SUBROUTINE iau_PMAT76 ( DATE1, DATE2, RMATP ) *+ * - - - - - - - - - - - * i a u _ P M A T 7 6 * - - - - - - - - - - - * * Precession matrix from J2000.0 to a specified date, IAU 1976 model. * * This routine is part of the International Astronomical Union's * SOFA (Standards of Fundamental Astronomy) software collection. * * Status: support routine. * * Given: * DATE1,DATE2 d ending date, TT (Note 1) * * Returned: * RMATP d(3,3) precession matrix, J2000.0 -> DATE1+DATE2 * * Notes: * * 1) The ending date DATE1+DATE2 is a Julian Date, apportioned * in any convenient way between the arguments DATE1 and DATE2. * 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 matrix operates in the sense V(date) = RMATP * V(J2000), * where the p-vector V(J2000) is with respect to the mean * equatorial triad of epoch J2000.0 and the p-vector V(date) * is with respect to the mean equatorial triad of the given * date. * * 3) Though the matrix method itself is rigorous, the precession * angles are expressed through canonical polynomials which are * valid only for a limited time span. In addition, the IAU 1976 * precession rate is known to be imperfect. The absolute accuracy * of the present formulation is better than 0.1 arcsec from * 1960AD to 2040AD, better than 1 arcsec from 1640AD to 2360AD, * and remains below 3 arcsec for the whole of the period * 500BC to 3000AD. The errors exceed 10 arcsec outside the * range 1200BC to 3900AD, exceed 100 arcsec outside 4200BC to * 5600AD and exceed 1000 arcsec outside 6800BC to 8200AD. * * Called: * iau_PREC76 accumulated precession angles, IAU 1976 * iau_IR initialize r-matrix to identity * iau_RZ rotate around Z-axis * iau_RY rotate around Y-axis * iau_CR copy r-matrix * * References: * * Lieske, J.H., 1979, Astron.Astrophys. 73, 282. * equations (6) & (7), p283. * * Kaplan, G.H., 1981, USNO circular no. 163, pA2. * * This revision: 2009 December 18 * * SOFA release 2023-10-11 * * Copyright (C) 2023 IAU SOFA Board. See notes at end. * *----------------------------------------------------------------------- IMPLICIT NONE DOUBLE PRECISION DATE1, DATE2, RMATP(3,3) * Reference epoch (J2000.0), JD DOUBLE PRECISION DJ00 PARAMETER ( DJ00 = 2451545D0 ) DOUBLE PRECISION ZETA, Z, THETA, WMAT(3,3) * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * Precession Euler angles, J2000.0 to specified date. CALL iau_PREC76 ( DJ00, 0D0, DATE1, DATE2, ZETA, Z, THETA ) * Form the rotation matrix. CALL iau_IR ( WMAT ) CALL iau_RZ ( -ZETA, WMAT ) CALL iau_RY ( THETA, WMAT ) CALL iau_RZ ( -Z, WMAT ) CALL iau_CR ( WMAT, RMATP ) * 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. 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