SUBROUTINE sla_NUTC (DATE, DPSI, DEPS, EPS0) *+ * - - - - - * N U T C * - - - - - * * Nutation: longitude & obliquity components and mean obliquity, * using the Shirai & Fukushima (2001) theory. * * Given: * DATE d TDB (loosely ET) as Modified Julian Date * (JD-2400000.5) * Returned: * DPSI,DEPS d nutation in longitude,obliquity * EPS0 d mean obliquity * * Notes: * * 1 The routine predicts forced nutation (but not free core nutation) * plus corrections to the IAU 1976 precession model. * * 2 Earth attitude predictions made by combining the present nutation * model with IAU 1976 precession are accurate to 1 mas (with respect * to the ICRF) for a few decades around 2000. * * 3 The sla_NUTC80 routine is the equivalent of the present routine * but using the IAU 1980 nutation theory. The older theory is less * accurate, leading to errors as large as 350 mas over the interval * 1900-2100, mainly because of the error in the IAU 1976 precession. * * References: * * Shirai, T. & Fukushima, T., Astron.J. 121, 3270-3283 (2001). * * Fukushima, T., Astron.Astrophys. 244, L11 (1991). * * Simon, J. L., Bretagnon, P., Chapront, J., Chapront-Touze, M., * Francou, G. & Laskar, J., Astron.Astrophys. 282, 663 (1994). * * This revision: 24 November 2005 * * Copyright P.T.Wallace. All rights reserved. * * License: * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 2 of the License, or * (at your option) any later version. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program (see SLA_CONDITIONS); if not, write to the * Free Software Foundation, Inc., 59 Temple Place, Suite 330, * Boston, MA 02111-1307 USA * *- IMPLICIT NONE DOUBLE PRECISION DATE,DPSI,DEPS,EPS0 * Degrees to radians DOUBLE PRECISION DD2R PARAMETER (DD2R=1.745329251994329576923691D-2) * Arc seconds to radians DOUBLE PRECISION DAS2R PARAMETER (DAS2R=4.848136811095359935899141D-6) * Arc seconds in a full circle DOUBLE PRECISION TURNAS PARAMETER (TURNAS=1296000D0) * Reference epoch (J2000), MJD DOUBLE PRECISION DJM0 PARAMETER (DJM0=51544.5D0 ) * Days per Julian century DOUBLE PRECISION DJC PARAMETER (DJC=36525D0) INTEGER I,J DOUBLE PRECISION T,EL,ELP,F,D,OM,VE,MA,JU,SA,THETA,C,S,DP,DE * Number of terms in the nutation model INTEGER NTERMS PARAMETER (NTERMS=194) * The SF2001 forced nutation model INTEGER NA(9,NTERMS) DOUBLE PRECISION PSI(4,NTERMS), EPS(4,NTERMS) * Coefficients of fundamental angles DATA ( ( NA(I,J), I=1,9 ), J=1,10 ) / : 0, 0, 0, 0, -1, 0, 0, 0, 0, : 0, 0, 2, -2, 2, 0, 0, 0, 0, : 0, 0, 2, 0, 2, 0, 0, 0, 0, : 0, 0, 0, 0, -2, 0, 0, 0, 0, : 0, 1, 0, 0, 0, 0, 0, 0, 0, : 0, 1, 2, -2, 2, 0, 0, 0, 0, : 1, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 0, 2, 0, 1, 0, 0, 0, 0, : 1, 0, 2, 0, 2, 0, 0, 0, 0, : 0, -1, 