DOUBLE PRECISION FUNCTION iau_S00 ( DATE1, DATE2, X, Y ) *+ * - - - - - - - - * i a u _ S 0 0 * - - - - - - - - * * The CIO locator s, positioning the Celestial Intermediate Origin on * the equator of the Celestial Intermediate Pole, given the CIP's X,Y * coordinates. Compatible with IAU 2000A precession-nutation. * * 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) * X,Y d CIP coordinates (Note 3) * * Returned: * iau_S00 d the CIO locator s in radians (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 CIO locator s is the difference between the right ascensions * of the same point in two systems: the two systems are the GCRS * and the CIP,CIO, and the point is the ascending node of the * CIP equator. The quantity s remains below 0.1 arcsecond * throughout 1900-2100. * * 3) The series used to compute s is in fact for s+XY/2, where X and Y * are the x and y components of the CIP unit vector; this series is * more compact than a direct series for s would be. This routine * requires X,Y to be supplied by the caller, who is responsible for * providing values that are consistent with the supplied date. * * 4) The model is consistent with the IAU 2000A precession-nutation. * * 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., Chapront, J., Lambert, S. and Wallace, P., * "Expressions for the Celestial Intermediate Pole and Celestial * Ephemeris Origin consistent with the IAU 2000A precession-nutation * model", Astron.Astrophys. 400, 1145-1154 (2003) * * n.b. The celestial ephemeris origin (CEO) was renamed "celestial * intermediate origin" (CIO) by IAU 2006 Resolution 2. * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * * This revision: 2010 January 18 * * SOFA release 2021-01-25 * * Copyright (C) 2021 IAU SOFA Board. See notes at end. * *----------------------------------------------------------------------- IMPLICIT NONE DOUBLE PRECISION DATE1, DATE2, X, Y * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * 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, S2, S3, S4, S5 DOUBLE PRECISION iau_FAL03, iau_FALP03, iau_FAF03, : iau_FAD03, iau_FAOM03, iau_FAVE03, iau_FAE03, : iau_FAPA03 * Fundamental arguments DOUBLE PRECISION FA(8) * --------------------- * The series for s+XY/2 * --------------------- * Number of terms in the series INTEGER NSP, NS0, NS1, NS2, NS3, NS4 PARAMETER ( NSP=6, NS0=33, NS1=3, NS2=25, NS3=4, NS4=1 ) * Polynomial coefficients DOUBLE PRECISION SP ( NSP ) * Coefficients of l,l',F,D,Om,LVe,LE,pA INTEGER KS0 ( 8, NS0 ), : KS1 ( 8, NS1 ), : KS2 ( 8, NS2 ), : KS3 ( 8, NS3 ), : KS4 ( 8, NS4 ) * Sine and cosine coefficients DOUBLE PRECISION SS0 ( 2, NS0 ), : SS1 ( 2, NS1 ), : SS2 ( 2, NS2 ), : SS3 ( 2, NS3 ), : SS4 ( 2, NS4 ) * Polynomial coefficients DATA SP / 94 D-6, : 3808.35 D-6, : -119.94 D-6, : -72574.09 D-6, : 27.70 D-6, : 15.61 D-6 / * Argument coefficients for t^0 DATA ( ( KS0(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 ( ( KS0(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 ( ( KS0(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, : 0, 1, 2, -2, 2, 0, 0, 0, : 1, 0, 0, -2, 1, 0, 0, 0, : 1, 0, 0, -2, -1, 0, 0, 0, : 0, 0, 4, -2, 4, 0, 0, 0 / DATA ( ( KS0(I,J), I=1,8), J=31,NS0 ) / : 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 ( ( KS1(I,J), I=1,8), J=1,NS1 ) / : 0, 0, 0, 0, 2, 0, 0, 0, : 0, 0, 0, 0, 1, 0, 0, 0, : 0, 0, 2, -2, 3, 0, 0, 0 / * Argument coefficients for t^2 DATA ( ( KS2(I,J), I=1,8), J=1,10 ) / : 0, 0, 0, 0, 1, 0, 0, 0, : 0, 0, 2, -2, 2, 0, 0, 0, : 0, 0, 2, 