#include "sofa.h" #include "sofam.h" void iauPrec76(double date01, double date02, double date11, double date12, double *zeta, double *z, double *theta) /* ** - - - - - - - - - - ** i a u P r e c 7 6 ** - - - - - - - - - - ** ** IAU 1976 precession model. ** ** This function forms the three Euler angles which implement general ** precession between two dates, using the IAU 1976 model (as for the ** FK5 catalog). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date01,date02 double TDB starting date (Note 1) ** date11,date12 double TDB ending date (Note 1) ** ** Returned: ** zeta double 1st rotation: radians cw around z ** z double 3rd rotation: radians cw around z ** theta double 2nd rotation: radians ccw 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 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (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: 2021 May 11 ** ** SOFA release 2023-10-11 ** ** Copyright (C) 2023 IAU SOFA Board. See notes at end. */ { double 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 = 2306.2181 + (1.39656 - 0.000139 * t0) * t0; *zeta = (w + ((0.30188 - 0.000344 * t0) + 0.017998 * t) * t) * tas2r; *z = (w + ((1.09468 + 0.000066 * t0) + 0.018203 * t) * t) * tas2r; *theta = ((2004.3109 + (-0.85330 - 0.000217 * t0) * t0) + ((-0.42665 - 0.000217 * t0) - 0.041833 * t) * t) * tas2r; /* 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 ** **--------------------------------------------------------------------*/ }