2, -2, 2, 0, 0, 0, 0 / DATA ( ( NA(I,J), I=1,9 ), J=11,20 ) / : 0, 0, 2, -2, 1, 0, 0, 0, 0, : -1, 0, 2, 0, 2, 0, 0, 0, 0, : -1, 0, 0, 2, 0, 0, 0, 0, 0, : 1, 0, 0, 0, 1, 0, 0, 0, 0, : 1, 0, 0, 0, -1, 0, 0, 0, 0, : -1, 0, 2, 2, 2, 0, 0, 0, 0, : 1, 0, 2, 0, 1, 0, 0, 0, 0, : -2, 0, 2, 0, 1, 0, 0, 0, 0, : 0, 0, 0, 2, 0, 0, 0, 0, 0, : 0, 0, 2, 2, 2, 0, 0, 0, 0 / DATA ( ( NA(I,J), I=1,9 ), J=21,30 ) / : 2, 0, 0, -2, 0, 0, 0, 0, 0, : 2, 0, 2, 0, 2, 0, 0, 0, 0, : 1, 0, 2, -2, 2, 0, 0, 0, 0, : -1, 0, 2, 0, 1, 0, 0, 0, 0, : 2, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 0, 2, 0, 0, 0, 0, 0, 0, : 0, 1, 0, 0, 1, 0, 0, 0, 0, : -1, 0, 0, 2, 1, 0, 0, 0, 0, : 0, 2, 2, -2, 2, 0, 0, 0, 0, : 0, 0, 2, -2, 0, 0, 0, 0, 0 / DATA ( ( NA(I,J), I=1,9 ), J=31,40 ) / : -1, 0, 0, 2, -1, 0, 0, 0, 0, : 0, 1, 0, 0, -1, 0, 0, 0, 0, : 0, 2, 0, 0, 0, 0, 0, 0, 0, : -1, 0, 2, 2, 1, 0, 0, 0, 0, : 1, 0, 2, 2, 2, 0, 0, 0, 0, : 0, 1, 2, 0, 2, 0, 0, 0, 0, : -2, 0, 2, 0, 0, 0, 0, 0, 0, : 0, 0, 2, 2, 1, 0, 0, 0, 0, : 0, -1, 2, 0, 2, 0, 0, 0, 0, : 0, 0, 0, 2, 1, 0, 0, 0, 0 / DATA ( ( NA(I,J), I=1,9 ), J=41,50 ) / : 1, 0, 2, -2, 1, 0, 0, 0, 0, : 2, 0, 0, -2, -1, 0, 0, 0, 0, : 2, 0, 2, -2, 2, 0, 0, 0, 0, : 2, 0, 2, 0, 1, 0, 0, 0, 0, : 0, 0, 0, 2, -1, 0, 0, 0, 0, : 0, -1, 2, -2, 1, 0, 0, 0, 0, : -1, -1, 0, 2, 0, 0, 0, 0, 0, : 2, 0, 0, -2, 1, 0, 0, 0, 0, : 1, 0, 0, 2, 0, 0, 0, 0, 0, : 0, 1, 2, -2, 1, 0, 0, 0, 0 / DATA ( ( NA(I,J), I=1,9 ), J=51,60 ) / : 1, -1, 0, 0, 0, 0, 0, 0, 0, : -2, 0, 2, 0, 2, 0, 0, 0, 0, : 0, -1, 0, 2, 0, 0, 0, 0, 0, : 3, 0, 2, 0, 2, 0, 0, 0, 0, : 0, 0, 0, 1, 0, 0, 0, 0, 0, : 1, -1, 2, 0, 2, 0, 0, 0, 0, : 1, 0, 0, -1, 0, 0, 0, 0, 0, : -1, -1, 2, 2, 2, 0, 0, 0, 0, : -1, 0, 2, 0, 0, 0, 0, 0, 0, : 2, 0, 0, 0, -1, 0, 0, 0, 0 / DATA ( ( NA(I,J), I=1,9 ), J=61,70 ) / : 0, -1, 2, 2, 2, 0, 0, 0, 0, : 1, 1, 2, 0, 2, 0, 0, 0, 0, : 2, 0, 0, 0, 1, 0, 0, 0, 0, : 1, 1, 0, 0, 0, 0, 0, 0, 0, : 1, 0, -2, 2, -1, 0, 0, 0, 0, : 1, 0, 2, 0, 0, 0, 0, 0, 0, : -1, 1, 0, 1, 0, 0, 0, 0, 0, : 1, 0, 0, 0, 2, 0, 0, 0, 0, : -1, 0, 1, 0, 1, 0, 0, 0, 0, : 0, 0, 2, 1, 2, 0, 0, 0, 0 / DATA ( ( NA(I,J), I=1,9 ), J=71,80 ) / : -1, 1, 0, 1, 1, 0, 0, 0, 0, : -1, 0, 2, 4, 2, 0, 0, 0, 0, : 0, -2, 2, -2, 1, 0, 0, 0, 0, : 1, 0, 2, 2, 1, 0, 0, 0, 0, : 1, 0, 0, 0, -2, 0, 0, 0, 0, : -2, 0, 2, 2, 2, 0, 0, 0, 0, : 1, 1, 2, -2, 2, 0, 0, 0, 0, : -2, 0, 2, 4, 2, 0, 0, 0, 0, : -1, 0, 4, 0, 2, 0, 0, 0, 0, : 2, 0, 2, -2, 1, 0, 0, 0, 0 / DATA ( ( NA(I,J), I=1,9 ), J=81,90 ) / : 1, 0, 0, -1, -1, 0, 0, 0, 0, : 2, 0, 2, 2, 2, 0, 0, 0, 0, : 1, 0, 0, 2, 1, 0, 0, 0, 0, : 3, 0, 0, 0, 0, 0, 0, 0, 0, : 0, 0, 2, -2, -1, 0, 0, 0, 0, : 3, 0, 2, -2, 2, 0, 0, 0, 0, : 0, 0, 4, -2, 2, 0, 0, 0, 0, : -1, 0, 0, 4, 0, 0, 0, 0, 0, : 0, 1, 2, 0, 1, 0, 0, 0, 0, : 0, 0, 2, -2, 