1 /* 2 * - - - - - - - - - - - 3 * g a l _ n u t 0 0 a 4 * - - - - - - - - - - - 5 * 6 * This routine is part of the General Astrodynamics Library 7 * 8 * Description: 9 * 10 * Nutation, IAU 2000A model (MHB2000 luni-solar and planetary nutation 11 * with free core nutation omitted). 12 * 13 * This routine is an independent translation of a FORTRAN routine 14 * that is part of IAU's SOFA software collection. 15 * 16 * Status: 17 * 18 * canonical model. 19 * 20 * Given: 21 * 22 * date1,date2 d TT as a 2-part Julian Date (Note 1) 23 * 24 * Returned: 25 * 26 * *dpsi,*deps d nutation, luni-solar + planetary (Note 2) 27 * 28 * Notes: 29 * 30 * 1) The TT date date1+date2 is a Julian Date, apportioned in any 31 * convenient way between the two arguments. For example, 32 * JD(TT)=2450123.7 could be expressed in any of these ways, 33 * among others: 34 * 35 * date1 date2 36 * 37 * 2450123.7 0.0 (JD method) 38 * 2451545.0 -1421.3 (J2000 method) 39 * 2400000.5 50123.2 (MJD method) 40 * 2450123.5 0.2 (date & time method) 41 * 42 * The JD method is the most natural and convenient to use in 43 * cases where the loss of several decimal digits of resolution 44 * is acceptable. The J2000 method is best matched to the way 45 * the argument is handled internally and will deliver the 46 * optimum resolution. The MJD method and the date & time methods 47 * are both good compromises between resolution and convenience. 48 * 49 * 2) The nutation components in longitude and obliquity are in radians 50 * and with respect to the equinox and ecliptic of date. The 51 * obliquity at J2000 is assumed to be the Lieske et al. (1977) value 52 * of 84381.448 arcsec. 53 * 54 * Both the luni-solar and planetary nutations are included. The 55 * latter are due to direct planetary nutations and the perturbations 56 * of the lunar and terrestrial orbits. 57 * 58 * 3) The routine computes the MHB2000 nutation series with the 59 * associated corrections for planetary nutations. It is an 60 * implementation of the nutation part of the IAU 2000A precession- 61 * nutation model, formally adopted by the IAU General Assembly in 62 * 2000, namely MHB2000 (Mathews et al. 2002), but with the free core 63 * nutation (FCN - see Note 4) omitted. 64 * 65 * 4) The full MHB2000 model also contains contributions to the 66 * nutations in longitude and obliquity due to the free-excitation of 67 * the free-core-nutation during the period 1979-2000. These FCN 68 * terms, which are time-dependent and unpredictable, are NOT 69 * included in the present routine and, if required, must be 70 * independently computed. With the FCN corrections included, the 71 * present routine delivers a pole which is at current epochs 72 * accurate to a few hundred microarcseconds. The omission of FCN 73 * introduces further errors of about that size. 74 * 75 * 5) The present routine provides classical nutation. The MHB2000 76 * algorithm, from which it is adapted, deals also with (i) the 77 * offsets between the GCRS and mean poles and (ii) the adjustments 78 * in longitude and obliquity due to the changed precession rates. 79 * These additional functions, namely frame bias and precession 80 * adjustments, are supported by the SOFA routines gal_bi00 and 81 * gal_pr00. 82 * 83 * 6) The MHB2000 algorithm also provides "total" nutations, comprising 84 * the arithmetic sum of the frame bias, precession adjustments, 85 * luni-solar nutation and planetary nutation. These total nutations 86 * can be used in combination with an existing IAU 1976 precession 87 * implementation, such as gal_pmat76, to deliver GCRS-to-true 88 * predictions of sub-mas accuracy at current epochs. However, there 89 * are three shortcomings in the MHB2000 model that must be taken 90 * into account if more accurate or definitive results are required 91 * (see Wallace 2002): 92 * 93 * (i) The MHB2000 total nutations are simply arithmetic sums, 94 * yet in reality the various components are successive Euler 95 * rotations. This slight lack of rigor leads to cross terms 96 * that exceed 1 mas after a century. The rigorous procedure 97 * is to form the GCRS-to-true rotation matrix by applying the 98 * bias, precession and nutation in that order. 