DOUBLE PRECISION FUNCTION iau_S00 ( DATE1, DATE2, X, Y ) *+ * - - - - - - - - * i a u _ S 0 0 * - - - - - - - - * * The quantity s, positioning the Celestial Ephemeris Origin on the * equator of the Celestial Intermediate Pole, given the CIP's X,Y * coordinates. * * 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 quantity 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 quantity s is the difference between the right ascensions * of the same point in two frames. The two systems are the GCRS * and the CIP,CEO, and the point is the ascending node of the * respective equators. The quantity s remains a small fraction of * 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. * * Called: * iau_ANPM normalize angle into range +/- pi * * 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", submitted to A&A (2002) * * McCarthy, D.D., IERS Conventions 2000, Chapter 5 (2002). * * This revision: 2003 January 14 * * Copyright (C) 2003 IAU SOFA Review Board. See notes at end. * *----------------------------------------------------------------------- IMPLICIT NONE DOUBLE PRECISION DATE1, DATE2, X, Y * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * 2Pi DOUBLE PRECISION D2PI PARAMETER ( D2PI = 6.283185307179586476925287D0 ) * Arcseconds to radians DOUBLE PRECISION DAS2R PARAMETER ( DAS2R = 4.848136811095359935899141D-6 ) * Reference epoch (J2000), JD DOUBLE PRECISION DJ0 PARAMETER ( DJ0 = 2451545D0 ) * Days per Julian century DOUBLE PRECISION DJC PARAMETER ( DJC = 36525D0 ) * Time since J2000, in Julian centuries DOUBLE PRECISION T * Miscellaneous INTEGER I, J DOUBLE PRECISION A, S0, S1, S2, S3, S4, S5 DOUBLE PRECISION iau_ANPM * Fundamental arguments DOUBLE PRECISION FA(14) * --------------------- * 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,LMe,LVe,LE,LMa,LJu,LSa,LU,LN,pA INTEGER KS0 ( 14, NS0 ), : KS1 ( 14, NS1 ), : KS2 ( 14, NS2 ), : KS3 ( 14, NS3 ), : KS4 ( 14, 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=1,14), J = 1, 10 ) / : 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 0, 2, -2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 0, 2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 0, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 0, 2, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0 / DATA ( ( KS0(I,J), I=1,14), J = 11, 20 ) / : 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 1, 2, -2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 1, 2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 0, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 0, 1, -1, 1, 0, -8, 12, 0, 0, 0, 0, 0, 0, : 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 1, 0, 2, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 / DATA ( ( KS0(I,J), I=1,14), J = 21, 30 ) / : 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 1, -2, 2, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 1, -2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 0, 0, 0, 0, 0, 8,-13, 0, 0, 0, 0, 0, -1, : 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 2, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 1, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 1, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 1, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 0, 4, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0 / DATA ( ( KS0(I,J), I=1,14), J = 31, NS0 ) / : 0, 0, 2, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 1, 0, -2, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 1, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0 / * Argument coefficients for t^1 DATA ( ( KS1(I,J), I=1,14), J = 1, NS1 ) / : 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 0, 2, -2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0 / * Argument coefficients for t^2 DATA ( ( KS2(I,J), I=1,14), J = 1, 10 ) / : 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 0, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 1, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 1, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 1, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0 / DATA ( ( KS2(I,J), I=1,14), J = 11, 20 ) / : 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 0, 2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 1, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 1, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 2, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0 / DATA ( ( KS2(I,J), I=1,14), J = 21, NS2 ) / : 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 1, 0, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 / * Argument coefficients for t^3 DATA ( ( KS3(I,J), I=1,14), J = 1, NS3 ) / : 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 0, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0 / * Argument coefficients for t^4 DATA ( ( KS4(I,J), I=1,14), J = 1, NS4 ) / : 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 