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 McCarthy, * 2002). * * Called: * iau_ANPM normalize angle into range +/- pi * * References: * * IAU Resolution C7, Recommendation 3 (1994) * * Capitaine, N. & Gontier, A.-M., Astron. Astrophys., 275, * 645-650 (1993) * * Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions for * the Earth Rotation Angle and Sidereal Time consistent with the IAU * 2000A precession-nutation model", in preparation (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 * 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 DOUBLE PRECISION iau_ANPM * 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,LMe,LVe,LE,LMa,LJu,LSa,LU,LN,pA INTEGER KE0 ( 14, NE0 ), : KE1 ( 14, NE1 ) * Sine and cosine coefficients DOUBLE PRECISION SE0 ( 2, NE0 ), : SE1 ( 2, NE1 ) * Argument coefficients for t^0 DATA ( ( KE0(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 ( ( KE0(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 ( ( KE0(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, : 1, 0, 0, -2, 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, : 0, 0, 4, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0 / DATA ( ( KE0(I,J), I=1,14), J = 31, NE0 ) / : 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 ( ( KE1(I,J), I=1,14), J = 1, NE1 ) / : 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 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-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 the EE complementary terms. S0 = 0D0 S1 = 0D0 DO 2 I = NE0,1,-1 A = 0D0 DO 1 J=1,14 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=1,14 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) 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