#include "sofa.h" #include "sofam.h" void iauNut80(double date1, double date2, double *dpsi, double *deps) /* ** - - - - - - - - - ** i a u N u t 8 0 ** - - - - - - - - - ** ** Nutation, IAU 1980 model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** dpsi double nutation in longitude (radians) ** deps double nutation in obliquity (radians) ** ** 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 ** ** 2450123.7 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 resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The nutation components are with respect to the ecliptic of ** date. ** ** Called: ** iauAnpm normalize angle into range +/- pi ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992), ** Section 3.222 (p111). ** ** This revision: 2021 May 11 ** ** SOFA release 2023-10-11 ** ** Copyright (C) 2023 IAU SOFA Board. See notes at end. */ { double t, el, elp, f, d, om, dp, de, arg, s, c; int j; /* Units of 0.1 milliarcsecond to radians */ const double U2R = DAS2R / 1e4; /* ------------------------------------------------ */ /* Table of multiples of arguments and coefficients */ /* ------------------------------------------------ */ /* The units for the sine and cosine coefficients are 0.1 mas and */ /* the same per Julian century */ static const struct { int nl,nlp,nf,nd,nom; /* coefficients of l,l',F,D,Om */ double sp,spt; /* longitude sine, 1 and t coefficients */ double ce,cet; /* obliquity cosine, 1 and t coefficients */ } x[] = { /* 1-10 */ { 0, 0, 0, 0, 1, -171996.0, -174.2, 92025.0, 8.9 }, { 0, 0, 0, 0, 2, 2062.0, 0.2, -895.0, 0.5 }, { -2, 0, 2, 0, 1, 46.0, 0.0, -24.0, 0.0 }, { 2, 0, -2, 0, 0, 11.0, 0.0, 0.0, 0.0 }, { -2, 0, 2, 0, 2, -3.0, 0.0, 1.0, 0.0 }, { 1, -1, 0, -1, 0, -3.0, 0.0, 0.0, 0.0 }, { 0, -2, 2, -2, 1, -2.0, 0.0, 1.0, 0.0 }, { 2, 0, -2, 0, 1, 1.0, 0.0, 0.0, 0.0 }, { 0, 0, 2, -2, 2, -13187.0, -1.6, 5736.0, -3.1 }, { 0, 1, 0, 0, 0, 1426.0, -3.4, 54.0, -0.1 }, /* 11-20 */ { 0, 1, 2, -2, 2, -517.0, 1.2, 224.0, -0.6 }, { 0, -1, 2, -2, 2, 217.0, -0.5, -95.0, 0.3 }, { 0, 0, 2, -2, 1, 129.0, 0.1, -70.0, 0.0 }, { 2, 0, 0, -2, 0, 48.0, 0.0, 1.0, 0.0 }, { 0, 0, 2, -2, 0, -22.0, 0.0, 0.0, 0.0 }, { 0, 2, 0, 0, 0, 17.0, -0.1, 0.0, 0.0 }, { 0, 1, 0, 0, 1, -15.0, 0.0, 9.0, 0.0 }, { 0, 2, 2, -2, 2, -16.0, 0.1, 7.0, 0.0 }, { 0, -1, 0, 0, 1, -12.0, 0.0, 6.0, 0.0 }, { -2, 0, 0, 2, 1, -6.0, 0.0, 3.0, 0.0 }, /* 21-30 */ { 0, -1, 2, -2, 1, -5.0, 0.0, 3.0, 0.0 }, { 2, 0, 0, -2, 1, 4.0, 0.0, -2.0, 0.0 }, { 0, 1, 2, -2, 1, 4.0, 0.0, -2.0, 0.0 }, { 1, 0, 0, -1, 0, -4.0, 0.0, 0.0, 0.0 }, { 2, 1, 0, -2, 0, 1.0, 0.0, 0.0, 0.0 }, { 0, 0, -2, 2, 1, 1.0, 0.0, 0.0, 0.0 }, { 0, 1, -2, 2, 0, -1.0, 0.0, 0.0, 0.0 }, { 0, 1, 0, 0, 2, 