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-DJ0 ) + DATE2 ) / DJC * Fundamental Arguments (from IERS Conventions 2000) * Mean Anomaly of the Moon. FA(1) = iau_ANPM ( ( 485868.249036D0 + : ( 715923.2178D0 + : ( 31.8792D0 + : ( 0.051635D0 + : ( -0.00024470D0 ) : * T ) * T ) * T ) * T ) * DAS2R : + MOD ( 1325D0*T, 1D0 ) * D2PI ) * Mean Anomaly of the Sun. FA(2) = iau_ANPM ( ( 1287104.793048D0 + : ( 1292581.0481D0 + : ( -0.5532D0 + : ( +0.000136D0 + : ( -0.00001149D0 ) : * T ) * T ) * T ) * T ) * DAS2R : + MOD ( 99D0*T, 1D0 ) * D2PI ) * Mean Longitude of the Moon minus Mean Longitude of the Ascending * Node of the Moon. FA(3) = iau_ANPM ( ( 335779.526232D0 + : ( 295262.8478D0 + : ( -12.7512D0 + : ( -0.001037D0 + : ( 0.00000417D0 ) : * T ) * T ) * T ) * T ) * DAS2R : + MOD ( 1342D0*T, 1D0 ) * D2PI ) * Mean Elongation of the Moon from the Sun. FA(4) = iau_ANPM ( ( 1072260.703692D0 + : ( 1105601.2090D0 + : ( -6.3706D0 + : ( 0.006593D0 + : ( -0.00003169D0 ) : * T ) * T ) * T ) * T ) * DAS2R : + MOD ( 1236D0*T, 1D0 ) * D2PI ) * Mean Longitude of the Ascending Node of the Moon. FA(5) = iau_ANPM ( ( 450160.398036D0 + : ( -482890.5431D0 + : ( 7.4722D0 + : ( 0.007702D0 + : ( -0.00005939D0 ) : * T ) * T ) * T ) * T ) * DAS2R : + MOD ( -5D0*T, 1D0 ) * D2PI ) FA( 6) = iau_ANPM ( 4.402608842D0 + 2608.7903141574D0 * T ) FA( 7) = iau_ANPM ( 3.176146697D0 + 1021.3285546211D0 * T ) FA( 8) = iau_ANPM ( 1.753470314D0 + 628.3075849991D0 * T ) FA( 9) = iau_ANPM ( 6.203480913D0 + 334.0612426700D0 * T ) FA(10) = iau_ANPM ( 0.599546497D0 + 52.9690962641D0 * T ) FA(11) = iau_ANPM ( 0.874016757D0 + 21.3299104960D0 * T ) FA(12) = iau_ANPM ( 5.481293872D0 + 7.4781598567D0 * T ) FA(13) = iau_ANPM ( 5.311886287D0 + 3.8133035638D0 * T ) FA(14) = ( 0.024381750D0 + 0.00000538691D0 * T ) * 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=1,14 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=1,14 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=1,14 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=1,14 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=1,14 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) 2003 * Standards Of Fundamental Astronomy Review 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 Review Board ("the Board"). * * 2. The Software is made available free of charge for use by: * * a) private individuals for non-profit research; and * * b) non-profit educational, academic and research institutions. * * 3. Commercial use of the Software is specifically excluded from the * terms and conditions of this license. Commercial use of the * Software is subject to the prior written agreement of the Board on * terms to be agreed. * * 4. The provision of any version of the 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. * * 5. The user may modify the Software for his/her own purposes. The * user may distribute the modified software provided that the Board * is informed and that a copy of the modified software is made * available to the Board on request. All modifications made by the * user shall be clearly identified to show how the modified software * differs from the original Software, and the name(s) of the * affected routine(s) shall be changed. The original SOFA Software * License text must be present. * * 6. In any published work produced by the user and which includes * results achieved by using the Software, the user shall acknowledge * that the Software was used in producing the information contained * in such publication. * * 7. The user may incorporate or embed the Software into other software * products which he/she may then give away free of charge but not * sell provided the user makes due acknowledgement of the use which * he/she has made of the Software in creating such software * products. Any redistribution of the Software in this way shall be * made under the same terms and conditions under which the user * received it from the SOFA Center. * * 8. The user shall not cause the Software to be brought into * disrepute, either by misuse, or use for inappropriate tasks, or by * inappropriate modification. * * 9. The Software is provided to the user "as is" and the Board makes * no warranty as to its use or performance. The Board does not and * cannot warrant the performance or results which the user may * obtain by using the Software. The Board 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 the Board be liable to the user for any consequential, * incidental, or special damages, including any lost profits or lost * savings, even if a Board representative has been advised of such * damages, or for any claim by any third party. * * Correspondence concerning SOFA software should be addressed as * follows: * * Internet email: sofa@rl.ac.uk * Postal address: IAU SOFA Center * Rutherford Appleton Laboratory * Chilton, Didcot, Oxon OX11 0QX * United Kingdom * * *----------------------------------------------------------------------- END