3, 0, 0, 0, 0 / DATA ( ( NA(I,J), I=1,9 ), J=91,100 ) / : -2, 0, 0, 4, 0, 0, 0, 0, 0, : -1, -1, 0, 2, 1, 0, 0, 0, 0, : -2, 0, 2, 0, -1, 0, 0, 0, 0, : 0, 0, 2, 0, -1, 0, 0, 0, 0, : 0, -1, 2, 0, 1, 0, 0, 0, 0, : 0, 1, 0, 0, 2, 0, 0, 0, 0, : 0, 0, 2, -1, 2, 0, 0, 0, 0, : 2, 1, 0, -2, 0, 0, 0, 0, 0, : 0, 0, 2, 4, 2, 0, 0, 0, 0, : -1, -1, 0, 2, -1, 0, 0, 0, 0 / DATA ( ( NA(I,J), I=1,9 ), J=101,110 ) / : -1, 1, 0, 2, 0, 0, 0, 0, 0, : 1, -1, 0, 0, 1, 0, 0, 0, 0, : 0, -1, 2, -2, 0, 0, 0, 0, 0, : 0, 1, 0, 0, -2, 0, 0, 0, 0, : 1, -1, 2, 2, 2, 0, 0, 0, 0, : 1, 0, 0, 2, -1, 0, 0, 0, 0, : -1, 1, 2, 2, 2, 0, 0, 0, 0, : 3, 0, 2, 0, 1, 0, 0, 0, 0, : 0, 1, 2, 2, 2, 0, 0, 0, 0, : 1, 0, 2, -2, 0, 0, 0, 0, 0 / DATA ( ( NA(I,J), I=1,9 ), J=111,120 ) / : -1, 0, -2, 4, -1, 0, 0, 0, 0, : -1, -1, 2, 2, 1, 0, 0, 0, 0, : 0, -1, 2, 2, 1, 0, 0, 0, 0, : 2, -1, 2, 0, 2, 0, 0, 0, 0, : 0, 0, 0, 2, 2, 0, 0, 0, 0, : 1, -1, 2, 0, 1, 0, 0, 0, 0, : -1, 1, 2, 0, 2, 0, 0, 0, 0, : 0, 1, 0, 2, 0, 0, 0, 0, 0, : 0, 1, 2, -2, 0, 0, 0, 0, 0, : 0, 3, 2, -2, 2, 0, 0, 0, 0 / DATA ( ( NA(I,J), I=1,9 ), J=121,130 ) / : 0, 0, 0, 1, 1, 0, 0, 0, 0, : -1, 0, 2, 2, 0, 0, 0, 0, 0, : 2, 1, 2, 0, 2, 0, 0, 0, 0, : 1, 1, 0, 0, 1, 0, 0, 0, 0, : 2, 0, 0, 2, 0, 0, 0, 0, 0, : 1, 1, 2, 0, 1, 0, 0, 0, 0, : -1, 0, 0, 2, 2, 0, 0, 0, 0, : 1, 0, -2, 2, 0, 0, 0, 0, 0, : 0, -1, 0, 2, -1, 0, 0, 0, 0, : -1, 0, 1, 0, 2, 0, 0, 0, 0 / DATA ( ( NA(I,J), I=1,9 ), J=131,140 ) / : 0, 1, 0, 1, 0, 0, 0, 0, 0, : 1, 0, -2, 2, -2, 0, 0, 0, 0, : 0, 0, 0, 1, -1, 0, 0, 0, 0, : 1, -1, 0, 0, -1, 0, 0, 0, 0, : 0, 0, 0, 4, 0, 0, 0, 0, 0, : 1, -1, 0, 2, 0, 0, 0, 0, 0, : 1, 0, 2, 1, 2, 0, 0, 0, 0, : 1, 0, 2, -1, 2, 0, 0, 0, 0, : -1, 0, 0, 2, -2, 0, 0, 0, 0, : 0, 0, 2, 1, 1, 0, 0, 0, 0 / DATA ( ( NA(I,J), I=1,9 ), J=141,150 ) / : -1, 0, 2, 0, -1, 0, 0, 0, 0, : -1, 0, 2, 4, 1, 0, 0, 0, 0, : 0, 0, 2, 2, 0, 0, 0, 0, 0, : 1, 1, 2, -2, 1, 0, 0, 0, 0, : 0, 0, 1, 0, 1, 0, 0, 0, 0, : -1, 0, 2, -1, 1, 0, 0, 0, 0, : -2, 0, 2, 2, 1, 0, 0, 0, 0, : 2, -1, 0, 0, 0, 0, 0, 0, 0, : 4, 0, 2, 0, 2, 0, 0, 0, 0, : 2, 1, 2, -2, 2, 0, 0, 0, 0 / DATA ( ( NA(I,J), I=1,9 ), J=151,160 ) / : 0, 1, 2, 1, 2, 0, 0, 0, 0, : 1, 0, 4, -2, 2, 0, 0, 0, 0, : 1, 1, 0, 0, -1, 0, 0, 0, 0, : -2, 0, 2, 4, 1, 0, 0, 0, 0, : 2, 0, 2, 0, 0, 0, 0, 0, 0, : -1, 0, 1, 0, 0, 0, 0, 0, 0, : 1, 0, 0, 1, 0, 0, 0, 0, 0, : 0, 1, 0, 2, 1, 0, 0, 0, 0, : -1, 0, 4, 0, 1, 0, 0, 0, 0, : -1, 0, 0, 4, 1, 0, 0, 0, 0 / DATA ( ( NA(I,J), I=1,9 ), J=161,170 ) / : 2, 0, 2, 2, 1, 0, 0, 0, 0, : 2, 1, 0, 0, 0, 0, 0, 0, 0, : 0, 0, 5, -5, 5, -3, 0, 0, 0, : 0, 0, 0, 0, 0, 0, 0, 2, 0, : 0, 0, 1, -1, 1, 0, 0, -1, 0, : 0, 0, -1, 1, -1, 1, 0, 0, 0, : 0, 0, -1, 1, 0, 0, 2, 0, 0, : 0, 0, 3, -3, 3, 0, 0, -1, 0, : 0, 0, -8, 8, -7, 5, 0, 0, 0, : 0, 0, -1, 