SUBROUTINE iau_NUT00B ( DATE1, DATE2, DPSI, DEPS ) *+ * - - - - - - - - - - - * i a u _ N U T 0 0 B * - - - - - - - - - - - * * Nutation, IAU 2000B 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,DEPS d nutation, luni-solar + planetary (Note 2) * * 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 * * 2450123.7D0 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 in longitude and obliquity are in radians * and with respect to the equinox and ecliptic of date. The * obliquity at J2000.0 is assumed to be the Lieske et al. (1977) * value of 84381.448 arcsec. (The errors that result from using * this routine with the IAU 2006 value of 84381.406 arcsec can be * neglected.) * * The nutation model consists only of luni-solar terms, but includes * also a fixed offset which compensates for certain long-period * planetary terms (Note 7). * * 3) This routine is an implementation of the IAU 2000B abridged * nutation model formally adopted by the IAU General Assembly in * 2000. The routine computes the MHB_2000_SHORT luni-solar nutation * series (Luzum 2001), but without the associated corrections for * the precession rate adjustments and the offset between the GCRS * and J2000.0 mean poles. * * 4) The full IAU 2000A (MHB2000) nutation model contains nearly 1400 * terms. The IAU 2000B model (McCarthy & Luzum 2003) contains only * 77 terms, plus additional simplifications, yet still delivers * results of 1 mas accuracy at present epochs. This combination of * accuracy and size makes the IAU 2000B abridged nutation model * suitable for most practical applications. * * The routine delivers a pole accurate to 1 mas from 1900 to 2100 * (usually better than 1 mas, very occasionally just outside 1 mas). * The full IAU 2000A model, which is implemented in the routine * iau_NUT00A (q.v.), delivers considerably greater accuracy at * current epochs; however, to realize this improved accuracy, * corrections for the essentially unpredictable free-core-nutation * (FCN) must also be included. * * 5) The present routine provides classical nutation. The * MHB_2000_SHORT algorithm, from which it is adapted, deals also * with (i) the offsets between the GCRS and mean poles and (ii) the * adjustments in longitude and obliquity due to the changed * precession rates. These additional functions, namely frame bias * and precession adjustments, are supported by the SOFA routines * iau_BI00 and iau_PR00. * * 6) The MHB_2000_SHORT algorithm also provides "total" nutations, * comprising the arithmetic sum of the frame bias, precession * adjustments, and nutation (luni-solar + planetary). These total * nutations can be used in