0, 2, 0, 0, 0, : 0, 0, 0, 0, 2, 0, 0, 0, : 0, 1, 0, 0, 0, 0, 0, 0, : 1, 0, 0, 0, 0, 0, 0, 0, : 0, 1, 2, -2, 2, 0, 0, 0, : 0, 0, 2, 0, 1, 0, 0, 0, : 1, 0, 2, 0, 2, 0, 0, 0, : 0, 1, -2, 2, -2, 0, 0, 0 / DATA ( ( KS2(I,J), I=1,8), J=11,20 ) / : 1, 0, 0, -2, 0, 0, 0, 0, : 0, 0, 2, -2, 1, 0, 0, 0, : 1, 0, -2, 0, -2, 0, 0, 0, : 0, 0, 0, 2, 0, 0, 0, 0, : 1, 0, 0, 0, 1, 0, 0, 0, : 1, 0, -2, -2, -2, 0, 0, 0, : 1, 0, 0, 0, -1, 0, 0, 0, : 1, 0, 2, 0, 1, 0, 0, 0, : 2, 0, 0, -2, 0, 0, 0, 0, : 2, 0, -2, 0, -1, 0, 0, 0 / DATA ( ( KS2(I,J), I=1,8), J=21,NS2 ) / : 0, 0, 2, 2, 2, 0, 0, 0, : 2, 0, 2, 0, 2, 0, 0, 0, : 2, 0, 0, 0, 0, 0, 0, 0, : 1, 0, 2, -2, 2, 0, 0, 0, : 0, 0, 2, 0, 0, 0, 0, 0 / * Argument coefficients for t^3 DATA ( ( KS3(I,J), I=1,8), J=1,NS3 ) / : 0, 0, 0, 0, 1, 0, 0, 0, : 0, 0, 2, -2, 2, 0, 0, 0, : 0, 0, 2, 0, 2, 0, 0, 0, : 0, 0, 0, 0, 2, 0, 0, 0 / * Argument coefficients for t^4 DATA ( ( KS4(I,J), I=1,8), J=1,NS4 ) / : 0, 0, 0, 0, 1, 0, 0, 0 / * Sine and cosine coefficients for t^0 DATA ( ( SS0(I,J), I=1,2), J=1,10 ) / : -2640.73D-6, +0.39D-6, : -63.53D-6, +0.02D-6, : -11.75D-6, -0.01D-6, : -11.21D-6, -0.01D-6, : +4.57D-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 ( ( SS0(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 ( ( SS0(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 ( ( SS0(I,J), I=1,2), J=31,NS0 ) / : +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 ( ( SS1(I,J), I=1,2), J=1,NS1 ) / : -0.07D-6, +3.57D-6, : +1.71D-6, -0.03D-6, : 0.00D-6, +0.48D-6 / * Sine and cosine coefficients for t^2 DATA ( ( SS2(I,J), I=1,2), J=1,10 ) / : +743.53D-6, -0.17D-6, : +56.91D-6, +0.06D-6, : +9.84D-6, -0.01D-6, : -8.85D-6, +0.01D-6, : -6.38D-6, -0.05D-6, : -3.07D-6, 0.00D-6, : +2.23D-6, 0.00D-6, : +1.67D-6, 0.00D-6, : +1.30D-6, 0.00D-6, : +0.93D-6, 0.00D-6 / DATA ( ( SS2(I,J), I=1,2), J=11,20 ) / : +0.68D-6, 0.00D-6, : -0.55D-6, 0.00D-6, : +0.53D-6, 0.00D-6, : -0.27D-6, 0.00D-6, : -0.27D-6, 0.00D-6, : -0.26D-6, 0.00D-6, : -0.25D-6, 0.00D-6, : +0.22D-6, 0.00D-6, : -0.21D-6, 0.00D-6, : +0.20D-6, 0.00D-6 / DATA ( ( SS2(I,J), I=1,2), J=21,NS2 ) / : +0.17D-6, 0.00D-6, : +0.13D-6, 0.00D-6, : -0.13D-6, 0.00D-6, : -0.12D-6, 0.00D-6, : -0.11D-6, 0.00D-6 / * Sine and cosine coefficients for t^3 DATA ( ( SS3(I,J), I=1,2), J=1,NS3 ) / : +0.30D-6, -23.51D-6, : -0.03D-6, -1.39D-6, : -0.01D-6, -0.24D-6, : 0.00D-6, +0.22D-6 / * Sine and cosine coefficients for t^4 DATA ( ( SS4(I,J), I=1,2), J=1,NS4 ) / : -0.26D-6, -0.01D-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 s. S0 = SP(1) S1 = SP(2) S2 = SP(3) S3 = SP(4) S4 = SP(5) S5 = SP(6) DO 2 I = NS0,1,-1 A = 0D0 DO 1 J=1,8 A = A + DBLE(KS0(J,I))*FA(J) 1 CONTINUE S0 = S0 + ( SS0(1,I)*SIN(A) + SS0(2,I)*COS(A) ) 2 CONTINUE DO 4 I = NS1,1,-1 A = 0D0 DO 3 J=1,8 A = A + DBLE(KS1(J,I))*FA(J) 3 CONTINUE S1 = S1 + ( SS1(1,I)*SIN(A) + SS1(2,I)*COS(A) ) 4 CONTINUE DO 6 I = NS2,1,-1 A = 0D0 DO 5 J=1,8 A = A + DBLE(KS2(J,I))*FA(J) 5 CONTINUE S2 = S2 + ( SS2(1,I)*SIN(A) + SS2(2,I)*COS(A) ) 6 CONTINUE DO 8 I = NS3,1,-1 A = 0D0 DO 7 J=1,8 A = A + DBLE(KS3(J,I))*FA(J) 7 CONTINUE S3 = S3 + ( SS3(1,I)*SIN(A) + SS3(2,I)*COS(A) ) 8 CONTINUE DO 10 I = NS4,1,-1 A = 0D0 DO 9 J=1,8 A = A + DBLE(KS4(J,I))*FA(J) 9 CONTINUE S4 = S4 + ( SS4(1,I)*SIN(A) + SS4(2,I)*COS(A) ) 10 CONTINUE iau_S00 = ( S0 + : ( S1 + : ( S2 + : ( S3 + : ( S4 + : S5 * T ) * T ) * T ) * T ) * T ) * DAS2R - X*Y/2D0 * 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 * *----------------------------------------------------------------------- END