1, -1, 0, 2, 0, 0 / DATA ( ( NA(I,J), I=1,9 ), J=171,180 ) / : 0, 0, -2, 2, -2, 2, 0, 0, 0, : 0, 0, -6, 6, -6, 4, 0, 0, 0, : 0, 0, -2, 2, -2, 0, 8, -3, 0, : 0, 0, 6, -6, 6, 0, -8, 3, 0, : 0, 0, 4, -4, 4, -2, 0, 0, 0, : 0, 0, -3, 3, -3, 2, 0, 0, 0, : 0, 0, 4, -4, 3, 0, -8, 3, 0, : 0, 0, -4, 4, -5, 0, 8, -3, 0, : 0, 0, 0, 0, 0, 2, 0, 0, 0, : 0, 0, -4, 4, -4, 3, 0, 0, 0 / DATA ( ( NA(I,J), I=1,9 ), J=181,190 ) / : 0, 1, -1, 1, -1, 0, 0, 1, 0, : 0, 0, 0, 0, 0, 0, 0, 1, 0, : 0, 0, 1, -1, 1, 1, 0, 0, 0, : 0, 0, 2, -2, 2, 0, -2, 0, 0, : 0, -1, -7, 7, -7, 5, 0, 0, 0, : -2, 0, 2, 0, 2, 0, 0, -2, 0, : -2, 0, 2, 0, 1, 0, 0, -3, 0, : 0, 0, 2, -2, 2, 0, 0, -2, 0, : 0, 0, 1, -1, 1, 0, 0, 1, 0, : 0, 0, 0, 0, 0, 0, 0, 0, 2 / DATA ( ( NA(I,J), I=1,9 ), J=191,NTERMS ) / : 0, 0, 0, 0, 0, 0, 0, 0, 1, : 2, 0, -2, 0, -2, 0, 0, 3, 0, : 0, 0, 1, -1, 1, 0, 0, -2, 0, : 0, 0, -7, 7, -7, 5, 0, 0, 0 / * Nutation series: longitude DATA ( ( PSI(I,J), I=1,4 ), J=1,10 ) / : 3341.5D0, 17206241.8D0, 3.1D0, 17409.5D0, : -1716.8D0, -1317185.3D0, 1.4D0, -156.8D0, : 285.7D0, -227667.0D0, 0.3D0, -23.5D0, : -68.6D0, -207448.0D0, 0.0D0, -21.4D0, : 950.3D0, 147607.9D0, -2.3D0, -355.0D0, : -66.7D0, -51689.1D0, 0.2D0, 122.6D0, : -108.6D0, 71117.6D0, 0.0D0, 7.0D0, : 35.6D0, -38740.2D0, 0.1D0, -36.2D0, : 85.4D0, -30127.6D0, 0.0D0, -3.1D0, : 9.0D0, 21583.0D0, 0.1D0, -50.3D0 / DATA ( ( PSI(I,J), I=1,4 ), J=11,20 ) / : 22.1D0, 12822.8D0, 0.0D0, 13.3D0, : 3.4D0, 12350.8D0, 0.0D0, 1.3D0, : -21.1D0, 15699.4D0, 0.0D0, 1.6D0, : 4.2D0, 6313.8D0, 0.0D0, 6.2D0, : -22.8D0, 5796.9D0, 0.0D0, 6.1D0, : 15.7D0, -5961.1D0, 0.0D0, -0.6D0, : 13.1D0, -5159.1D0, 0.0D0, -4.6D0, : 1.8D0, 4592.7D0, 0.0D0, 4.5D0, : -17.5D0, 6336.0D0, 0.0D0, 0.7D0, : 16.3D0, -3851.1D0, 0.0D0, -0.4D0 / DATA ( ( PSI(I,J), I=1,4 ), J=21,30 ) / : -2.8D0, 4771.7D0, 0.0D0, 0.5D0, : 13.8D0, -3099.3D0, 0.0D0, -0.3D0, : 0.2D0, 2860.3D0, 0.0D0, 0.3D0, : 1.4D0, 2045.3D0, 0.0D0, 2.0D0, : -8.6D0, 2922.6D0, 0.0D0, 0.3D0, : -7.7D0, 2587.9D0, 0.0D0, 0.2D0, : 8.8D0, -1408.1D0, 0.0D0, 3.7D0, : 1.4D0, 1517.5D0, 0.0D0, 1.5D0, : -1.9D0, -1579.7D0, 0.0D0, 7.7D0, : 1.3D0, -2178.6D0, 0.0D0, -0.2D0 / DATA ( ( PSI(I,J), I=1,4 ), J=31,40 ) / : -4.8D0, 1286.8D0, 0.0D0, 1.3D0, : 6.3D0, 1267.2D0, 0.0D0, -4.0D0, : -1.0D0, 1669.3D0, 0.0D0, -8.3D0, : 2.4D0, -1020.0D0, 0.0D0, -0.9D0, : 4.5D0, -766.9D0, 0.0D0, 0.0D0, : -1.1D0, 756.5D0, 0.0D0, -1.7D0, : -1.4D0, -1097.3D0, 0.0D0, -0.5D0, : 2.6D0, -663.0D0, 0.0D0, -0.6D0, : 0.8D0, -714.1D0, 0.0D0, 1.6D0, : 0.4D0, -629.9D0, 0.0D0, -0.6D0 / DATA ( ( PSI(I,J), I=1,4 ), J=41,50 ) / : 0.3D0, 580.4D0, 0.0D0, 0.6D0, : -1.6D0, 577.3D0, 0.0D0, 0.5D0, : -0.9D0, 644.4D0, 0.0D0, 0.0D0, : 2.2D0, -534.0D0, 0.0D0, -0.5D0, : -2.5D0, 493.3D0, 0.0D0, 0.5D0, : -0.1D0, -477.3D0, 