combination with an existing IAU 1976 * precession implementation, such as iau_PMAT76, to deliver GCRS-to- * true predictions of mas accuracy at current epochs. However, for * symmetry with the iau_NUT00A routine (q.v. for the reasons), the * SOFA routines do not generate the "total nutations" directly. * Should they be required, they could of course easily be generated * by calling iau_BI00, iau_PR00 and the present routine and adding * the results. * * 7) The IAU 2000B model includes "planetary bias" terms that are fixed * in size but compensate for long-period nutations. The amplitudes * quoted in McCarthy & Luzum (2003), namely Dpsi = -1.5835 mas and * Depsilon = +1.6339 mas, are optimized for the "total nutations" * method described in Note 6. The Luzum (2001) values used in this * SOFA implementation, namely -0.135 mas and +0.388 mas, are * optimized for the "rigorous" method, where frame bias, precession * and nutation are applied separately and in that order. During the * interval 1995-2050, the SOFA implementation delivers a maximum * error of 1.001 mas (not including FCN). * * References: * * Lieske, J.H., Lederle, T., Fricke, W., Morando, B., "Expressions * for the precession quantities based upon the IAU /1976/ system of * astronomical constants", Astron.Astrophys. 58, 1-2, 1-16. (1977) * * Luzum, B., private communication, 2001 (Fortran code * MHB_2000_SHORT) * * McCarthy, D.D. & Luzum, B.J., "An abridged model of the * precession-nutation of the celestial pole", Cel.Mech.Dyn.Astron. * 85, 37-49 (2003) * * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., * Francou, G., Laskar, J., Astron.Astrophys. 282, 663-683 (1994) * * This revision: 2009 December 15 * * SOFA release 2021-05-12 * * 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 ) * Milliarcseconds to radians DOUBLE PRECISION DMAS2R PARAMETER ( DMAS2R = DAS2R / 1D3 ) * Arcseconds in a full circle DOUBLE PRECISION TURNAS PARAMETER ( TURNAS = 1296000D0 ) * 2Pi DOUBLE PRECISION D2PI PARAMETER ( D2PI = 6.283185307179586476925287D0 ) * Units of 0.1 microarcsecond to radians DOUBLE PRECISION U2R PARAMETER ( U2R = DAS2R/1D7 ) * Reference epoch (J2000.0), JD DOUBLE PRECISION DJ00 PARAMETER ( DJ00 = 2451545D0 ) * Days per Julian century DOUBLE PRECISION DJC PARAMETER ( DJC = 36525D0 ) * Miscellaneous DOUBLE PRECISION T, EL, ELP, F, D, OM, ARG, DP, DE, SARG, CARG, : DPSILS, DEPSLS, DPSIPL, DEPSPL INTEGER I, J * ------------------------- * Luni-Solar nutation model * ------------------------- * Number of terms in the luni-solar nutation model INTEGER NLS PARAMETER ( NLS = 77 ) * Coefficients for fundamental arguments INTEGER