#include "sofa.h" double iauGmst82(double dj1, double dj2) /* ** - - - - - - - - - - ** i a u G m s t 8 2 ** - - - - - - - - - - ** ** Universal Time to Greenwich mean sidereal time (IAU 1982 model). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** dj1,dj2 double UT1 Julian Date (see note) ** ** Returned (function value): ** double Greenwich mean sidereal time (radians) ** ** Notes: ** ** 1) The UT1 date dj1+dj2 is a Julian Date, apportioned in any ** convenient way between the arguments dj1 and dj2. For example, ** JD(UT1)=2450123.7 could be expressed in any of these ways, ** among others: ** ** dj1 dj2 ** ** 2450123.7 0 (JD method) ** 2451545 -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 and MJD methods are good compromises ** between resolution and convenience. The date & time method is ** best matched to the algorithm used: maximum accuracy (or, at ** least, minimum noise) is delivered when the dj1 argument is for ** 0hrs UT1 on the day in question and the dj2 argument lies in the ** range 0 to 1, or vice versa. ** ** 2) The algorithm is based on the IAU 1982 expression. This is ** always described as giving the GMST at 0 hours UT1. In fact, it ** gives the difference between the GMST and the UT, the steady ** 4-minutes-per-day drawing-ahead of ST with respect to UT. When ** whole days are ignored, the expression happens to equal the GMST ** at 0 hours UT1 each day. ** ** 3) In this function, the entire UT1 (the sum of the two arguments ** dj1 and dj2) is used directly as the argument for the standard ** formula, the constant term of which is adjusted by 12 hours to ** take account of the noon phasing of Julian Date. The UT1 is then ** added, but omitting whole days to conserve accuracy. ** ** Called: ** iauAnp normalize angle into range 0 to 2pi ** ** References: ** ** Transactions of the International Astronomical Union, ** XVIII B, 67 (1983). ** ** Aoki et al., Astron.Astrophys., 105, 359-361 (1982). ** ** This revision: 2017 October 12 ** ** SOFA release 2019-07-22 ** ** Copyright (C) 2019 IAU SOFA Board. See notes at end. */ { /* Coefficients of IAU 1982 GMST-UT1 model */ double A = 24110.54841 - DAYSEC / 2.0; double B = 8640184.812866; double C = 0.093104; double D = -6.2e-6; /* Note: the first constant, A, has to be adjusted by 12 hours */ /* because the UT1 is supplied as a Julian date, which begins */ /* at noon. */ double d1, d2, t, f, gmst; /* Julian centuries since fundamental epoch. */ if (dj1 < dj2) { d1 = dj1; d2 = dj2; } else { d1 = dj2; d2 = dj1; } t = (d1 + (d2 - DJ00)) / DJC; /* Fractional part of JD(UT1), in seconds. */ f = DAYSEC * (fmod(d1, 1.0) + fmod(d2, 1.0)); /* GMST at this UT1. */ gmst = iauAnp(DS2R * ((A + (B + (C + D * t) * t) * t) + f)); return gmst; /*---------------------------------------------------------------------- ** ** Copyright (C) 2019 ** 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 ** **--------------------------------------------------------------------*/ }