0.0D0, -2.4D0, : -0.9D0, 735.0D0, 0.0D0, -1.7D0, : 0.7D0, 406.2D0, 0.0D0, 0.4D0, : -2.8D0, 656.9D0, 0.0D0, 0.0D0, : 0.6D0, 358.0D0, 0.0D0, 2.0D0 / DATA ( ( PSI(I,J), I=1,4 ), J=51,60 ) / : -0.7D0, 472.5D0, 0.0D0, -1.1D0, : -0.1D0, -300.5D0, 0.0D0, 0.0D0, : -1.2D0, 435.1D0, 0.0D0, -1.0D0, : 1.8D0, -289.4D0, 0.0D0, 0.0D0, : 0.6D0, -422.6D0, 0.0D0, 0.0D0, : 0.8D0, -287.6D0, 0.0D0, 0.6D0, : -38.6D0, -392.3D0, 0.0D0, 0.0D0, : 0.7D0, -281.8D0, 0.0D0, 0.6D0, : 0.6D0, -405.7D0, 0.0D0, 0.0D0, : -1.2D0, 229.0D0, 0.0D0, 0.2D0 / DATA ( ( PSI(I,J), I=1,4 ), J=61,70 ) / : 1.1D0, -264.3D0, 0.0D0, 0.5D0, : -0.7D0, 247.9D0, 0.0D0, -0.5D0, : -0.2D0, 218.0D0, 0.0D0, 0.2D0, : 0.6D0, -339.0D0, 0.0D0, 0.8D0, : -0.7D0, 198.7D0, 0.0D0, 0.2D0, : -1.5D0, 334.0D0, 0.0D0, 0.0D0, : 0.1D0, 334.0D0, 0.0D0, 0.0D0, : -0.1D0, -198.1D0, 0.0D0, 0.0D0, : -106.6D0, 0.0D0, 0.0D0, 0.0D0, : -0.5D0, 165.8D0, 0.0D0, 0.0D0 / DATA ( ( PSI(I,J), I=1,4 ), J=71,80 ) / : 0.0D0, 134.8D0, 0.0D0, 0.0D0, : 0.9D0, -151.6D0, 0.0D0, 0.0D0, : 0.0D0, -129.7D0, 0.0D0, 0.0D0, : 0.8D0, -132.8D0, 0.0D0, -0.1D0, : 0.5D0, -140.7D0, 0.0D0, 0.0D0, : -0.1D0, 138.4D0, 0.0D0, 0.0D0, : 0.0D0, 129.0D0, 0.0D0, -0.3D0, : 0.5D0, -121.2D0, 0.0D0, 0.0D0, : -0.3D0, 114.5D0, 0.0D0, 0.0D0, : -0.1D0, 101.8D0, 0.0D0, 0.0D0 / DATA ( ( PSI(I,J), I=1,4 ), J=81,90 ) / : -3.6D0, -101.9D0, 0.0D0, 0.0D0, : 0.8D0, -109.4D0, 0.0D0, 0.0D0, : 0.2D0, -97.0D0, 0.0D0, 0.0D0, : -0.7D0, 157.3D0, 0.0D0, 0.0D0, : 0.2D0, -83.3D0, 0.0D0, 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PSI(I,J), I=1,4 ), J=141,150 ) / : 0.1D0, -25.2D0, 0.0D0, 0.0D0, : 0.1D0, -26.2D0, 0.0D0, 0.0D0, : -0.2D0, 41.5D0, 0.0D0, 0.0D0, : 0.0D0, 24.5D0, 0.0D0, 0.1D0, : -16.2D0, 0.0D0, 0.0D0, 0.0D0, : 0.0D0, -22.3D0, 0.0D0, 0.0D0, : 0.0D0, 23.1D0, 0.0D0, 0.0D0, : -0.1D0, 37.5D0, 0.0D0, 0.0D0, : 0.2D0, -25.7D0, 0.0D0, 0.0D0, : 0.0D0, 25.2D0, 0.0D0, 0.0D0 / DATA ( ( PSI(I,J), I=1,4 ), J=151,160 ) / : 0.1D0, -24.5D0, 0.0D0, 0.0D0, : -0.1D0, 24.3D0, 0.0D0, 0.0D0, : 0.1D0, -20.7D0, 0.0D0, 0.0D0, : 0.1D0, -20.8D0, 0.0D0, 0.0D0, : -0.2D0, 33.4D0, 0.0D0, 0.0D0, : 32.9D0, 0.0D0, 0.0D0, 0.0D0, : 0.1D0, -32.6D0, 0.0D0, 0.0D0, : 0.0D0, 19.9D0, 0.0D0, 0.0D0, : -0.1D0, 19.6D0, 0.0D0, 0.0D0, : 0.0D0, -18.7D0, 0.0D0, 0.0D0 / DATA ( ( PSI(I,J), I=1,4 ), J=161,170 ) / : 0.1D0, -19.0D0, 0.0D0, 0.0D0, : 0.1D0, -28.6D0, 0.0D0, 0.0D0, : 4.0D0, 178.8D0,-11.8D0, 0.3D0, : 39.8D0, -107.3D0, -5.6D0, -1.0D0, : 9.9D0, 164.0D0, -4.1D0, 0.1D0, : -4.8D0, -135.3D0, -3.4D0, -0.1D0, : 50.5D0, 75.0D0, 1.4D0, -1.2D0, : -1.1D0, 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2.4D0, 0.6D0 / * Nutation series: obliquity DATA ( ( EPS(I,J), I=1,4 ), J=1,10 ) / : 9205365.8D0, -1506.2D0, 885.7D0, -0.2D0, : 573095.9D0, -570.2D0, -305.0D0, -0.3D0, : 