NALS(5,NLS) * Longitude and obliquity coefficients DOUBLE PRECISION CLS(6,NLS) * --------------------------------------- * Fixed offset in lieu of planetary terms (radians) * --------------------------------------- DOUBLE PRECISION DPPLAN, DEPLAN PARAMETER ( DPPLAN = - 0.135D0 * DMAS2R, : DEPLAN = + 0.388D0 * DMAS2R ) * ---------------------------------------- * Tables of argument and term coefficients * ---------------------------------------- * * Luni-Solar argument multipliers: * * L L' F D Om DATA ( ( NALS(I,J), I=1,5 ), J= 1,10 ) / : 0, 0, 0, 0, 1, : 0, 0, 2, -2, 2, : 0, 0, 2, 0, 2, : 0, 0, 0, 0, 2, : 0, 1, 0, 0, 0, : 0, 1, 2, -2, 2, : 1, 0, 0, 0, 0, : 0, 0, 2, 0, 1, : 1, 0, 2, 0, 2, : 0, -1, 2, -2, 2 / DATA ( ( NALS(I,J), I=1,5 ), J=11,20 ) / : 0, 0, 2, -2, 1, : -1, 0, 2, 0, 2, : -1, 0, 0, 2, 0, : 1, 0, 0, 0, 1, : -1, 0, 0, 0, 1, : -1, 0, 2, 2, 2, : 1, 0, 2, 0, 1, : -2, 0, 2, 0, 1, : 0, 0, 0, 2, 0, : 0, 0, 2, 2, 2 / DATA ( ( NALS(I,J), I=1,5 ), J=21,30 ) / : 0, -2, 2, -2, 2, : -2, 0, 0, 2, 0, : 2, 0, 2, 0, 2, : 1, 0, 2, -2, 2, : -1, 0, 2, 0, 1, : 2, 0, 0, 0, 0, : 0, 0, 2, 0, 0, : 0, 1, 0, 0, 1, : -1, 0, 0, 2, 1, : 0, 2, 2, -2, 2 / DATA ( ( NALS(I,J), I=1,5 ), J=31,40 ) / : 0, 0, -2, 2, 0, : 1, 0, 0, -2, 1, : 0, -1, 0, 0, 1, : -1, 0, 2, 2, 1, : 0, 2, 0, 0, 0, : 1, 0, 2, 2, 2, : -2, 0, 2, 0, 0, : 0, 1, 2, 0, 2, : 0, 0, 2, 2, 1, : 0, -1, 2, 0, 2 / DATA ( ( NALS(I,J), I=1,5 ), J=41,50 ) / : 0, 0, 0, 2, 1, : 1, 0, 2, -2, 1, : 2, 0, 2, -2, 2, : -2, 0, 0, 2, 1, : 2, 0, 2, 0, 1, : 0, -1, 2, -2, 1, : 0, 0, 0, -2, 1, : -1, -1, 0, 2, 0, : 2, 0, 0, -2, 1, : 1, 0, 0, 2, 0 / DATA ( ( NALS(I,J), I=1,5 ), J=51,60 ) / : 0, 1, 2, -2, 1, : 1, -1, 0, 0, 0, : -2, 0, 2, 0, 2, : 3, 0, 2, 0, 2, : 0, -1, 0, 2, 0, : 1, -1, 2, 0, 2, : 0, 0, 0, 1, 0, : -1, -1, 2, 2, 2, : -1, 0, 2, 0, 0, : 0, -1, 2, 2, 2 / DATA ( ( NALS(I,J), I=1,5 ), J=61,70 ) / : -2, 0, 0, 0, 1, : 1, 1, 2, 0, 2, : 2, 0, 0, 0, 1, : -1, 1, 0, 1, 0, : 1, 1, 0, 0, 0, : 1, 0, 2, 0, 0, : -1, 0, 2, -2, 1, : 1, 0, 0, 0, 2, : -1, 0, 0, 1, 0, : 0, 0, 2, 1, 2 / DATA ( ( NALS(I,J), I=1,5 ), J=71,77 ) / : -1, 0, 2, 4, 2, : -1, 1, 0, 1, 1, : 0, -2, 2, -2, 1, : 1, 0, 2, 2, 1, : -2, 0, 2, 2, 2, : -1, 0, 0, 0, 2, : 1, 1, 2, -2, 2 / * * Luni-Solar nutation coefficients, unit 1e-7 arcsec: * longitude (sin, t*sin, cos), obliquity (cos, t*cos, sin) * DATA ( ( CLS(I,J), I=1,6 ), J= 1,10 ) / : -172064161D0, -174666D0, 33386D0, 92052331D0, 9086D0, 15377D0, : -13170906D0, -1675D0, -13696D0, 5730336D0, -3015D0, -4587D0, : -2276413D0, -234D0, 2796D0, 978459D0, -485D0, 1374D0, : 2074554D0, 207D0, -698D0, -897492D0, 470D0, -291D0, : 1475877D0, -3633D0, 11817D0, 73871D0, -184D0, -1924D0, : -516821D0, 