SUBROUTINE sla_CLDJ (IY, IM, ID, DJM, J) *+ * - - - - - * C L D J * - - - - - * * Gregorian Calendar to Modified Julian Date * * Given: * IY,IM,ID int year, month, day in Gregorian calendar * * Returned: * DJM dp modified Julian Date (JD-2400000.5) for 0 hrs * J int status: * 0 = OK * 1 = bad year (MJD not computed) * 2 = bad month (MJD not computed) * 3 = bad day (MJD computed) * * The year must be -4699 (i.e. 4700BC) or later. * * The algorithm is adapted from Hatcher 1984 (QJRAS 25, 53-55). * * Last revision: 27 July 2004 * * 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., 51 Franklin Street, Fifth Floor, * Boston, MA 02110-1301 USA * *- IMPLICIT NONE INTEGER IY,IM,ID DOUBLE PRECISION DJM INTEGER J * Month lengths in days INTEGER MTAB(12) DATA MTAB / 31,28,31,30,31,30,31,31,30,31,30,31 / * Preset status. J = 0 * Validate year. IF ( IY .LT. -4699 ) THEN J = 1 ELSE * Validate month. IF ( IM.GE.1 .AND. IM.LE.12 ) THEN * Allow for leap year. IF ( MOD(IY,4) .EQ. 0 ) THEN MTAB(2) = 29 ELSE MTAB(2) = 28 END IF IF ( MOD(IY,100).EQ.0 .AND. MOD(IY,400).NE.0 ) : MTAB(2) = 28 * Validate day. IF ( ID.LT.1 .OR. ID.GT.MTAB(IM) ) J=3 * Modified Julian Date. DJM = DBLE ( ( 1461 * ( IY - (12-IM)/10 + 4712 ) ) / 4 : + ( 306 * MOD ( IM+9, 12 ) + 5 ) / 10 : - ( 3 * ( ( IY - (12-IM)/10 + 4900 ) / 100 ) ) / 4 : + ID - 2399904 ) * Bad month. ELSE J=2 END IF END IF END DOUBLE PRECISION FUNCTION sla_DAT (UTC) *+ * - - - - * D A T * - - - - * * Increment to be applied to Coordinated Universal Time UTC to give * International Atomic Time TAI (double precision) * * Given: * UTC d UTC date as a modified JD (JD-2400000.5) * * Result: TAI-UTC in seconds * * Notes: * * 1 The UTC is specified to be a date rather than a time to indicate * that care needs to be taken not to specify an instant which lies * within a leap second. Though in most cases UTC can include the * fractional part, correct behaviour on the day of a leap second * can only be guaranteed up to the end of the second 23:59:59. * * 2 For epochs from 1961 January 1 onwards, the expressions from the * file ftp://maia.usno.navy.mil/ser7/tai-utc.dat are used. * * 3 The 5ms time step at 1961 January 1 is taken from 2.58.1 (p87) of * the 1992 Explanatory Supplement. * * 4 UTC began at 1960 January 1.0 (JD 2436934.5) and it is improper * to call the routine with an earlier epoch. However, if this * is attempted, the TAI-UTC expression for the year 1960 is used. * * * :-----------------------------------------: * : : * : IMPORTANT : * : : * : This routine must be updated on each : * : occasion that a leap second is : * : announced : * : : * : Latest leap second: 2015 July 1 : * : : * :-----------------------------------------: * * Last revision: 5 July 2008 * * Copyright P.T.Wallace. All rights reserved. *- IMPLICIT NONE DOUBLE PRECISION UTC DOUBLE PRECISION DT IF (.FALSE.) THEN * - - - - - - - - - - - - - - - - - - - - - - * * Add new code here on each occasion that a * * leap second is announced, and update the * * preamble comments appropriately. * * - - - - - - - - - - - - - - - - - - - - - - * * 2015 July 1 ELSE IF (UTC.GE.57204D0) THEN DT=36D0 * 2012 July 1 ELSE IF (UTC.GE.56109D0) THEN DT=35D0 * 2009 January 1 ELSE IF (UTC.GE.54832D0) THEN DT=34D0 * 2006 January 1 ELSE IF (UTC.GE.53736D0) THEN DT=33D0 * 1999 January 1 ELSE IF (UTC.GE.51179D0) THEN DT=32D0 * 1997 July 1 ELSE IF (UTC.GE.50630D0) THEN DT=31D0 * 1996 January 1 ELSE IF (UTC.GE.50083D0) THEN DT=30D0 * 1994 July 1 ELSE