SUBROUTINE iau_PREC76 ( DATE01, DATE02, DATE11, DATE12, : ZETA, Z, THETA ) *+ * - - - - - - - - - - - * i a u _ P R E C 7 6 * - - - - - - - - - - - * * IAU 1976 precession model. * * This routine forms the three Euler angles which implement general * precession between two dates, using the IAU 1976 model (as for * the FK5 catalog). * * This routine is part of the International Astronomical Union's * SOFA (Standards of Fundamental Astronomy) software collection. * * Status: canonical model. * * Given: * DATE01,DATE02 d TDB starting date (Note 1) * DATE11,DATE12 d TDB ending date (Note 1) * * Returned: * ZETA d 1st rotation: radians clockwise around z * Z d 3rd rotation: radians clockwise around z * THETA d 2nd rotation: radians counterclockwise around y * * Notes: * * 1) The dates DATE01+DATE02 and DATE11+DATE12 are Julian Dates, * apportioned in any convenient way between the arguments DATEn1 and * DATEn2. For example, JD(TDB)=2450123.7 could be expressed in any * of these ways, among others: * * DATEn1 DATEn2 * * 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 * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * The two dates may be expressed using different methods, but at * the risk of losing some resolution. * * 2) The accumulated precession angles zeta, z, theta 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. * * 3) The three angles are returned in the conventional order, which * is not the same as the order of the corresponding Euler rotations. * The precession matrix is R_3(-z) x R_2(+theta) x R_3(-zeta). * * Reference: * * Lieske, J.H., 1979, Astron.Astrophys. 73, 282. * equations (6) & (7), p283. * * This revision: 2013 November 19 * * SOFA release 2021-01-25 * * Copyright (C) 2021 IAU SOFA Board. See notes at end. * *----------------------------------------------------------------------- IMPLICIT NONE DOUBLE PRECISION DATE01, DATE02, DATE11, DATE12, ZETA, Z, THETA * 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 ) DOUBLE PRECISION T0, T, TAS2R, W * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * Interval between fundamental epoch J2000.0 and start date (JC). T0 = ( ( DATE01-DJ00 ) + DATE02 ) / DJC * Interval over which precession required (JC). T = ( ( DATE11-DATE01 ) + ( DATE12-DATE02 ) ) / DJC * Euler angles. TAS2R = T * DAS2R W = 2306.2181D0 + ( : 1.39656D0 : - 0.000139D0 * T0 ) * T0 ZETA = ( W + ( ( 0.30188D0 : - 0.000344D0 * T0 ) : + 0.017998D0 * T ) * T ) * TAS2R Z = ( W + ( ( 1.09468D0 : + 0.000066D0 * T0 ) : + 0.018203D0 * T ) * T ) * TAS2R THETA = ( ( 2004.3109D0 + ( : - 0.85330D0 : - 0.000217D0 * T0 ) * T0 ) + ( ( : - 0.42665D0 : - 0.000217D0 * T0 ) : - 0.041833D0 * T ) * T ) * TAS2R * 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