97845.5D0, 147.8D0, -48.8D0, -0.2D0, : -89753.6D0, 28.0D0, 46.9D0, 0.0D0, : 7406.7D0, -327.1D0, -18.2D0, 0.8D0, : 22442.3D0, -22.3D0, -67.6D0, 0.0D0, : -683.6D0, 46.8D0, 0.0D0, 0.0D0, : 20070.7D0, 36.0D0, 1.6D0, 0.0D0, : 12893.8D0, 39.5D0, -6.2D0, 0.0D0, : -9593.2D0, 14.4D0, 30.2D0, -0.1D0 / DATA ( ( EPS(I,J), I=1,4 ), J=11,20 ) / : -6899.5D0, 4.8D0, -0.6D0, 0.0D0, : -5332.5D0, -0.1D0, 2.7D0, 0.0D0, : -125.2D0, 10.5D0, 0.0D0, 0.0D0, : -3323.4D0, -0.9D0, -0.3D0, 0.0D0, : 3142.3D0, 8.9D0, 0.3D0, 0.0D0, : 2552.5D0, 7.3D0, -1.2D0, 0.0D0, : 2634.4D0, 8.8D0, 0.2D0, 0.0D0, : -2424.4D0, 1.6D0, -0.4D0, 0.0D0, : -123.3D0, 3.9D0, 0.0D0, 0.0D0, : 1642.4D0, 7.3D0, -0.8D0, 0.0D0 / DATA ( ( EPS(I,J), I=1,4 ), J=21,30 ) / : 47.9D0, 3.2D0, 0.0D0, 0.0D0, : 1321.2D0, 6.2D0, -0.6D0, 0.0D0, : -1234.1D0, -0.3D0, 0.6D0, 0.0D0, : -1076.5D0, 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-4.1D0, 0.3D0, 0.0D0, 0.0D0, : 130.6D0, -0.1D0, 0.0D0, 0.0D0, : 3.0D0, 0.3D0, 0.0D0, 0.0D0, : 122.9D0, 0.8D0, 0.0D0, 0.0D0, : 3.7D0, -0.3D0, 0.0D0, 0.0D0, : 123.1D0, 0.4D0, -0.3D0, 0.0D0, : -52.7D0, 15.3D0, 0.0D0, 0.0D0, : 120.7D0, 0.3D0, -0.3D0, 0.0D0, : 4.0D0, -0.3D0, 0.0D0, 0.0D0, : 126.5D0, 0.5D0, 0.0D0, 0.0D0 / DATA ( ( EPS(I,J), I=1,4 ), J=61,70 ) / : 112.7D0, 0.5D0, -0.3D0, 0.0D0, : -106.1D0, -0.3D0, 0.3D0, 0.0D0, : -112.9D0, -0.2D0, 0.0D0, 0.0D0, : 3.6D0, -0.2D0, 0.0D0, 0.0D0, : 107.4D0, 0.3D0, 0.0D0, 0.0D0, : -10.9D0, 0.2D0, 0.0D0, 0.0D0, : -0.9D0, 0.0D0, 0.0D0, 0.0D0, : 85.4D0, 0.0D0, 0.0D0, 0.0D0, : 0.0D0, -88.8D0, 0.0D0, 0.0D0, : -71.0D0, -0.2D0, 0.0D0, 0.0D0 / DATA ( ( EPS(I,J), I=1,4 ), J=71,80 ) / : -70.3D0, 0.0D0, 0.0D0, 0.0D0, : 64.5D0, 0.4D0, 0.0D0, 0.0D0, : 69.8D0, 0.0D0, 0.0D0, 0.0D0, : 66.1D0, 0.4D0, 0.0D0, 0.0D0, : -61.0D0, -0.2D0, 0.0D0, 0.0D0, : -59.5D0, -0.1D0, 0.0D0, 0.0D0, : -55.6D0, 0.0D0, 0.2D0, 0.0D0, : 51.7D0, 0.2D0, 0.0D0, 0.0D0, : -49.0D0, -0.1D0, 0.0D0, 0.0D0, : -52.7D0, -0.1D0, 0.0D0, 0.0D0 / DATA ( ( EPS(I,J), I=1,4 ), J=81,90 ) / : -49.6D0, 1.4D0, 0.0D0, 0.0D0, : 46.3D0, 0.4D0, 0.0D0, 0.0D0, : 49.6D0, 0.1D0, 0.0D0, 0.0D0, : -5.1D0, 0.1D0, 0.0D0, 0.0D0, : -44.0D0, -0.1D0, 0.0D0, 0.0D0, : -39.9D0, -0.1D0, 0.0D0, 0.0D0, : -39.5D0, -0.1D0, 0.0D0, 0.0D0, : -3.9D0, 0.1D0, 0.0D0, 0.0D0, : -42.1D0, -0.1D0, 0.0D0, 0.0D0, : -17.2D0, 0.1D0, 0.0D0, 0.0D0 / DATA ( ( EPS(I,J), I=1,4 ), J=91,100 ) / : -2.3D0, 0.1D0, 0.0D0, 0.0D0, : -39.2D0, 0.0D0, 0.0D0, 0.0D0, : -38.4D0, 0.1D0, 0.0D0, 0.0D0, : 36.8D0, 0.2D0, 0.0D0, 0.0D0, : 34.6D0, 0.1D0, 0.0D0, 0.0D0, : -32.7D0, 0.3D0, 0.0D0, 0.0D0, : 30.4D0, 0.0D0, 0.0D0, 0.0D0, : 0.4D0, 0.1D0, 0.0D0, 0.0D0, : 29.3D0, 0.2D0, 0.0D0, 0.0D0, : 31.6D0, 0.1D0, 0.0D0, 0.0D0 / DATA ( ( EPS(I,J), I=1,4 ), J=101,110 ) / : 0.8D0, -0.1D0, 0.0D0, 