SUBROUTINE sla_DMOON (DATE, PV) *+ * - - - - - - * D M O O N * - - - - - - * * Approximate geocentric position and velocity of the Moon * (double precision) * * Given: * DATE D TDB (loosely ET) as a Modified Julian Date * (JD-2400000.5) * * Returned: * PV D(6) Moon x,y,z,xdot,ydot,zdot, mean equator and * equinox of date (AU, AU/s) * * Notes: * * 1 This routine is a full implementation of the algorithm * published by Meeus (see reference). * * 2 Meeus quotes accuracies of 10 arcsec in longitude, 3 arcsec in * latitude and 0.2 arcsec in HP (equivalent to about 20 km in * distance). Comparison with JPL DE200 over the interval * 1960-2025 gives RMS errors of 3.7 arcsec and 83 mas/hour in * longitude, 2.3 arcsec and 48 mas/hour in latitude, 11 km * and 81 mm/s in distance. The maximum errors over the same * interval are 18 arcsec and 0.50 arcsec/hour in longitude, * 11 arcsec and 0.24 arcsec/hour in latitude, 40 km and 0.29 m/s * in distance. * * 3 The original algorithm is expressed in terms of the obsolete * timescale Ephemeris Time. Either TDB or TT can be used, but * not UT without incurring significant errors (30 arcsec at * the present time) due to the Moon's 0.5 arcsec/sec movement. * * 4 The algorithm is based on pre IAU 1976 standards. However, * the result has been moved onto the new (FK5) equinox, an * adjustment which is in any case much smaller than the * intrinsic accuracy of the procedure. * * 5 Velocity is obtained by a complete analytical differentiation * of the Meeus model. * * Reference: * Meeus, l'Astronomie, June 1984, p348. * * P.T.Wallace Starlink 22 January 1998 * * Copyright (C) 1998 Rutherford Appleton Laboratory * * 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,PV(6) * Degrees, arcseconds and seconds of time to radians DOUBLE PRECISION D2R,DAS2R,DS2R PARAMETER (D2R=0.0174532925199432957692369D0, : DAS2R=4.848136811095359935899141D-6, : DS2R=7.272205216643039903848712D-5) * Seconds per Julian century (86400*36525) DOUBLE PRECISION CJ PARAMETER (CJ=3155760000D0) * Julian epoch of B1950 DOUBLE PRECISION B1950 PARAMETER (B1950=1949.9997904423D0) * Earth equatorial radius in AU ( = 6378.137 / 149597870 ) DOUBLE PRECISION ERADAU PARAMETER (ERADAU=4.2635212653763D-5) DOUBLE PRECISION T,THETA,SINOM,COSOM,DOMCOM,WA,DWA,WB,DWB,WOM, : DWOM,SINWOM,COSWOM,V,DV,COEFF,EMN,EMPN,DN,FN,EN, : DEN,DTHETA,FTHETA,EL,DEL,B,DB,BF,DBF,P,DP,SP,R, : DR,X,Y,Z,XD,YD,ZD,SEL,CEL,SB,CB,RCB,RBD,W,EPJ, : EQCOR,EPS,SINEPS,COSEPS,ES,EC INTEGER N,I * * Coefficients for fundamental arguments * * at J1900: T**0, T**1, T**2, T**3 * at epoch: T**0, T**1 * * Units are degrees for position and Julian centuries for time * * Moon's mean longitude DOUBLE PRECISION ELP0,ELP1,ELP2,ELP3,ELP,DELP PARAMETER (ELP0=270.434164D0, : ELP1=481267.8831D0, : ELP2=-0.001133D0, : ELP3=0.0000019D0) * Sun's mean anomaly DOUBLE PRECISION EM0,EM1,EM2,EM3,EM,DEM PARAMETER (EM0=358.475833D0, : EM1=35999.0498D0, : EM2=-0.000150D0, : EM3=-0.0000033D0) * Moon's mean anomaly DOUBLE PRECISION EMP0,EMP1,EMP2,EMP3,EMP,DEMP PARAMETER (EMP0=296.104608D0, : EMP1=477198.8491D0, : EMP2=0.009192D0, : EMP3=0.0000144D0) * Moon's mean elongation DOUBLE PRECISION D0,D1,D2,D3,D,DD PARAMETER (D0=350.737486D0, : D1=445267.1142D0, : D2=-0.001436D0, : D3=0.0000019D0) * Mean distance of the Moon from its ascending node DOUBLE PRECISION F0,F1,F2,F3,F,DF PARAMETER (F0=11.250889D0, : F1=483202.0251D0, : F2=-0.003211D0, : F3=-0.0000003D0) * Longitude of the Moon's ascending node DOUBLE PRECISION OM0,OM1,OM2,OM3,OM,DOM PARAMETER (OM0=259.183275D0, : OM1=-1934.1420D0, : OM2=0.002078D0, : OM3=0.0000022D0) * Coefficients for (dimensionless) E factor DOUBLE PRECISION E1,E2,E,DE,ESQ,DESQ PARAMETER (E1=-0.002495D0,E2=-0.00000752D0) * Coefficients for periodic variations etc DOUBLE PRECISION PAC,PA0,PA1 PARAMETER (PAC=0.000233D0,PA0=51.2D0,PA1=20.2D0) DOUBLE PRECISION PBC PARAMETER (PBC=-0.001778D0) DOUBLE PRECISION PCC PARAMETER (PCC=0.000817D0) DOUBLE PRECISION PDC PARAMETER (PDC=0.002011D0) DOUBLE PRECISION PEC,PE0,PE1,PE2 PARAMETER (PEC=0.003964D0, : PE0=346.560D0,PE1=132.870D0,PE2=-0.0091731D0) DOUBLE PRECISION PFC PARAMETER (PFC=0.001964D0) DOUBLE PRECISION PGC PARAMETER (PGC=0.002541D0) DOUBLE PRECISION PHC PARAMETER (PHC=0.001964D0) DOUBLE PRECISION PIC PARAMETER (PIC=-0.024691D0) DOUBLE