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dmoon.f
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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