0.0D0, : -27.9D0, 0.0D0, 0.0D0, 0.0D0, : 2.9D0, 0.0D0, 0.0D0, 0.0D0, : -25.3D0, 0.0D0, 0.0D0, 0.0D0, : 25.0D0, 0.1D0, 0.0D0, 0.0D0, : 27.5D0, 0.1D0, 0.0D0, 0.0D0, : -24.4D0, -0.1D0, 0.0D0, 0.0D0, : 24.9D0, 0.2D0, 0.0D0, 0.0D0, : -22.8D0, -0.1D0, 0.0D0, 0.0D0, : 0.9D0, -0.1D0, 0.0D0, 0.0D0 / DATA ( ( EPS(I,J), I=1,4 ), J=111,120 ) / : 24.4D0, 0.1D0, 0.0D0, 0.0D0, : 23.9D0, 0.1D0, 0.0D0, 0.0D0, : 22.5D0, 0.1D0, 0.0D0, 0.0D0, : 20.8D0, 0.1D0, 0.0D0, 0.0D0, : 20.1D0, 0.0D0, 0.0D0, 0.0D0, : 21.5D0, 0.1D0, 0.0D0, 0.0D0, : -20.0D0, 0.0D0, 0.0D0, 0.0D0, : 1.4D0, 0.0D0, 0.0D0, 0.0D0, : -0.2D0, -0.1D0, 0.0D0, 0.0D0, : 19.0D0, 0.0D0, -0.1D0, 0.0D0 / DATA ( ( EPS(I,J), I=1,4 ), J=121,130 ) / : 20.5D0, 0.0D0, 0.0D0, 0.0D0, : -2.0D0, 0.0D0, 0.0D0, 0.0D0, : -17.6D0, -0.1D0, 0.0D0, 0.0D0, : 19.0D0, 0.0D0, 0.0D0, 0.0D0, : -2.4D0, 0.0D0, 0.0D0, 0.0D0, : -18.4D0, -0.1D0, 0.0D0, 0.0D0, : 17.1D0, 0.0D0, 0.0D0, 0.0D0, : 0.4D0, 0.0D0, 0.0D0, 0.0D0, : 18.4D0, 0.1D0, 0.0D0, 0.0D0, : 0.0D0, 17.4D0, 0.0D0, 0.0D0 / DATA ( ( EPS(I,J), I=1,4 ), J=131,140 ) / : -0.6D0, 0.0D0, 0.0D0, 0.0D0, : -15.4D0, 0.0D0, 0.0D0, 0.0D0, : -16.8D0, -0.1D0, 0.0D0, 0.0D0, : 16.3D0, 0.0D0, 0.0D0, 0.0D0, : -2.0D0, 0.0D0, 0.0D0, 0.0D0, : -1.5D0, 0.0D0, 0.0D0, 0.0D0, : -14.3D0, -0.1D0, 0.0D0, 0.0D0, : 14.4D0, 0.0D0, 0.0D0, 0.0D0, : -13.4D0, 0.0D0, 0.0D0, 0.0D0, : -14.3D0, -0.1D0, 0.0D0, 0.0D0 / DATA ( ( EPS(I,J), I=1,4 ), J=141,150 ) / : -13.7D0, 0.0D0, 0.0D0, 0.0D0, : 13.1D0, 0.1D0, 0.0D0, 0.0D0, : -1.7D0, 0.0D0, 0.0D0, 0.0D0, : -12.8D0, 0.0D0, 0.0D0, 0.0D0, : 0.0D0, -14.4D0, 0.0D0, 0.0D0, : 12.4D0, 0.0D0, 0.0D0, 0.0D0, : -12.0D0, 0.0D0, 0.0D0, 0.0D0, : -0.8D0, 0.0D0, 0.0D0, 0.0D0, : 10.9D0, 0.1D0, 0.0D0, 0.0D0, : -10.8D0, 0.0D0, 0.0D0, 0.0D0 / DATA ( ( EPS(I,J), I=1,4 ), J=151,160 ) / : 10.5D0, 0.0D0, 0.0D0, 0.0D0, : -10.4D0, 0.0D0, 0.0D0, 0.0D0, : -11.2D0, 0.0D0, 0.0D0, 0.0D0, : 10.5D0, 0.1D0, 0.0D0, 0.0D0, : -1.4D0, 0.0D0, 0.0D0, 0.0D0, : 0.0D0, 0.1D0, 0.0D0, 0.0D0, : 0.7D0, 0.0D0, 0.0D0, 0.0D0, : -10.3D0, 0.0D0, 0.0D0, 0.0D0, : -10.0D0, 0.0D0, 0.0D0, 0.0D0, : 9.6D0, 0.0D0, 0.0D0, 0.0D0 / DATA ( ( EPS(I,J), I=1,4 ), J=161,170 ) / : 9.4D0, 0.1D0, 0.0D0, 0.0D0, : 0.6D0, 0.0D0, 0.0D0, 0.0D0, : -87.7D0, 4.4D0, -0.4D0, -6.3D0, : 46.3D0, 22.4D0, 0.5D0, -2.4D0, : 15.6D0, -3.4D0, 0.1D0, 0.4D0, : 5.2D0, 5.8D0, 0.2D0, -0.1D0, : -30.1D0, 26.9D0, 0.7D0, 0.0D0, : 23.2D0, -0.5D0, 0.0D0, 0.6D0, : 1.0D0, 23.2D0, 3.4D0, 0.0D0, : -12.2D0, -4.3D0, 0.0D0, 0.0D0 / DATA ( ( EPS(I,J), I=1,4 ), J=171,180 ) / : -2.1D0, -3.7D0, -0.2D0, 0.1D0, : -18.6D0, -3.8D0, -0.4D0, 1.8D0, : 5.5D0, -18.7D0, -1.8D0, -0.5D0, : -5.5D0, -18.7D0, 1.8D0, -0.5D0, : 18.4D0, -3.6D0, 0.3D0, 0.9D0, : -0.6D0, 1.3D0, 0.0D0, 0.0D0, : -5.6D0, -19.5D0, 1.9D0, 0.0D0, : 5.5D0, -19.1D0, -1.9D0, 