PRECISION PJC,PJ0,PJ1 PARAMETER (PJC=-0.004328D0,PJ0=275.05D0,PJ1=-2.30D0) DOUBLE PRECISION CW1 PARAMETER (CW1=0.0004664D0) DOUBLE PRECISION CW2 PARAMETER (CW2=0.0000754D0) * * Coefficients for Moon position * * Tx(N) = coefficient of L, B or P term (deg) * ITx(N,1-5) = coefficients of M, M', D, F, E**n in argument * INTEGER NL,NB,NP PARAMETER (NL=50,NB=45,NP=31) DOUBLE PRECISION TL(NL),TB(NB),TP(NP) INTEGER ITL(5,NL),ITB(5,NB),ITP(5,NP) * * Longitude * M M' D F n DATA TL( 1)/ +6.288750D0 /, : (ITL(I, 1),I=1,5)/ +0, +1, +0, +0, 0 / DATA TL( 2)/ +1.274018D0 /, : (ITL(I, 2),I=1,5)/ +0, -1, +2, +0, 0 / DATA TL( 3)/ +0.658309D0 /, : (ITL(I, 3),I=1,5)/ +0, +0, +2, +0, 0 / DATA TL( 4)/ +0.213616D0 /, : (ITL(I, 4),I=1,5)/ +0, +2, +0, +0, 0 / DATA TL( 5)/ -0.185596D0 /, : (ITL(I, 5),I=1,5)/ +1, +0, +0, +0, 1 / DATA TL( 6)/ -0.114336D0 /, : (ITL(I, 6),I=1,5)/ +0, +0, +0, +2, 0 / DATA TL( 7)/ +0.058793D0 /, : (ITL(I, 7),I=1,5)/ +0, -2, +2, +0, 0 / DATA TL( 8)/ +0.057212D0 /, : (ITL(I, 8),I=1,5)/ -1, -1, +2, +0, 1 / DATA TL( 9)/ +0.053320D0 /, : (ITL(I, 9),I=1,5)/ +0, +1, +2, +0, 0 / DATA TL(10)/ +0.045874D0 /, : (ITL(I,10),I=1,5)/ -1, +0, +2, +0, 1 / DATA TL(11)/ +0.041024D0 /, : (ITL(I,11),I=1,5)/ -1, +1, +0, +0, 1 / DATA TL(12)/ -0.034718D0 /, : (ITL(I,12),I=1,5)/ +0, +0, +1, +0, 0 / DATA TL(13)/ -0.030465D0 /, : (ITL(I,13),I=1,5)/ +1, +1, +0, +0, 1 / DATA TL(14)/ +0.015326D0 /, : (ITL(I,14),I=1,5)/ +0, +0, +2, -2, 0 / DATA TL(15)/ -0.012528D0 /, : (ITL(I,15),I=1,5)/ +0, +1, +0, +2, 0 / DATA TL(16)/ -0.010980D0 /, : (ITL(I,16),I=1,5)/ +0, -1, +0, +2, 0 / DATA TL(17)/ +0.010674D0 /, : (ITL(I,17),I=1,5)/ +0, -1, +4, +0, 0 / DATA TL(18)/ +0.010034D0 /, : (ITL(I,18),I=1,5)/ +0, +3, +0, +0, 0 / DATA TL(19)/ +0.008548D0 /, : (ITL(I,19),I=1,5)/ +0, -2, +4, +0, 0 / DATA TL(20)/ -0.007910D0 /, : (ITL(I,20),I=1,5)/ +1, -1, +2, +0, 1 / DATA TL(21)/ -0.006783D0 /, : (ITL(I,21),I=1,5)/ +1, +0, +2, +0, 1 / DATA TL(22)/ +0.005162D0 /, : (ITL(I,22),I=1,5)/ +0, +1, -1, +0, 0 / DATA TL(23)/ +0.005000D0 /, : (ITL(I,23),I=1,5)/ +1, +0, +1, +0, 1 / DATA TL(24)/ +0.004049D0 /, : (ITL(I,24),I=1,5)/ -1, +1, +2, +0, 1 / DATA TL(25)/ +0.003996D0 /, : (ITL(I,25),I=1,5)/ +0, +2, +2, +0, 0 / DATA TL(26)/ +0.003862D0 /, : (ITL(I,26),I=1,5)/ +0, +0, +4, +0, 0 / DATA TL(27)/ +0.003665D0 /, : (ITL(I,27),I=1,5)/ +0, -3, +2, +0, 0 / DATA TL(28)/ +0.002695D0 /, : (ITL(I,28),I=1,5)/ -1, +2, +0, +0, 1 / DATA TL(29)/ +0.002602D0 /, : (ITL(I,29),I=1,5)/ +0, +1, -2, -2, 0 / DATA TL(30)/ +0.002396D0 /, : (ITL(I,30),I=1,5)/ -1, -2, +2, +0, 1 / DATA TL(31)/ -0.002349D0 /, : (ITL(I,31),I=1,5)/ +0, +1, +1, +0, 0 / DATA TL(32)/ +0.002249D0 /, : (ITL(I,32),I=1,5)/ -2, +0, +2, +0, 2 / DATA TL(33)/ -0.002125D0 /, : (ITL(I,33),I=1,5)/ +1, +2, +0, +0, 1 / DATA TL(34)/ -0.002079D0 /, : (ITL(I,34),I=1,5)/ +2, +0, +0, +0, 2 / DATA TL(35)/ +0.002059D0 /, : (ITL(I,35),I=1,5)/ -2, -1, +2, +0, 2 / DATA TL(36)/ -0.001773D0 /, : (ITL(I,36),I=1,5)/ +0, +1, +2, -2, 0 / DATA TL(37)/ -0.001595D0 /, : (ITL(I,37),I=1,5)/ +0, +0, +2, +2, 0 / DATA TL(38)/ +0.001220D0 /, : (ITL(I,38),I=1,5)/ -1, -1, +4, +0, 1 / DATA TL(39)/ -0.001110D0 /, : (ITL(I,39),I=1,5)/ +0, +2, +0, +2, 0 / DATA TL(40)/ +0.000892D0 /, : (ITL(I,40),I=1,5)/ +0, +1, -3, +0, 0 / DATA TL(41)/ -0.000811D0 /, : (ITL(I,41),I=1,5)/ +1, +1, +2, +0, 1 / DATA TL(42)/ +0.000761D0 /, : (ITL(I,42),I=1,5)/ -1, -2, +4, +0, 1 / DATA TL(43)/ +0.000717D0 /, : (ITL(I,43),I=1,5)/ -2, +1, +0, +0, 2 / DATA TL(44)/ +0.000704D0 /, : (ITL(I,44),I=1,5)/ -2, +1, -2, +0, 2 / DATA TL(45)/ +0.000693D0 /, : (ITL(I,45),I=1,5)/ +1, -2, +2, +0, 1 / DATA TL(46)/ +0.000598D0 /, : (ITL(I,46),I=1,5)/ -1, +0, +2, -2, 1 / DATA TL(47)/ +0.000550D0 /, : (ITL(I,47),I=1,5)/ +0, +1, +4, +0, 0 / DATA TL(48)/ +0.000538D0 /, : (ITL(I,48),I=1,5)/ +0, +4, +0, +0, 0 / DATA TL(49)/ +0.000521D0 /, : (ITL(I,49),I=1,5)/ -1, +0, +4, +0, 1 / DATA TL(50)/ +0.000486D0 /, : (ITL(I,50),I=1,5)/ +0, +2, -1, +0, 0 / * * Latitude * M M' D F n DATA TB( 1)/ +5.128189D0 /, : (ITB(I, 1),I=1,5)/ +0, +0, +0, +1, 0 / DATA TB( 2)/ +0.280606D0 /, : (ITB(I, 2),I=1,5)/ +0, +1, +0, +1, 0 / DATA TB( 3)/ +0.277693D0 /, : (ITB(I, 3),I=1,5)/ +0, +1, +0, -1, 0 / DATA TB( 4)/ +0.173238D0 /, : (ITB(I, 4),I=1,5)/ +0, +0, +2, -1, 0 / DATA TB( 5)/ +0.055413D0 /, : (ITB(I, 5),I=1,5)/ +0, -1, +2, +1, 0 / DATA