1226D0, -524D0, 224386D0, -677D0, -174D0, : 711159D0, 73D0, -872D0, -6750D0, 0D0, 358D0, : -387298D0, -367D0, 380D0, 200728D0, 18D0, 318D0, : -301461D0, -36D0, 816D0, 129025D0, -63D0, 367D0, : 215829D0, -494D0, 111D0, -95929D0, 299D0, 132D0 / DATA ( ( CLS(I,J), I=1,6 ), J=11,20 ) / : 128227D0, 137D0, 181D0, -68982D0, -9D0, 39D0, : 123457D0, 11D0, 19D0, -53311D0, 32D0, -4D0, : 156994D0, 10D0, -168D0, -1235D0, 0D0, 82D0, : 63110D0, 63D0, 27D0, -33228D0, 0D0, -9D0, : -57976D0, -63D0, -189D0, 31429D0, 0D0, -75D0, : -59641D0, -11D0, 149D0, 25543D0, -11D0, 66D0, : -51613D0, -42D0, 129D0, 26366D0, 0D0, 78D0, : 45893D0, 50D0, 31D0, -24236D0, -10D0, 20D0, : 63384D0, 11D0, -150D0, -1220D0, 0D0, 29D0, : -38571D0, -1D0, 158D0, 16452D0, -11D0, 68D0 / DATA ( ( CLS(I,J), I=1,6 ), J=21,30 ) / : 32481D0, 0D0, 0D0, -13870D0, 0D0, 0D0, : -47722D0, 0D0, -18D0, 477D0, 0D0, -25D0, : -31046D0, -1D0, 131D0, 13238D0, -11D0, 59D0, : 28593D0, 0D0, -1D0, -12338D0, 10D0, -3D0, : 20441D0, 21D0, 10D0, -10758D0, 0D0, -3D0, : 29243D0, 0D0, -74D0, -609D0, 0D0, 13D0, : 25887D0, 0D0, -66D0, -550D0, 0D0, 11D0, : -14053D0, -25D0, 79D0, 8551D0, -2D0, -45D0, : 15164D0, 10D0, 11D0, -8001D0, 0D0, -1D0, : -15794D0, 72D0, -16D0, 6850D0, -42D0, -5D0 / DATA ( ( CLS(I,J), I=1,6 ), J=31,40 ) / : 21783D0, 0D0, 13D0, -167D0, 0D0, 13D0, : -12873D0, -10D0, -37D0, 6953D0, 0D0, -14D0, : -12654D0, 11D0, 63D0, 6415D0, 0D0, 26D0, : -10204D0, 0D0, 25D0, 5222D0, 0D0, 15D0, : 16707D0, -85D0, -10D0, 168D0, -1D0, 10D0, : -7691D0, 0D0, 44D0, 3268D0, 0D0, 19D0, : -11024D0, 0D0, -14D0, 104D0, 0D0, 2D0, : 7566D0, -21D0, -11D0, -3250D0, 0D0, -5D0, : -6637D0, -11D0, 25D0, 3353D0, 0D0, 14D0, : -7141D0, 21D0, 8D0, 3070D0, 0D0, 4D0 / DATA ( ( CLS(I,J), I=1,6 ), J=41,50 ) / : -6302D0, -11D0, 2D0, 3272D0, 0D0, 4D0, : 5800D0, 10D0, 2D0, -3045D0, 0D0, -1D0, : 6443D0, 0D0, -7D0, -2768D0, 0D0, -4D0, : -5774D0, -11D0, -15D0, 3041D0, 0D0, -5D0, : -5350D0, 0D0, 21D0, 2695D0, 0D0, 12D0, : -4752D0, -11D0, -3D0, 2719D0, 0D0, -3D0, : -4940D0, -11D0, -21D0, 2720D0, 0D0, -9D0, : 7350D0, 0D0, -8D0, -51D0, 0D0, 4D0, : 4065D0, 0D0, 6D0, -2206D0, 0D0, 1D0, : 6579D0, 0D0, -24D0, -199D0, 0D0, 2D0 / DATA ( ( CLS(I,J), I=1,6 ), J=51,60 ) / : 3579D0, 0D0, 5D0, -1900D0, 0D0, 1D0, : 4725D0, 0D0, -6D0, -41D0, 0D0, 3D0, : -3075D0, 0D0, -2D0, 1313D0, 0D0, -1D0, : -2904D0, 0D0, 15D0, 1233D0, 0D0, 7D0, : 4348D0, 0D0, -10D0, -81D0, 0D0, 2D0, : -2878D0, 0D0, 8D0, 1232D0, 0D0, 4D0, : -4230D0, 0D0, 5D0, -20D0, 0D0, -2D0, : -2819D0, 0D0, 7D0, 1207D0, 0D0, 3D0, : -4056D0, 0D0, 5D0, 40D0, 0D0, -2D0, : -2647D0, 0D0, 11D0, 1129D0, 0D0, 5D0 / DATA ( ( CLS(I,J), I=1,6 ), J=61,70 ) / : -2294D0, 