1.0, 0.0, 0.0, 0.0 }, { -1, 0, 0, 1, 1, 1.0, 0.0, 0.0, 0.0 }, { 0, 1, 2, -2, 0, -1.0, 0.0, 0.0, 0.0 }, /* 31-40 */ { 0, 0, 2, 0, 2, -2274.0, -0.2, 977.0, -0.5 }, { 1, 0, 0, 0, 0, 712.0, 0.1, -7.0, 0.0 }, { 0, 0, 2, 0, 1, -386.0, -0.4, 200.0, 0.0 }, { 1, 0, 2, 0, 2, -301.0, 0.0, 129.0, -0.1 }, { 1, 0, 0, -2, 0, -158.0, 0.0, -1.0, 0.0 }, { -1, 0, 2, 0, 2, 123.0, 0.0, -53.0, 0.0 }, { 0, 0, 0, 2, 0, 63.0, 0.0, -2.0, 0.0 }, { 1, 0, 0, 0, 1, 63.0, 0.1, -33.0, 0.0 }, { -1, 0, 0, 0, 1, -58.0, -0.1, 32.0, 0.0 }, { -1, 0, 2, 2, 2, -59.0, 0.0, 26.0, 0.0 }, /* 41-50 */ { 1, 0, 2, 0, 1, -51.0, 0.0, 27.0, 0.0 }, { 0, 0, 2, 2, 2, -38.0, 0.0, 16.0, 0.0 }, { 2, 0, 0, 0, 0, 29.0, 0.0, -1.0, 0.0 }, { 1, 0, 2, -2, 2, 29.0, 0.0, -12.0, 0.0 }, { 2, 0, 2, 0, 2, -31.0, 0.0, 13.0, 0.0 }, { 0, 0, 2, 0, 0, 26.0, 0.0, -1.0, 0.0 }, { -1, 0, 2, 0, 1, 21.0, 0.0, -10.0, 0.0 }, { -1, 0, 0, 2, 1, 16.0, 0.0, -8.0, 0.0 }, { 1, 0, 0, -2, 1, -13.0, 0.0, 7.0, 0.0 }, { -1, 0, 2, 2, 1, -10.0, 0.0, 5.0, 0.0 }, /* 51-60 */ { 1, 1, 0, -2, 0, -7.0, 0.0, 0.0, 0.0 }, { 0, 1, 2, 0, 2, 7.0, 0.0, -3.0, 0.0 }, { 0, -1, 2, 0, 2, -7.0, 0.0, 3.0, 0.0 }, { 1, 0, 2, 2, 2, -8.0, 0.0, 3.0, 0.0 }, { 1, 0, 0, 2, 0, 6.0, 0.0, 0.0, 0.0 }, { 2, 0, 2, -2, 2, 6.0, 0.0, -3.0, 0.0 }, { 0, 0, 0, 2, 1, -6.0, 0.0, 3.0, 0.0 }, { 0, 0, 2, 2, 1, -7.0, 0.0, 3.0, 0.0 }, { 1, 0, 2, -2, 1, 6.0, 0.0, -3.0, 0.0 }, { 0, 0, 0, -2, 1, -5.0, 0.0, 3.0, 0.0 }, /* 61-70 */ { 1, -1, 0, 0, 0, 5.0, 0.0, 0.0, 0.0 }, { 2, 0, 2, 0, 1, -5.0, 0.0, 3.0, 0.0 }, { 0, 1, 0, -2, 0, -4.0, 0.0, 0.0, 0.0 }, { 1, 0, -2, 0, 0, 4.0, 0.0, 0.0, 0.0 }, { 0, 0, 0, 1, 0, -4.0, 0.0, 0.0, 0.0 }, { 1, 1, 0, 0, 0, -3.0, 0.0, 0.0, 0.0 }, { 1, 0, 2, 0, 0, 3.0, 0.0, 0.0, 0.0 }, { 1, -1, 2, 0, 2, -3.0, 0.0, 1.0, 0.0 }, { -1, -1, 2, 2, 2, -3.0, 0.0, 1.0, 0.0 }, { -2, 0, 0, 0, 1, -2.0, 0.0, 1.0, 0.0 }, /* 71-80 */ { 3, 0, 2, 0, 2, -3.0, 0.0, 1.0, 0.0 }, { 0, -1, 2, 2, 2, -3.0, 0.0, 1.0, 0.0 }, { 1, 1, 2, 0, 2, 2.0, 0.0, -1.0, 0.0 }, { -1, 0, 2, -2, 1, -2.0, 0.0, 1.0, 0.0 }, { 2, 0, 0, 0, 1, 2.0, 0.0, -1.0, 0.0 }, { 1, 0, 0, 0, 2, -2.0, 0.0, 1.0, 0.0 }, { 3, 0, 0, 0, 0, 2.0, 0.0, 0.0, 0.0 }, { 0, 0, 2, 1, 2, 2.0, 0.0, -1.0, 0.0 }, { -1, 0, 0, 0, 2, 1.0, 0.0, -1.0, 0.0 }, { 1, 0, 0, -4, 0, -1.0, 0.0, 0.0, 0.0 }, /* 81-90 */ { -2, 0, 2, 2, 2, 1.0, 0.0, -1.0, 0.0 }, { -1, 0, 2, 4, 2, -2.0, 0.0, 1.0, 0.0 }, { 2, 0, 0, -4, 0, -1.0, 0.0, 0.0, 0.0 }, { 1, 1, 2, -2, 2, 1.0, 0.0, -1.0, 0.0 }, { 1, 0, 2, 2, 1, -1.0, 0.0, 1.0, 0.0 }, { -2, 0, 2, 4, 2, -1.0, 0.0, 1.0, 0.0 }, { -1, 0, 4, 0, 2, 1.0, 0.0, 0.0, 0.0 }, { 1, -1, 0, -2, 0, 1.0, 0.0, 0.0, 0.0 }, { 2, 0, 2, -2, 1, 1.0, 0.0, -1.0, 0.0 }, { 2, 0, 2, 2, 2, -1.0, 0.0, 0.0, 0.0 }, /* 91-100 */ { 1, 0, 0, 2, 1, -1.0, 