#include "erfa.h" void eraNut80(double date1, double date2, double *dpsi, double *deps) /* ** - - - - - - - - - ** e r a N u t 8 0 ** - - - - - - - - - ** ** Nutation, IAU 1980 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: ** eraAnpm normalize angle into range +/- pi ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992), ** Section 3.222 (p111). ** ** Copyright (C) 2013-2017, NumFOCUS Foundation. ** Derived, with permission, from the SOFA library. See notes at end of file. */ { double t, el, elp, f, d, om, dp, de, arg, s, c; int j; /* Units of 0.1 milliarcsecond to radians */ const double U2R = ERFA_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 - ERFA_DJ00) + date2) / ERFA_DJC; /* --------------------- */ /* Fundamental arguments */ /* --------------------- */ /* Mean longitude of Moon minus mean longitude of Moon's perigee. */ el = eraAnpm( (485866.733 + (715922.633 + (31.310 + 0.064 * t) * t) * t) * ERFA_DAS2R + fmod(1325.0 * t, 1.0) * ERFA_D2PI); /* Mean longitude of Sun minus mean longitude of Sun's perigee. */ elp = eraAnpm( (1287099.804 + (1292581.224 + (-0.577 - 0.012 * t) * t) * t) * ERFA_DAS2R + fmod(99.0 * t, 1.0) * ERFA_D2PI); /* Mean longitude of Moon minus mean longitude of Moon's node. */ f = eraAnpm( (335778.877 + (295263.137 + (-13.257 + 0.011 * t) * t) * t) * ERFA_DAS2R + fmod(1342.0 * t, 1.0) * ERFA_D2PI); /* Mean elongation of Moon from Sun. */ d = eraAnpm( (1072261.307 + (1105601.328 + (-6.891 + 0.019 * t) * t) * t) * ERFA_DAS2R + fmod(1236.0 * t, 1.0) * ERFA_D2PI); /* Longitude of the mean ascending node of the lunar orbit on the */ /* ecliptic, measured from the mean equinox of date. */ om = eraAnpm( (450160.280 + (-482890.539 + (7.455 + 0.008 * t) * t) * t) * ERFA_DAS2R + fmod(-5.0 * t, 1.0) * ERFA_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; return; } /*---------------------------------------------------------------------- ** ** ** Copyright (C) 2013-2017, NumFOCUS Foundation. ** All rights reserved. ** ** This library is derived, with permission, from the International ** Astronomical Union's "Standards of Fundamental Astronomy" library, ** available from http://www.iausofa.org. ** ** The ERFA version is intended to retain identical functionality to ** the SOFA library, but made distinct through different function and ** file names, as set out in the SOFA license conditions. The SOFA ** original has a role as a reference standard for the IAU and IERS, ** and consequently redistribution is permitted only in its unaltered ** state. The ERFA version is not subject to this restriction and ** therefore can be included in distributions which do not support the ** concept of "read only" software. ** ** Although the intent is to replicate the SOFA API (other than ** replacement of prefix names) and results (with the exception of ** bugs; any that are discovered will be fixed), SOFA is not ** responsible for any errors found in this version of the library. ** ** If you wish to acknowledge the SOFA heritage, please acknowledge ** that you are using a library derived from SOFA, rather than SOFA ** itself. ** ** ** TERMS AND CONDITIONS ** ** Redistribution and use in source and binary forms, with or without ** modification, are permitted provided that the following conditions ** are met: ** ** 1 Redistributions of source code must retain the above copyright ** notice, this list of conditions and the following disclaimer. ** ** 2 Redistributions in binary form must reproduce the above copyright ** notice, this list of conditions and the following disclaimer in ** the documentation and/or other materials provided with the ** distribution. ** ** 3 Neither the name of the Standards Of Fundamental Astronomy Board, ** the International Astronomical Union nor the names of its ** contributors may be used to endorse or promote products derived ** from this software without specific prior written permission. ** ** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT ** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS ** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE ** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, ** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, ** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; ** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT ** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ** POSSIBILITY OF SUCH DAMAGE. ** */