TB( 6)/ +0.046272D0 /, : (ITB(I, 6),I=1,5)/ +0, -1, +2, -1, 0 / DATA TB( 7)/ +0.032573D0 /, : (ITB(I, 7),I=1,5)/ +0, +0, +2, +1, 0 / DATA TB( 8)/ +0.017198D0 /, : (ITB(I, 8),I=1,5)/ +0, +2, +0, +1, 0 / DATA TB( 9)/ +0.009267D0 /, : (ITB(I, 9),I=1,5)/ +0, +1, +2, -1, 0 / DATA TB(10)/ +0.008823D0 /, : (ITB(I,10),I=1,5)/ +0, +2, +0, -1, 0 / DATA TB(11)/ +0.008247D0 /, : (ITB(I,11),I=1,5)/ -1, +0, +2, -1, 1 / DATA TB(12)/ +0.004323D0 /, : (ITB(I,12),I=1,5)/ +0, -2, +2, -1, 0 / DATA TB(13)/ +0.004200D0 /, : (ITB(I,13),I=1,5)/ +0, +1, +2, +1, 0 / DATA TB(14)/ +0.003372D0 /, : (ITB(I,14),I=1,5)/ -1, +0, -2, +1, 1 / DATA TB(15)/ +0.002472D0 /, : (ITB(I,15),I=1,5)/ -1, -1, +2, +1, 1 / DATA TB(16)/ +0.002222D0 /, : (ITB(I,16),I=1,5)/ -1, +0, +2, +1, 1 / DATA TB(17)/ +0.002072D0 /, : (ITB(I,17),I=1,5)/ -1, -1, +2, -1, 1 / DATA TB(18)/ +0.001877D0 /, : (ITB(I,18),I=1,5)/ -1, +1, +0, +1, 1 / DATA TB(19)/ +0.001828D0 /, : (ITB(I,19),I=1,5)/ +0, -1, +4, -1, 0 / DATA TB(20)/ -0.001803D0 /, : (ITB(I,20),I=1,5)/ +1, +0, +0, +1, 1 / DATA TB(21)/ -0.001750D0 /, : (ITB(I,21),I=1,5)/ +0, +0, +0, +3, 0 / DATA TB(22)/ +0.001570D0 /, : (ITB(I,22),I=1,5)/ -1, +1, +0, -1, 1 / DATA TB(23)/ -0.001487D0 /, : (ITB(I,23),I=1,5)/ +0, +0, +1, +1, 0 / DATA TB(24)/ -0.001481D0 /, : (ITB(I,24),I=1,5)/ +1, +1, +0, +1, 1 / DATA TB(25)/ +0.001417D0 /, : (ITB(I,25),I=1,5)/ -1, -1, +0, +1, 1 / DATA TB(26)/ +0.001350D0 /, : (ITB(I,26),I=1,5)/ -1, +0, +0, +1, 1 / DATA TB(27)/ +0.001330D0 /, : (ITB(I,27),I=1,5)/ +0, +0, -1, +1, 0 / DATA TB(28)/ +0.001106D0 /, : (ITB(I,28),I=1,5)/ +0, +3, +0, +1, 0 / DATA TB(29)/ +0.001020D0 /, : (ITB(I,29),I=1,5)/ +0, +0, +4, -1, 0 / DATA TB(30)/ +0.000833D0 /, : (ITB(I,30),I=1,5)/ +0, -1, +4, +1, 0 / DATA TB(31)/ +0.000781D0 /, : (ITB(I,31),I=1,5)/ +0, +1, +0, -3, 0 / DATA TB(32)/ +0.000670D0 /, : (ITB(I,32),I=1,5)/ +0, -2, +4, +1, 0 / DATA TB(33)/ +0.000606D0 /, : (ITB(I,33),I=1,5)/ +0, +0, +2, -3, 0 / DATA TB(34)/ +0.000597D0 /, : (ITB(I,34),I=1,5)/ +0, +2, +2, -1, 0 / DATA TB(35)/ +0.000492D0 /, : (ITB(I,35),I=1,5)/ -1, +1, +2, -1, 1 / DATA TB(36)/ +0.000450D0 /, : (ITB(I,36),I=1,5)/ +0, +2, -2, -1, 0 / DATA TB(37)/ +0.000439D0 /, : (ITB(I,37),I=1,5)/ +0, +3, +0, -1, 0 / DATA TB(38)/ +0.000423D0 /, : (ITB(I,38),I=1,5)/ +0, +2, +2, +1, 0 / DATA TB(39)/ +0.000422D0 /, : (ITB(I,39),I=1,5)/ +0, -3, +2, -1, 0 / DATA TB(40)/ -0.000367D0 /, : (ITB(I,40),I=1,5)/ +1, -1, +2, +1, 1 / DATA TB(41)/ -0.000353D0 /, : (ITB(I,41),I=1,5)/ +1, +0, +2, +1, 1 / DATA TB(42)/ +0.000331D0 /, : (ITB(I,42),I=1,5)/ +0, +0, +4, +1, 0 / DATA TB(43)/ +0.000317D0 /, : (ITB(I,43),I=1,5)/ -1, +1, +2, +1, 1 / DATA TB(44)/ +0.000306D0 /, : (ITB(I,44),I=1,5)/ -2, +0, +2, -1, 2 / DATA TB(45)/ -0.000283D0 /, : (ITB(I,45),I=1,5)/ +0, +1, +0, +3, 0 / * * Parallax * M M' D F n DATA TP( 1)/ +0.950724D0 /, : (ITP(I, 1),I=1,5)/ +0, +0, +0, +0, 0 / DATA TP( 2)/ +0.051818D0 /, : (ITP(I, 2),I=1,5)/ +0, +1, +0, +0, 0 / DATA TP( 3)/ +0.009531D0 /, : (ITP(I, 3),I=1,5)/ +0, -1, +2, +0, 0 / DATA TP( 4)/ +0.007843D0 /, : (ITP(I, 4),I=1,5)/ +0, +0, +2, +0, 0 / DATA TP( 5)/ +0.002824D0 /, : (ITP(I, 5),I=1,5)/ +0, +2, +0, +0, 0 / DATA TP( 6)/ +0.000857D0 /, : (ITP(I, 6),I=1,5)/ +0, +1, +2, +0, 0 / DATA TP( 7)/ +0.000533D0 /, : (ITP(I, 7),I=1,5)/ -1, +0, +2, +0, 1 / DATA TP( 8)/ +0.000401D0 /, : (ITP(I, 8),I=1,5)/ -1, -1, +2, +0, 1 / DATA TP( 9)/ +0.000320D0 /, : (ITP(I, 9),I=1,5)/ -1, +1, +0, +0, 1 / DATA TP(10)/ -0.000271D0 /, : (ITP(I,10),I=1,5)/ +0, +0, +1, +0, 0 / DATA TP(11)/ -0.000264D0 /, : (ITP(I,11),I=1,5)/ +1, +1, +0, +0, 1 / DATA TP(12)/ -0.000198D0 /, : (ITP(I,12),I=1,5)/ +0, -1, +0, +2, 0 / DATA TP(13)/ +0.000173D0 /, : (ITP(I,13),I=1,5)/ +0, +3, +0, +0, 0 / DATA TP(14)/ +0.000167D0 /, : (ITP(I,14),I=1,5)/ +0, -1, +4, +0, 0 / DATA TP(15)/ -0.000111D0 /, : (ITP(I,15),I=1,5)/ +1, +0, +0, +0, 1 / DATA TP(16)/ +0.000103D0 /, : (ITP(I,16),I=1,5)/ +0, -2, +4, +0, 0 / DATA TP(17)/ -0.000084D0 /, : (ITP(I,17),I=1,5)/ +0, +2, -2, +0, 0 / DATA TP(18)/ -0.000083D0 /, : (ITP(I,18),I=1,5)/ +1, +0, +2, +0, 1 / DATA TP(19)/ +0.000079D0 /, : (ITP(I,19),I=1,5)/ +0, +2, +2, +0, 0 / DATA TP(20)/ +0.000072D0 /, : (ITP(I,20),I=1,5)/ +0, +0, +4, +0, 0 / DATA TP(21)/ +0.000064D0 /, : (ITP(I,21),I=1,5)/ -1, +1, +2, +0, 1 / DATA TP(22)/ -0.000063D0 /, : (ITP(I,22),I=1,5)/ +1, -1, +2, +0, 1 / DATA