0.0D0, : -17.3D0, -0.8D0, 0.0D0, 0.9D0, : -3.2D0, -8.3D0, -0.8D0, 0.3D0 / DATA ( ( EPS(I,J), I=1,4 ), J=181,190 ) / : -0.1D0, 0.0D0, 0.0D0, 0.0D0, : -5.4D0, 7.8D0, -0.3D0, 0.0D0, : -14.8D0, 1.4D0, 0.0D0, 0.3D0, : -3.8D0, 0.4D0, 0.0D0, -0.2D0, : 12.6D0, 3.2D0, 0.5D0, -1.5D0, : 0.1D0, 0.0D0, 0.0D0, 0.0D0, : -13.6D0, 2.4D0, -0.1D0, 0.0D0, : 0.9D0, 1.2D0, 0.0D0, 0.0D0, : -11.9D0, -0.5D0, 0.0D0, 0.3D0, : 0.4D0, 12.0D0, 0.3D0, -0.2D0 / DATA ( ( EPS(I,J), I=1,4 ), J=191,NTERMS ) / : 8.3D0, 6.1D0, -0.1D0, 0.1D0, : 0.0D0, 0.0D0, 0.0D0, 0.0D0, : 0.4D0, -10.8D0, 0.3D0, 0.0D0, : 9.6D0, 2.2D0, 0.3D0, -1.2D0 / * Interval between fundamental epoch J2000.0 and given epoch (JC). T = (DATE-DJM0)/DJC * Mean anomaly of the Moon. EL = 134.96340251D0*DD2R+ : MOD(T*(1717915923.2178D0+ : T*( 31.8792D0+ : T*( 0.051635D0+ : T*( - 0.00024470D0)))),TURNAS)*DAS2R * Mean anomaly of the Sun. ELP = 357.52910918D0*DD2R+ : MOD(T*( 129596581.0481D0+ : T*( - 0.5532D0+ : T*( 0.000136D0+ : T*( - 0.00001149D0)))),TURNAS)*DAS2R * Mean argument of the latitude of the Moon. F = 93.27209062D0*DD2R+ : MOD(T*(1739527262.8478D0+ : T*( - 12.7512D0+ : T*( - 0.001037D0+ : T*( 0.00000417D0)))),TURNAS)*DAS2R * Mean elongation of the Moon from the Sun. D = 297.85019547D0*DD2R+ : MOD(T*(1602961601.2090D0+ : T*( - 6.3706D0+ : T*( 0.006539D0+ : T*( - 0.00003169D0)))),TURNAS)*DAS2R * Mean longitude of the ascending node of the Moon. OM = 125.04455501D0*DD2R+ : MOD(T*( - 6962890.5431D0+ : T*( 7.4722D0+ : T*( 0.007702D0+ : T*( - 0.00005939D0)))),TURNAS)*DAS2R * Mean longitude of Venus. VE = 181.97980085D0*DD2R+MOD(210664136.433548D0*T,TURNAS)*DAS2R * Mean longitude of Mars. MA = 355.43299958D0*DD2R+MOD( 68905077.493988D0*T,TURNAS)*DAS2R * Mean longitude of Jupiter. JU = 34.35151874D0*DD2R+MOD( 10925660.377991D0*T,TURNAS)*DAS2R * Mean longitude of Saturn. SA = 50.07744430D0*DD2R+MOD( 4399609.855732D0*T,TURNAS)*DAS2R * Geodesic nutation (Fukushima 1991) in microarcsec. DP = -153.1D0*SIN(ELP)-1.9D0*SIN(2D0*ELP) DE = 0D0 * Shirai & Fukushima (2001) nutation series. DO J=NTERMS,1,-1 THETA = DBLE(NA(1,J))*EL+ : DBLE(NA(2,J))*ELP+ : DBLE(NA(3,J))*F+ : DBLE(NA(4,J))*D+ : DBLE(NA(5,J))*OM+ : DBLE(NA(6,J))*VE+ : DBLE(NA(7,J))*MA+ : DBLE(NA(8,J))*JU+ : DBLE(NA(9,J))*SA C = COS(THETA) S = SIN(THETA) DP = DP+(PSI(1,J)+PSI(3,J)*T)*C+(PSI(2,J)+PSI(4,J)*T)*S DE = DE+(EPS(1,J)+EPS(3,J)*T)*C+(EPS(2,J)+EPS(4,J)*T)*S END DO * Change of units, and addition of the precession correction. DPSI = (DP*1D-6-0.042888D0-0.29856D0*T)*DAS2R DEPS = (DE*1D-6-0.005171D0-0.02408D0*T)*DAS2R * Mean obliquity of date (Simon et al. 1994). EPS0 = (84381.412D0+ : (-46.80927D0+ : (-0.000152D0+ : (0.0019989D0+ : (-0.00000051D0+ : (-0.000000025D0)*T)*T)*T)*T)*T)*DAS2R END