IF (UTC.GE.49534D0) THEN DT=29D0 * 1993 July 1 ELSE IF (UTC.GE.49169D0) THEN DT=28D0 * 1992 July 1 ELSE IF (UTC.GE.48804D0) THEN DT=27D0 * 1991 January 1 ELSE IF (UTC.GE.48257D0) THEN DT=26D0 * 1990 January 1 ELSE IF (UTC.GE.47892D0) THEN DT=25D0 * 1988 January 1 ELSE IF (UTC.GE.47161D0) THEN DT=24D0 * 1985 July 1 ELSE IF (UTC.GE.46247D0) THEN DT=23D0 * 1983 July 1 ELSE IF (UTC.GE.45516D0) THEN DT=22D0 * 1982 July 1 ELSE IF (UTC.GE.45151D0) THEN DT=21D0 * 1981 July 1 ELSE IF (UTC.GE.44786D0) THEN DT=20D0 * 1980 January 1 ELSE IF (UTC.GE.44239D0) THEN DT=19D0 * 1979 January 1 ELSE IF (UTC.GE.43874D0) THEN DT=18D0 * 1978 January 1 ELSE IF (UTC.GE.43509D0) THEN DT=17D0 * 1977 January 1 ELSE IF (UTC.GE.43144D0) THEN DT=16D0 * 1976 January 1 ELSE IF (UTC.GE.42778D0) THEN DT=15D0 * 1975 January 1 ELSE IF (UTC.GE.42413D0) THEN DT=14D0 * 1974 January 1 ELSE IF (UTC.GE.42048D0) THEN DT=13D0 * 1973 January 1 ELSE IF (UTC.GE.41683D0) THEN DT=12D0 * 1972 July 1 ELSE IF (UTC.GE.41499D0) THEN DT=11D0 * 1972 January 1 ELSE IF (UTC.GE.41317D0) THEN DT=10D0 * 1968 February 1 ELSE IF (UTC.GE.39887D0) THEN DT=4.2131700D0+(UTC-39126D0)*0.002592D0 * 1966 January 1 ELSE IF (UTC.GE.39126D0) THEN DT=4.3131700D0+(UTC-39126D0)*0.002592D0 * 1965 September 1 ELSE IF (UTC.GE.39004D0) THEN DT=3.8401300D0+(UTC-38761D0)*0.001296D0 * 1965 July 1 ELSE IF (UTC.GE.38942D0) THEN DT=3.7401300D0+(UTC-38761D0)*0.001296D0 * 1965 March 1 ELSE IF (UTC.GE.38820D0) THEN DT=3.6401300D0+(UTC-38761D0)*0.001296D0 * 1965 January 1 ELSE IF (UTC.GE.38761D0) THEN DT=3.5401300D0+(UTC-38761D0)*0.001296D0 * 1964 September 1 ELSE IF (UTC.GE.38639D0) THEN DT=3.4401300D0+(UTC-38761D0)*0.001296D0 * 1964 April 1 ELSE IF (UTC.GE.38486D0) THEN DT=3.3401300D0+(UTC-38761D0)*0.001296D0 * 1964 January 1 ELSE IF (UTC.GE.38395D0) THEN DT=3.2401300D0+(UTC-38761D0)*0.001296D0 * 1963 November 1 ELSE IF (UTC.GE.38334D0) THEN DT=1.9458580D0+(UTC-37665D0)*0.0011232D0 * 1962 January 1 ELSE IF (UTC.GE.37665D0) THEN DT=1.8458580D0+(UTC-37665D0)*0.0011232D0 * 1961 August 1 ELSE IF (UTC.GE.37512D0) THEN DT=1.3728180D0+(UTC-37300D0)*0.001296D0 * 1961 January 1 ELSE IF (UTC.GE.37300D0) THEN DT=1.4228180D0+(UTC-37300D0)*0.001296D0 * Before that ELSE DT=1.4178180D0+(UTC-37300D0)*0.001296D0 END IF sla_DAT=DT END SUBROUTINE sla_DC62S (V, A, B, R, AD, BD, RD) *+ * - - - - - - * D C 6 2 S * - - - - - - * * Conversion of position & velocity in Cartesian coordinates * to spherical coordinates (double precision) * * Given: * V d(6) Cartesian position & velocity vector * * Returned: * A d longitude (radians) * B d latitude (radians) * R d radial coordinate * AD d longitude derivative (radians per unit time) * BD d latitude derivative (radians per unit time) * RD d radial derivative * * P.T.Wallace Starlink 28 April 1996 * * Copyright (C) 1996 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., 51 Franklin Street, Fifth Floor, * Boston, MA 02110-1301 USA * *- IMPLICIT NONE DOUBLE PRECISION V(6),A,B,R,AD,BD,RD DOUBLE PRECISION X,Y,Z,XD,YD,ZD,RXY2,RXY,R2,XYP * Components of position/velocity vector X=V(1) Y=V(2) Z=V(3) XD=V(4) YD=V(5) ZD=V(6) * Component of R in XY plane squared RXY2=X*X+Y*Y * Modulus squared R2=RXY2+Z*Z * Protection against null vector IF (R2.EQ.0D0) THEN X=XD Y=YD Z=ZD RXY2=X*X+Y*Y R2=RXY2+Z*Z END IF * Position and velocity in spherical coordinates RXY=SQRT(RXY2) XYP=X*XD+Y*YD IF (RXY2.NE.0D0) THEN A=ATAN2(Y,X) B=ATAN2(Z,RXY) AD=(X*YD-Y*XD)/RXY2 BD=(ZD*RXY2-Z*XYP)/(R2*RXY) ELSE A=0D0 IF (Z.NE.0D0) THEN B=ATAN2(Z,RXY) ELSE B=0D0 END IF AD=0D0 BD=0D0 END IF R=SQRT(R2) IF (R.NE.0D0) THEN RD=(XYP+Z*ZD)/R ELSE RD=0D0 END IF END SUBROUTINE sla_DCC2S (V, A, B) *+ * - - - - - - * D C C 2 S * - - - - - - * * Cartesian to spherical coordinates (double precision) * * Given: * V d(3) x,y,z vector * * Returned: * A,B d spherical coordinates in radians * * The spherical coordinates are longitude (+ve anticlockwise looking * from the +ve latitude pole) and latitude. The Cartesian coordinates * are right handed, with the x axis at zero longitude and latitude, and * the z axis at the +ve latitude pole. * * If V is null, zero A and B are returned. At either pole, zero A is * returned. * * Last revision: 22 July 2004 * * 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., 51 Franklin Street, Fifth Floor, * Boston, MA 02110-1301 USA * *- IMPLICIT NONE DOUBLE PRECISION V(3),A,B DOUBLE PRECISION X,Y,Z,R X = V(1) Y = V(2) Z = V(3) R = SQRT(X*X+Y*Y) IF (R.EQ.0D0) THEN A = 0D0 ELSE A = ATAN2(Y,X) END IF IF (Z.EQ.0D0) THEN B = 0D0 ELSE B = ATAN2(Z,R) END IF END SUBROUTINE sla_DCS2C (A, B, V) *+ * - - - - - - * D C S 2 C * - - - - - - * * Spherical coordinates to direction cosines (double precision) * * Given: * A,B d spherical coordinates in radians * (RA,Dec), (long,lat) etc. * * Returned: * V d(3) x,y,z unit vector * * The spherical coordinates are longitude (+ve anticlockwise looking * from the +ve latitude pole) and latitude. The Cartesian coordinates * are right handed, with the x axis at zero longitude and latitude, and * the z axis at the +ve latitude pole. * * Last revision: 26 December 2004 * * 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., 51 Franklin Street, Fifth Floor, * Boston, MA 02110-1301 USA * *- IMPLICIT NONE DOUBLE PRECISION A,B,V(3) DOUBLE PRECISION COSB COSB = COS(B) V(1) = COS(A)*COSB V(2) = SIN(A)*COSB V(3) = SIN(B) END SUBROUTINE sla_DE2H (HA, DEC, PHI, AZ, EL) *+ * - - - - - * D E 2 H * - - - - - * * Equatorial to horizon coordinates: HA,Dec to Az,El * * (double precision) * * Given: * HA d hour angle * DEC d declination * PHI d observatory latitude * * Returned: * AZ d azimuth * EL d elevation * * Notes: * * 1) All the arguments are angles in radians. * * 2) Azimuth is returned in the range 0-2pi; north is zero, * and east is +pi/2. Elevation is returned in the range * +/-pi/2. * * 3) The latitude must be geodetic. In critical applications, * corrections for polar motion should be applied. * * 4) In some applications it will be important to specify the * correct type of hour angle and declination in order to * produce the required type of azimuth and elevation. In * particular, it may be important to distinguish between * elevation as affected by refraction, which would * require the "observed" HA,Dec, and the elevation * in vacuo, which would require the "topocentric" HA,Dec. * If the effects of diurnal aberration can be neglected, the * "apparent" HA,Dec may be used instead of the topocentric * HA,Dec. * * 5) No range checking of arguments is carried out. * * 6) In applications which involve many such calculations, rather * than calling the present routine it will be more efficient to * use inline code, having previously computed fixed terms such * as sine and cosine of latitude, and (for tracking a star) * sine and cosine of declination. * * P.T.Wallace Starlink 9 July 1994 * * Copyright (C) 1995 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., 51 Franklin Street, Fifth Floor, * Boston, MA 