TP(23)/ +0.000041D0 /, : (ITP(I,23),I=1,5)/ +1, +0, +1, +0, 1 / DATA TP(24)/ +0.000035D0 /, : (ITP(I,24),I=1,5)/ -1, +2, +0, +0, 1 / DATA TP(25)/ -0.000033D0 /, : (ITP(I,25),I=1,5)/ +0, +3, -2, +0, 0 / DATA TP(26)/ -0.000030D0 /, : (ITP(I,26),I=1,5)/ +0, +1, +1, +0, 0 / DATA TP(27)/ -0.000029D0 /, : (ITP(I,27),I=1,5)/ +0, +0, -2, +2, 0 / DATA TP(28)/ -0.000029D0 /, : (ITP(I,28),I=1,5)/ +1, +2, +0, +0, 1 / DATA TP(29)/ +0.000026D0 /, : (ITP(I,29),I=1,5)/ -2, +0, +2, +0, 2 / DATA TP(30)/ -0.000023D0 /, : (ITP(I,30),I=1,5)/ +0, +1, -2, +2, 0 / DATA TP(31)/ +0.000019D0 /, : (ITP(I,31),I=1,5)/ -1, -1, +4, +0, 1 / * Centuries since J1900 T=(DATE-15019.5D0)/36525D0 * * Fundamental arguments (radians) and derivatives (radians per * Julian century) for the current epoch * * Moon's mean longitude ELP=D2R*MOD(ELP0+(ELP1+(ELP2+ELP3*T)*T)*T,360D0) DELP=D2R*(ELP1+(2D0*ELP2+3D0*ELP3*T)*T) * Sun's mean anomaly EM=D2R*MOD(EM0+(EM1+(EM2+EM3*T)*T)*T,360D0) DEM=D2R*(EM1+(2D0*EM2+3D0*EM3*T)*T) * Moon's mean anomaly EMP=D2R*MOD(EMP0+(EMP1+(EMP2+EMP3*T)*T)*T,360D0) DEMP=D2R*(EMP1+(2D0*EMP2+3D0*EMP3*T)*T) * Moon's mean elongation D=D2R*MOD(D0+(D1+(D2+D3*T)*T)*T,360D0) DD=D2R*(D1+(2D0*D2+3D0*D3*T)*T) * Mean distance of the Moon from its ascending node F=D2R*MOD(F0+(F1+(F2+F3*T)*T)*T,360D0) DF=D2R*(F1+(2D0*F2+3D0*F3*T)*T) * Longitude of the Moon's ascending node OM=D2R*MOD(OM0+(OM1+(OM2+OM3*T)*T)*T,360D0) DOM=D2R*(OM1+(2D0*OM2+3D0*OM3*T)*T) SINOM=SIN(OM) COSOM=COS(OM) DOMCOM=DOM*COSOM * Add the periodic variations THETA=D2R*(PA0+PA1*T) WA=SIN(THETA) DWA=D2R*PA1*COS(THETA) THETA=D2R*(PE0+(PE1+PE2*T)*T) WB=PEC*SIN(THETA) DWB=D2R*PEC*(PE1+2D0*PE2*T)*COS(THETA) ELP=ELP+D2R*(PAC*WA+WB+PFC*SINOM) DELP=DELP+D2R*(PAC*DWA+DWB+PFC*DOMCOM) EM=EM+D2R*PBC*WA DEM=DEM+D2R*PBC*DWA EMP=EMP+D2R*(PCC*WA+WB+PGC*SINOM) DEMP=DEMP+D2R*(PCC*DWA+DWB+PGC*DOMCOM) D=D+D2R*(PDC*WA+WB+PHC*SINOM) DD=DD+D2R*(PDC*DWA+DWB+PHC*DOMCOM) WOM=OM+D2R*(PJ0+PJ1*T) DWOM=DOM+D2R*PJ1 SINWOM=SIN(WOM) COSWOM=COS(WOM) F=F+D2R*(WB+PIC*SINOM+PJC*SINWOM) DF=DF+D2R*(DWB+PIC*DOMCOM+PJC*DWOM*COSWOM) * E-factor, and square E=1D0+(E1+E2*T)*T DE=E1+2D0*E2*T ESQ=E*E DESQ=2D0*E*DE * * Series