0.0, 0.0, 0.0 }, { 0, 0, 4, -2, 2, 1.0, 0.0, 0.0, 0.0 }, { 3, 0, 2, -2, 2, 1.0, 0.0, 0.0, 0.0 }, { 1, 0, 2, -2, 0, -1.0, 0.0, 0.0, 0.0 }, { 0, 1, 2, 0, 1, 1.0, 0.0, 0.0, 0.0 }, { -1, -1, 0, 2, 1, 1.0, 0.0, 0.0, 0.0 }, { 0, 0, -2, 0, 1, -1.0, 0.0, 0.0, 0.0 }, { 0, 0, 2, -1, 2, -1.0, 0.0, 0.0, 0.0 }, { 0, 1, 0, 2, 0, -1.0, 0.0, 0.0, 0.0 }, { 1, 0, -2, -2, 0, -1.0, 0.0, 0.0, 0.0 }, /* 101-106 */ { 0, -1, 2, 0, 1, -1.0, 0.0, 0.0, 0.0 }, { 1, 1, 0, -2, 1, -1.0, 0.0, 0.0, 0.0 }, { 1, 0, -2, 2, 0, -1.0, 0.0, 0.0, 0.0 }, { 2, 0, 0, 2, 0, 1.0, 0.0, 0.0, 0.0 }, { 0, 0, 2, 4, 2, -1.0, 0.0, 0.0, 0.0 }, { 0, 1, 0, 1, 0, 1.0, 0.0, 0.0, 0.0 } }; /* Number of terms in the series */ const int NT = (int) (sizeof x / sizeof x[0]); /* ------------------------------------------------------------------ */ /* Interval between fundamental epoch J2000.0 and given date (JC). */ t = ((date1 - DJ00) + date2) / DJC; /* --------------------- */ /* Fundamental arguments */ /* --------------------- */ /* Mean longitude of Moon minus mean longitude of Moon's perigee. */ el = iauAnpm( (485866.733 + (715922.633 + (31.310 + 0.064 * t) * t) * t) * DAS2R + fmod(1325.0 * t, 1.0) * D2PI); /* Mean longitude of Sun minus mean longitude of Sun's perigee. */ elp = iauAnpm( (1287099.804 + (1292581.224 + (-0.577 - 0.012 * t) * t) * t) * DAS2R + fmod(99.0 * t, 1.0) * D2PI); /* Mean longitude of Moon minus mean longitude of Moon's node. */ f = iauAnpm( (335778.877 + (295263.137 + (-13.257 + 0.011 * t) * t) * t) * DAS2R + fmod(1342.0 * t, 1.0) * D2PI); /* Mean elongation of Moon from Sun. */ d = iauAnpm( (1072261.307 + (1105601.328 + (-6.891 + 0.019 * t) * t) * t) * DAS2R + fmod(1236.0 * t, 1.0) * D2PI); /* Longitude of the mean ascending node of the lunar orbit on the */ /* ecliptic, measured from the mean equinox of date. */ om = iauAnpm( (450160.280 + (-482890.539 + (7.455 + 0.008 * t) * t) * t) * DAS2R + fmod(-5.0 * t, 1.0) * D2PI); /* --------------- */ /* Nutation series */ /* --------------- */ /* Initialize nutation components. */ dp = 0.0; de = 0.0; /* Sum the nutation terms, ending with the biggest. */ for (j = NT-1; j >= 0; j--) { /* Form argument for current term. */ arg = (double)x[j].nl * el + (double)x[j].nlp * elp + (double)x[j].nf * f + (double)x[j].nd * d + (double)x[j].nom * om; /* Accumulate current nutation term. */ s = x[j].sp + x[j].spt * t; c = x[j].ce + x[j].cet * t; if (s != 0.0) dp += s * sin(arg); if (c != 0.0) de += c * cos(arg); } /* Convert results from 0.1 mas units to radians. */ *dpsi = dp * U2R; *deps = de * U2R; /* 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 ** **--------------------------------------------------------------------*/ }