0D0, -10D0, 1266D0, 0D0, -4D0, : 2481D0, 0D0, -7D0, -1062D0, 0D0, -3D0, : 2179D0, 0D0, -2D0, -1129D0, 0D0, -2D0, : 3276D0, 0D0, 1D0, -9D0, 0D0, 0D0, : -3389D0, 0D0, 5D0, 35D0, 0D0, -2D0, : 3339D0, 0D0, -13D0, -107D0, 0D0, 1D0, : -1987D0, 0D0, -6D0, 1073D0, 0D0, -2D0, : -1981D0, 0D0, 0D0, 854D0, 0D0, 0D0, : 4026D0, 0D0, -353D0, -553D0, 0D0, -139D0, : 1660D0, 0D0, -5D0, -710D0, 0D0, -2D0 / DATA ( ( CLS(I,J), I=1,6 ), J=71,77 ) / : -1521D0, 0D0, 9D0, 647D0, 0D0, 4D0, : 1314D0, 0D0, 0D0, -700D0, 0D0, 0D0, : -1283D0, 0D0, 0D0, 672D0, 0D0, 0D0, : -1331D0, 0D0, 8D0, 663D0, 0D0, 4D0, : 1383D0, 0D0, -2D0, -594D0, 0D0, -2D0, : 1405D0, 0D0, 4D0, -610D0, 0D0, 2D0, : 1290D0, 0D0, 0D0, -556D0, 0D0, 0D0 / * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * Interval between fundamental epoch J2000.0 and given date (JC). T = ( ( DATE1-DJ00 ) + DATE2 ) / DJC * ------------------- * LUNI-SOLAR NUTATION * ------------------- * * Fundamental (Delaunay) arguments from Simon et al. (1994) * * Mean anomaly of the Moon. EL = MOD ( 485868.249036D0 + : ( + 1717915923.2178D0 ) * T, TURNAS ) * DAS2R * Mean anomaly of the Sun. ELP = MOD ( 1287104.79305D0 + : ( + 129596581.0481D0 ) * T, TURNAS ) * DAS2R * Mean argument of the latitude of the Moon. F = MOD ( 335779.526232D0 + : ( + 1739527262.8478D0 ) * T, TURNAS ) * DAS2R * Mean elongation of the Moon from the Sun. D = MOD ( 1072260.70369D0 + : ( + 1602961601.2090D0 ) * T, TURNAS ) * DAS2R * Mean longitude of the ascending node of the Moon. OM = MOD ( 450160.398036D0 + : ( - 6962890.5431D0 ) * T, TURNAS ) * DAS2R * Initialize the nutation values. DP = 0D0 DE = 0D0 * Summation of luni-solar nutation series (in reverse order). DO 100 I = NLS, 1, -1 * Argument and functions. ARG = MOD ( DBLE ( NALS(1,I) ) * EL + : DBLE ( NALS(2,I) ) * ELP + : DBLE ( NALS(3,I) ) * F + : DBLE ( NALS(4,I) ) * D + : DBLE ( NALS(5,I) ) * OM, D2PI ) SARG = SIN(ARG) CARG = COS(ARG) * Term. DP = DP + ( CLS(1,I) + CLS(2,I) * T ) * SARG : + CLS(3,I) * CARG DE = DE + ( CLS(4,I) + CLS(5,I) * T ) * CARG : + CLS(6,I) * SARG 100 CONTINUE * Convert from 0.1 microarcsec units to radians. DPSILS = DP * U2R DEPSLS = DE * U2R * ----------------------------- * IN LIEU OF PLANETARY NUTATION * ----------------------------- * Fixed offset to correct for missing terms in truncated series. DPSIPL = DPPLAN DEPSPL = DEPLAN * ------- * RESULTS * ------- * Add luni-solar and planetary components. DPSI = DPSILS + DPSIPL DEPS = DEPSLS + DEPSPL * 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. 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 * *----------------------------------------------------------------------- END