expansions * * Longitude V=0D0 DV=0D0 DO N=NL,1,-1 COEFF=TL(N) EMN=DBLE(ITL(1,N)) EMPN=DBLE(ITL(2,N)) DN=DBLE(ITL(3,N)) FN=DBLE(ITL(4,N)) I=ITL(5,N) IF (I.EQ.0) THEN EN=1D0 DEN=0D0 ELSE IF (I.EQ.1) THEN EN=E DEN=DE ELSE EN=ESQ DEN=DESQ END IF THETA=EMN*EM+EMPN*EMP+DN*D+FN*F DTHETA=EMN*DEM+EMPN*DEMP+DN*DD+FN*DF FTHETA=SIN(THETA) V=V+COEFF*FTHETA*EN DV=DV+COEFF*(COS(THETA)*DTHETA*EN+FTHETA*DEN) END DO EL=ELP+D2R*V DEL=(DELP+D2R*DV)/CJ * Latitude V=0D0 DV=0D0 DO N=NB,1,-1 COEFF=TB(N) EMN=DBLE(ITB(1,N)) EMPN=DBLE(ITB(2,N)) DN=DBLE(ITB(3,N)) FN=DBLE(ITB(4,N)) I=ITB(5,N) IF (I.EQ.0) THEN EN=1D0 DEN=0D0 ELSE IF (I.EQ.1) THEN EN=E DEN=DE ELSE EN=ESQ DEN=DESQ END IF THETA=EMN*EM+EMPN*EMP+DN*D+FN*F DTHETA=EMN*DEM+EMPN*DEMP+DN*DD+FN*DF FTHETA=SIN(THETA) V=V+COEFF*FTHETA*EN DV=DV+COEFF*(COS(THETA)*DTHETA*EN+FTHETA*DEN) END DO BF=1D0-CW1*COSOM-CW2*COSWOM DBF=CW1*DOM*SINOM+CW2*DWOM*SINWOM B=D2R*V*BF DB=D2R*(DV*BF+V*DBF)/CJ * Parallax V=0D0 DV=0D0 DO N=NP,1,-1 COEFF=TP(N) EMN=DBLE(ITP(1,N)) EMPN=DBLE(ITP(2,N)) DN=DBLE(ITP(3,N)) FN=DBLE(ITP(4,N)) I=ITP(5,N) IF (I.EQ.0) THEN EN=1D0 DEN=0D0 ELSE IF (I.EQ.1) THEN EN=E DEN=DE ELSE EN=ESQ DEN=DESQ END IF THETA=EMN*EM+EMPN*EMP+DN*D+FN*F DTHETA=EMN*DEM+EMPN*DEMP+DN*DD+FN*DF FTHETA=COS(THETA) V=V+COEFF*FTHETA*EN DV=DV+COEFF*(-SIN(THETA)*DTHETA*EN+FTHETA*DEN) END DO P=D2R*V DP=D2R*DV/CJ * * Transformation into final form * * Parallax to distance (AU, AU/sec) SP=SIN(P) R=ERADAU/SP DR=-R*DP*COS(P)/SP * Longitude, latitude to x,y,z (AU) SEL=SIN(EL) CEL=COS(EL) SB=SIN(B) CB=COS(B) RCB=R*CB RBD=R*DB W=RBD*SB-CB*DR X=RCB*CEL Y=RCB*SEL Z=R*SB XD=-Y*DEL-W*CEL YD=X*DEL-W*SEL ZD=RBD*CB+SB*DR * Julian centuries since J2000 T=(DATE-51544.5D0)/36525D0 * Fricke equinox correction EPJ=2000D0+T*100D0 EQCOR=DS2R*(0.035D0+0.00085D0*(EPJ-B1950)) * Mean obliquity (IAU 1976) EPS=DAS2R*(84381.448D0+(-46.8150D0+(-0.00059D0+0.001813D0*T)*T)*T) * To the equatorial system, mean of date, FK5 system SINEPS=SIN(EPS) COSEPS=COS(EPS) ES=EQCOR*SINEPS EC=EQCOR*COSEPS PV(1)=X-EC*Y+ES*Z PV(2)=EQCOR*X+Y*COSEPS-Z*SINEPS PV(3)=Y*SINEPS+Z*COSEPS PV(4)=XD-EC*YD+ES*ZD PV(5)=EQCOR*XD+YD*COSEPS-ZD*SINEPS PV(6)=YD*SINEPS+ZD*COSEPS END