6 / DATA ( ( SE0(I,J), I=1,2), J = 21, 30 ) / : -0.21D-6, +0.00D-6, : +0.19D-6, +0.00D-6, : +0.18D-6, +0.00D-6, : -0.10D-6, +0.05D-6, : +0.15D-6, +0.00D-6, : -0.14D-6, +0.00D-6, : +0.14D-6, +0.00D-6, : -0.14D-6, +0.00D-6, : +0.14D-6, +0.00D-6, : +0.13D-6, +0.00D-6 / DATA ( ( SE0(I,J), I=1,2), J = 31, NE0 ) / : -0.11D-6, +0.00D-6, : +0.11D-6, +0.00D-6, : +0.11D-6, +0.00D-6 / * Sine and cosine coefficients for t^1 DATA ( ( SE1(I,J), I=1,2), J = 1, NE1 ) / : -0.87D-6, +0.00D-6 / * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * 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(1) = iau_FAL03 ( T ) * Mean anomaly of the Sun. FA(2) = iau_FALP03 ( T ) * Mean longitude of the Moon minus that of the ascending node. FA(3) = iau_FAF03 ( T ) * Mean elongation of the Moon from the Sun. FA(4) = iau_FAD03 ( T ) * Mean longitude of the ascending node of the Moon. FA(5) = iau_FAOM03 ( T ) * Mean longitude of Venus. FA(6) = iau_FAVE03 ( T ) * Mean longitude of Earth. FA(7) = iau_FAE03 ( T ) * General precession in longitude. FA(8) = iau_FAPA03 ( T ) * Evaluate the EE complementary terms. S0 = 0D0 S1 = 0D0 DO 2 I = NE0,1,-1 A = 0D0 DO 1 J=1,8 A = A + DBLE(KE0(J,I))*FA(J) 1 CONTINUE S0 = S0 + ( SE0(1,I)*SIN(A) + SE0(2,I)*COS(A) ) 2 CONTINUE DO 4 I = NE1,1,-1 A = 0D0 DO 3 J=1,8 A = A + DBLE(KE1(J,I))*FA(J) 3 CONTINUE S1 = S1 + ( SE1(1,I)*SIN(A) + SE1(2,I)*COS(A) ) 4 CONTINUE iau_EECT00 = ( S0 + S1 * T ) * DAS2R * Finished. *+---------------------------------------------------------------------- * * Copyright (C) 2023 * 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. 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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 * *----------------------------------------------------------------------- END