SUBROUTINE iau_NUT80 ( DATE1, DATE2, DPSI, DEPS ) *+ * - - - - - - - - - - * i a u _ N U T 8 0 * - - - - - - - - - - * * Nutation, IAU 1980 model. * * This routine is part of the International Astronomical Union's * SOFA (Standards of Fundamental Astronomy) software collection. * * Status: canonical model. * * Given: * DATE1,DATE2 d TT as a 2-part Julian Date (Note 1) * * Returned: * DPSI d nutation in longitude (radians) * DEPS d nutation in obliquity (radians) * * Notes: * * 1) The DATE DATE1+DATE2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TDB)=2450123.7 could be expressed in any of these ways, * among others: * * DATE1 DATE2 * * 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 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: * iau_ANPM 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: 2009 December 15 * * SOFA release 2021-01-25 * * Copyright (C) 2021 IAU SOFA Board. See notes at end. * *----------------------------------------------------------------------- IMPLICIT NONE DOUBLE PRECISION DATE1, DATE2, DPSI, DEPS * Arcseconds to radians DOUBLE PRECISION DAS2R PARAMETER ( DAS2R = 4.848136811095359935899141D-6 ) * 2Pi DOUBLE PRECISION D2PI PARAMETER ( D2PI = 6.283185307179586476925287D0 ) * Units of 0.1 milliarcsecond to radians DOUBLE PRECISION U2R PARAMETER ( U2R = DAS2R/1D4 ) * Reference epoch (J2000.0), JD DOUBLE PRECISION DJ00 PARAMETER ( DJ00 = 2451545D0 ) * Days per Julian century DOUBLE PRECISION DJC PARAMETER ( DJC = 36525D0 ) DOUBLE PRECISION T, EL, ELP, F, D, OM, DP, DE, ARG, S, C INTEGER I, J DOUBLE PRECISION iau_ANPM * ------------------------------------------------ * Table of multiples of arguments and coefficients * ------------------------------------------------ * * The coefficient values are in 0.1 mas units and the rates of change * are in mas per Julian millennium. REAL X(9,106) * Multiple of Longitude Obliquity * L L' F D Omega coeff. of sin coeff. of cos * 1 t 1 t DATA ((X(I,J),I=1,9),J=1,10) / : 0., 0., 0., 0., 1., -171996., -1742., 92025., 89., : 0., 0., 0., 0., 2., 2062., 2., -895., 5., : -2., 0., 2., 0., 1., 46., 0., -24., 0., : 2., 0., -2., 0., 0., 11., 0., 0., 0., : -2., 0., 2., 0., 2., -3., 0., 1., 0., : 1., -1., 0., -1., 0., -3., 0., 0., 0., : 0., -2., 2., -2., 1., -2., 0., 1., 0., : 2., 0., -2., 0., 1., 1., 0., 0., 0., : 0., 0., 2., -2., 2., -13187., -16., 5736., -31., : 0., 1., 0., 0., 0., 1426., -34., 54., -1. / DATA ((X(I,J),I=1,9),J=11,20) / : 0., 1., 2., -2., 2., -517., 12., 224., -6., : 0., -1., 2., -2., 2., 217., -5., -95., 3., : 0., 0., 2., -2., 1., 129., 1., -70., 0., : 2., 0., 0., -2., 0., 48., 0., 1., 0., : 0., 0., 2., -2., 0., -22., 0., 0., 0., : 0., 2., 0., 0., 0., 17., -1., 0., 0., : 0., 1., 0., 0., 1., -15., 0., 9., 0., : 0., 2., 2., -2., 2., -16., 1., 7., 0., : 0., -1., 0., 0., 1., -12., 0., 6., 0., : -2., 0., 0., 2., 1., -6., 0., 3., 0. / DATA ((X(I,J),I=1,9),J=21,30) / : 