99 * 100 * (ii) Although the precession adjustments are stated to be with 101 * respect to Lieske et al. (1977), the MHB2000 model does 102 * not specify which set of Euler angles are to be used and 103 * how the adjustments are to be applied. The most literal and 104 * straightforward procedure is to adopt the 4-rotation 105 * epsilon_0, psi_A, omega_A, xi_A option, and to add dpsipr to 106 * psi_A and depspr to both omega_A and eps_A. 107 * 108 * (iii) The MHB2000 model predates the determination by Chapront 109 * et al. (2002) of a 14.6 mas displacement between the J2000 110 * mean equinox and the origin of the ICRS frame. It should, 111 * however, be noted that neglecting this displacement when 112 * calculating star coordinates does not lead to a 14.6 mas 113 * change in right ascension, only a small second-order 114 * distortion in the pattern of the precession-nutation effect. 115 * 116 * For these reasons, the SOFA routines do not generate the "total 117 * nutations" directly, though they can of course easily be generated 118 * by calling gal_bi00, gal_pr00 and the present routine and adding 119 * the results. 120 * 121 * Called: 122 * 123 * gal_fal03 mean anomaly of the Moon 124 * gal_faf03 mean argument of the latitude of the Moon 125 * gal_faom03 mean longitude of the Moon's ascending node 126 * gal_fame03 mean longitude of Mercury 127 * gal_fave03 mean longitude of Venus 128 * gal_fae03 mean longitude of Earth 129 * gal_fama03 mean longitude of Mars 130 * gal_faju03 mean longitude of Jupiter 131 * gal_fasa03 mean longitude of Saturn 132 * gal_faur03 mean longitude of Uranus 133 * gal_fapa03 general accumulated precession in longitude 134 * 135 * References: 136 * 137 * Chapront, J., Chapront-Touze, M. & Francou, G. 2002, 138 * Astron.Astrophys. 387, 700 139 * 140 * Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977, 141 * Astron.Astrophys. 58, 1-16 142 * 143 * Mathews, P.M., Herring, T.A., Buffet, B.A. 2002, J.Geophys.Res. 144 * 107, B4. The MHB_2000 code itself was obtained on 9th September 145 * 2002 from ftp//maia.usno.navy.mil/conv2000/chapter5/IAU2000A. 146 * 147 * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., 148 * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 149 * 150 * Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, 151 * Astron.Astrophys.Supp.Ser. 135, 111 152 * 153 * Wallace, P.T., "Software for Implementing the IAU 2000 154 * Resolutions", in IERS Workshop 5.1 (2002) 155 * 156 * This revision: 157 * 158 * 2007 February 9 ( c version 2008 January 19 ) 159 * 160 * 161 * Copyright (C) 2008 Paul C. L. Willmott. See notes at end. 162 * 163 *----------------------------------------------------------------------- 164 */ 165 166 #ifndef _GAL_NUT00A_H_ 167 #define _GAL_NUT00A_H_ 1 168 169 #undef __BEGIN_DECLS 170 #undef __END_DECLS 171 #ifdef __cplusplus 172 #define __BEGIN_DECLS extern "C" { 173 #define __END_DECLS } 174 #else 175 #define __BEGIN_DECLS /* empty */ 176 #define __END_DECLS /* empty */ 177 #endif 178 179 __BEGIN_DECLS 180 181 void 182 gal_nut00a 183 ( 184 double date1, 185 double date2, 186 double *dpsi, 187 double *deps 188 ) ; 189 190 __END_DECLS 191 192 #endif /* !_GAL_NUT00A_H_ */ 193 194 /* 195 * gal - General Astrodynamics Library 196 * Copyright (C) 2008 Paul C. L. Willmott 197 * 198 * This program is free software; you can redistribute it and/or modify 199 * it under the terms of the GNU General Public License as published by 200 * the Free Software Foundation; either version 2 of the License, or 201 * (at your option) any later version. 202 * 203 * This program is distributed in the hope that it will be useful, 204 * but WITHOUT ANY WARRANTY; without even the implied warranty of 205 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 206 * GNU General Public License for more details. 207 * 208 * You should have received a copy of the GNU General Public License along 209 * with this program; if not, write to the Free Software Foundation, Inc., 210 * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. 211 * 212 * Contact: 213 * 214 * Paul Willmott 215 * vp9mu@amsat.org 216 */ 217