0., -1., 2., -2., 1., -5., 0., 3., 0., : 2., 0., 0., -2., 1., 4., 0., -2., 0., : 0., 1., 2., -2., 1., 4., 0., -2., 0., : 1., 0., 0., -1., 0., -4., 0., 0., 0., : 2., 1., 0., -2., 0., 1., 0., 0., 0., : 0., 0., -2., 2., 1., 1., 0., 0., 0., : 0., 1., -2., 2., 0., -1., 0., 0., 0., : 0., 1., 0., 0., 2., 1., 0., 0., 0., : -1., 0., 0., 1., 1., 1., 0., 0., 0., : 0., 1., 2., -2., 0., -1., 0., 0., 0. / DATA ((X(I,J),I=1,9),J=31,40) / : 0., 0., 2., 0., 2., -2274., -2., 977., -5., : 1., 0., 0., 0., 0., 712., 1., -7., 0., : 0., 0., 2., 0., 1., -386., -4., 200., 0., : 1., 0., 2., 0., 2., -301., 0., 129., -1., : 1., 0., 0., -2., 0., -158., 0., -1., 0., : -1., 0., 2., 0., 2., 123., 0., -53., 0., : 0., 0., 0., 2., 0., 63., 0., -2., 0., : 1., 0., 0., 0., 1., 63., 1., -33., 0., : -1., 0., 0., 0., 1., -58., -1., 32., 0., : -1., 0., 2., 2., 2., -59., 0., 26., 0./ DATA ((X(I,J),I=1,9),J=41,50) / : 1., 0., 2., 0., 1., -51., 0., 27., 0., : 0., 0., 2., 2., 2., -38., 0., 16., 0., : 2., 0., 0., 0., 0., 29., 0., -1., 0., : 1., 0., 2., -2., 2., 29., 0., -12., 0., : 2., 0., 2., 0., 2., -31., 0., 13., 0., : 0., 0., 2., 0., 0., 26., 0., -1., 0., : -1., 0., 2., 0., 1., 21., 0., -10., 0., : -1., 0., 0., 2., 1., 16., 0., -8., 0., : 1., 0., 0., -2., 1., -13., 0., 7., 0., : -1., 0., 2., 2., 1., -10., 0., 5., 0. / DATA ((X(I,J),I=1,9),J=51,60) / : 1., 1., 0., -2., 0., -7., 0., 0., 0., : 0., 1., 2., 0., 2., 7., 0., -3., 0., : 0., -1., 2., 0., 2., -7., 0., 3., 0., : 1., 0., 2., 2., 2., -8., 0., 3., 0., : 1., 0., 0., 2., 0., 6., 0., 0., 0., : 2., 0., 2., -2., 2., 6., 0., -3., 0., : 0., 0., 0., 2., 1., -6., 0., 3., 0., : 0., 0., 2., 2., 1., -7., 0., 3., 0., : 1., 0., 2., -2., 1., 6., 0., -3., 0., : 0., 0., 0., -2., 1., -5., 0., 3., 0. / DATA ((X(I,J),I=1,9),J=61,70) / : 1., -1., 0., 0., 0., 5., 0., 0., 0., : 2., 0., 2., 0., 1., -5., 0., 3., 0., : 0., 1., 0., -2., 0., -4., 0., 0., 0., : 1., 0., -2., 0., 0., 4., 0., 0., 0., : 0., 0., 0., 1., 0., -4., 0., 0., 0., : 1., 1., 0., 0., 0., -3., 0., 0., 0., : 1., 0., 2., 0., 0., 3., 0., 0., 0., : 1., -1., 2., 0., 2., -3., 0., 1., 0., : -1., -1., 2., 2., 2., -3., 0., 1., 0., : -2., 0., 0., 0., 1., -2., 0., 1., 0. / DATA ((X(I,J),I=1,9),J=71,80) / : 3., 0., 2., 0., 2., -3., 0., 1., 0., : 0., -1., 2., 2., 2., -3., 0., 1., 0., : 1., 1., 2., 0., 2., 2., 0., -1., 0., : -1., 0., 2., -2., 1., -2., 0., 1., 0., : 2., 0., 0., 0., 1., 2., 0., -1., 0., : 1., 0., 0., 0., 2., -2., 0., 1., 0., : 3., 0., 0., 0., 0., 2., 0., 0., 0., : 0., 0., 2., 1., 2., 2., 0., -1., 0., : -1., 0., 0., 0., 2., 1., 0., -1., 0., : 1., 0., 0., -4., 0., -1., 0., 0., 0. / DATA ((X(I,J),I=1,9),J=81,90) / : -2., 0., 2., 2., 2., 1., 0., -1., 0., : -1., 0., 2., 4., 2., -2., 0., 1., 0., : 2., 0., 0., -4., 0., -1., 0., 0., 0., : 1., 1., 2., -2., 2., 1., 0., -1., 0., : 1., 0., 2., 2., 1., -1., 0., 1., 0., : -2., 0., 2., 4., 2., -1., 0., 1., 0., : -1., 0., 4., 0., 2., 1., 0., 0., 0., : 1., -1., 0., -2., 0., 1., 0., 0., 0., : 2., 0., 2., -2., 1., 1., 0., -1., 0., : 2., 0., 2., 2., 2., -1., 0., 0., 0. / DATA ((X(I,J),I=1,9),J=91,100) / : 1., 0., 0., 2., 1., -1., 0., 0., 0., : 0., 0., 4., -2., 2., 1., 0., 0., 0., : 3., 0., 2., -2., 2., 1., 0., 0., 0., : 1., 0., 2., -2., 0., -1., 0., 0., 0., : 0., 1., 2., 0., 1., 1., 0., 0., 0., : -1., -1., 0., 2., 1., 1., 0., 0., 0., : 0., 0., -2., 0., 1., -1., 0., 0., 0., : 0., 0., 2., -1., 2., -1., 0., 0., 0., : 0., 1., 0., 2., 0., -1., 0., 0., 0., : 1., 0., -2., -2., 0., -1., 0., 0., 0. / DATA ((X(I,J),I=1,9),J=101,106) / : 0., -1., 2., 0., 1., -1., 0., 0., 0., : 1., 1., 0., -2., 1., -1., 0., 0., 0., : 1., 0., -2., 2., 0., -1., 0., 0., 0., : 2., 0., 0., 2., 0., 1., 0., 0., 0., : 0., 0., 2., 4., 2., -1., 0., 0., 0., : 0., 1., 0., 1., 0., 1., 0., 0., 0. / * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * Interval between fundamental epoch J2000.0 and given date (JC). T = ( ( DATE1-DJ00 ) + DATE2 ) / DJC * * FUNDAMENTAL ARGUMENTS in the FK5 reference system * * Mean longitude of the Moon minus mean longitude of the Moon's * perigee. EL = iau_ANPM ( ( 485866.733D0 + ( 715922.633D0 + : ( 31.310D0 + 0.064D0 * T ) * T ) * T ) * DAS2R : + MOD(1325D0*T, 1D0) * D2PI ) * Mean longitude of the Sun minus mean longitude of the Sun's perigee. ELP = iau_ANPM ( ( 1287099.804D0 + ( 1292581.224D0 + : ( -0.577D0 -0.012D0 * T ) * T ) * T ) * DAS2R : + MOD(99D0*T, 1D0) * D2PI ) * Mean longitude of the Moon minus mean longitude of the Moon's node. F = iau_ANPM ( ( 335778.877D0 + ( 295263.137D0 + : ( -13.257D0 + 0.011D0 * T ) * T ) * T ) * DAS2R : + MOD(1342D0*T, 1D0) * D2PI ) * Mean elongation of the Moon from the Sun. D = iau_ANPM ( ( 1072261.307D0 + ( 1105601.328D0 + : ( -6.891D0 + 0.019D0 * T ) * T ) * T ) * DAS2R : + MOD(1236D0*T, 1D0) * D2PI ) * Longitude of the mean ascending node of the lunar orbit on the * ecliptic, measured from the mean equinox of date. OM = iau_ANPM( ( 450160.280D0 + ( -482890.539D0 + : ( 7.455D0 + 0.008D0 * T ) * T ) * T ) * DAS2R : + MOD( -5D0*T, 1D0) * D2PI ) * --------------- * Nutation series * --------------- * Change time argument from centuries to millennia. T = T / 10D0 * Initialize nutation components. DP = 0D0 DE = 0D0 * Sum the nutation terms, ending with the biggest. DO 1 J=106,1,-1 * Form argument for current term. ARG = DBLE(X(1,J)) * EL : + DBLE(X(2,J)) * ELP : + DBLE(X(3,J)) * F : + DBLE(X(4,J)) * D : + DBLE(X(5,J)) * OM * Accumulate current nutation term. S = DBLE(X(6,J)) + DBLE(X(7,J)) * T C = DBLE(X(8,J)) + DBLE(X(9,J)) * T IF ( S .NE. 0D0 ) DP = DP + S * SIN(ARG) IF ( C .NE. 0D0 ) DE = DE + C * COS(ARG) * Next term. 1 CONTINUE * Convert results from 0.1 mas units to radians. DPSI = DP * U2R DEPS = DE * U2R * 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. 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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