02110-1301 USA * *- IMPLICIT NONE DOUBLE PRECISION HA,DEC,PHI,AZ,EL DOUBLE PRECISION D2PI PARAMETER (D2PI=6.283185307179586476925286766559D0) DOUBLE PRECISION SH,CH,SD,CD,SP,CP,X,Y,Z,R,A * Useful trig functions SH=SIN(HA) CH=COS(HA) SD=SIN(DEC) CD=COS(DEC) SP=SIN(PHI) CP=COS(PHI) * Az,El as x,y,z X=-CH*CD*SP+SD*CP Y=-SH*CD Z=CH*CD*CP+SD*SP * To spherical R=SQRT(X*X+Y*Y) IF (R.EQ.0D0) THEN A=0D0 ELSE A=ATAN2(Y,X) END IF IF (A.LT.0D0) A=A+D2PI AZ=A EL=ATAN2(Z,R) END SUBROUTINE sla_DEULER (ORDER, PHI, THETA, PSI, RMAT) *+ * - - - - - - - * D E U L E R * - - - - - - - * * Form a rotation matrix from the Euler angles - three successive * rotations about specified Cartesian axes (double precision) * * Given: * ORDER c*(*) specifies about which axes the rotations occur * PHI d 1st rotation (radians) * THETA d 2nd rotation ( " ) * PSI d 3rd rotation ( " ) * * Returned: * RMAT d(3,3) rotation matrix * * A rotation is positive when the reference frame rotates * anticlockwise as seen looking towards the origin from the * positive region of the specified axis. * * The characters of ORDER define which axes the three successive * rotations are about. A typical value is 'ZXZ', indicating that * RMAT is to become the direction cosine matrix corresponding to * rotations of the reference frame through PHI radians about the * old Z-axis, followed by THETA radians about the resulting X-axis, * then PSI radians about the resulting Z-axis. * * The axis names can be any of the following, in any order or * combination: X, Y, Z, uppercase or lowercase, 1, 2, 3. Normal * axis labelling/numbering conventions apply; the xyz (=123) * triad is right-handed. Thus, the 'ZXZ' example given above * could be written 'zxz' or '313' (or even 'ZxZ' or '3xZ'). ORDER * is terminated by length or by the first unrecognized character. * * Fewer than three rotations are acceptable, in which case the later * angle arguments are ignored. If all rotations are zero, the * identity matrix is produced. * * P.T.Wallace Starlink 23 May 1997 * * Copyright (C) 1997 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., 51 Franklin Street, Fifth Floor, * Boston, MA 02110-1301 USA * *- IMPLICIT NONE CHARACTER*(*) ORDER DOUBLE PRECISION PHI,THETA,PSI,RMAT(3,3) INTEGER J,I,L,N,K DOUBLE PRECISION RESULT(3,3),ROTN(3,3),ANGLE,S,C,W,WM(3,3) CHARACTER AXIS * Initialize result matrix DO J=1,3 DO I=1,3 IF (I.NE.J) THEN RESULT(I,J) = 0D0 ELSE RESULT(I,J) = 1D0 END IF END DO END DO * Establish length of axis string L = LEN(ORDER) * Look at each character of axis string until finished DO N=1,3 IF (N.LE.L) THEN * Initialize rotation matrix for the current rotation DO J=1,3 DO I=1,3 IF (I.NE.J) THEN ROTN(I,J) = 0D0 ELSE ROTN(I,J) = 1D0 END IF END DO END DO * Pick up the appropriate Euler angle and take sine & cosine IF (N.EQ.1) THEN ANGLE = PHI ELSE IF (N.EQ.2) THEN ANGLE = THETA ELSE ANGLE = PSI END IF S = SIN(ANGLE) C = COS(ANGLE) * Identify the axis AXIS = ORDER(N:N) IF (AXIS.EQ.'X'.OR. : AXIS.EQ.'x'.OR. : AXIS.EQ.'1') THEN * Matrix for x-rotation ROTN(2,2) = C ROTN(2,3) = S ROTN(3,2) = -S ROTN(3,3) = C ELSE IF (AXIS.EQ.'Y'.OR. : AXIS.EQ.'y'.OR. : AXIS.EQ.'2') THEN * Matrix for y-rotation ROTN(1,1) = C ROTN(1,3) = -S ROTN(3,1) = S ROTN(3,3) = C ELSE IF (AXIS.EQ.'Z'.OR. : AXIS.EQ.'z'.OR. : AXIS.EQ.'3') THEN * Matrix for z-rotation ROTN(1,1) = C ROTN(1,2) = S ROTN(2,1) = -S ROTN(2,2) = C ELSE * Unrecognized character - fake end of string L = 0 END IF * Apply the current rotation (matrix ROTN x matrix RESULT) DO I=1,3 DO J=1,3 W = 0D0 DO K=1,3 W = W+ROTN(I,K)*RESULT(K,J) END DO WM(I,J) = W END DO END DO DO J=1,3 DO I=1,3 RESULT(I,J) = WM(I,J) END DO END DO END IF END DO * Copy the result DO J=1,3 DO I=1,3 RMAT(I,J) = RESULT(I,J) END DO END DO END 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., 51 Franklin Street, Fifth Floor, * Boston, MA 02110-1301 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 SUBROUTINE sla_DMXV (DM, VA, VB) *+ * - - - - - * D M X V * - - - - - * * Performs the 3-D forward unitary transformation: * * vector VB = matrix DM * vector VA * * (double precision) * * Given: * DM dp(3,3) matrix * VA dp(3) vector * * Returned: * VB dp(3) result vector * * To comply with the ANSI Fortran 77 standard, VA and VB must be * different arrays. However, the routine is coded so as to work * properly on many platforms even if this rule is violated. * * Last revision: 26 December 2004 * * 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., 51 Franklin Street, Fifth Floor, * Boston, MA 02110-1301 USA * *- IMPLICIT NONE DOUBLE PRECISION DM(3,3),VA(3),VB(3) INTEGER I,J DOUBLE PRECISION W,VW(3) * Matrix DM * vector VA -> vector VW DO J=1,3 W=0D0 DO I=1,3 W=W+DM(J,I)*VA(I) END DO VW(J)=W END DO * Vector VW -> vector VB DO J=1,3 VB(J)=VW(J) END DO END DOUBLE PRECISION FUNCTION sla_DRANGE (ANGLE) *+ * - - - - - - - * D R A N G E * - - - - - - - * * Normalize angle into range +/- pi (double precision) * * Given: * ANGLE dp the angle in radians * * The result (double precision) is ANGLE expressed in the range +/- pi. * * P.T.Wallace Starlink 23 November 1995 * * Copyright (C) 1995 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., 51 Franklin Street, Fifth Floor, * Boston, MA 02110-1301 USA * *- IMPLICIT NONE DOUBLE PRECISION ANGLE DOUBLE PRECISION DPI,D2PI PARAMETER (DPI=3.141592653589793238462643D0) PARAMETER (D2PI=6.283185307179586476925287D0) sla_DRANGE=MOD(ANGLE,D2PI) IF (ABS(sla_DRANGE).GE.DPI) : sla_DRANGE=sla_DRANGE-SIGN(D2PI,ANGLE) END DOUBLE PRECISION FUNCTION sla_DRANRM (ANGLE) *+ * - - - - - - - * D R A N R M * - - - - - - - * * Normalize angle into range 0-2 pi (double precision) * * Given: * ANGLE dp the angle in radians * * The result is ANGLE expressed in the range 0-2 pi. * * Last revision: 22 July 2004 * * 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., 51 Franklin Street, Fifth Floor, * Boston, MA 02110-1301 USA * *- IMPLICIT NONE DOUBLE PRECISION ANGLE DOUBLE PRECISION D2PI PARAMETER (D2PI=6.283185307179586476925286766559D0) sla_DRANRM = MOD(ANGLE,D2PI) IF (sla_DRANRM.LT.0D0) sla_DRANRM = sla_DRANRM+D2PI END DOUBLE PRECISION FUNCTION sla_DTT (UTC) *+ * - - - - * D T T * - - - - * * Increment to be applied to Coordinated Universal Time UTC to give * Terrestrial Time TT (formerly Ephemeris Time ET) * * (double precision) * * Given: * UTC d UTC date as a modified JD (JD-2400000.5) * * Result: TT-UTC in seconds * * Notes: * * 1 The UTC is specified to be a date rather than a time to indicate * that care needs to be taken not to specify an instant which lies * within a leap second. Though in most cases UTC can include the * fractional part, correct behaviour on the day of a leap second * can only be guaranteed up to the end of the second 23:59:59. * * 2 Pre 1972 January 1 a fixed value of 10 + ET-TAI is returned. * * 3 See also the routine sla_DT, which roughly estimates ET-UT for * historical epochs. * * Called: sla_DAT * * P.T.Wallace Starlink 6 December 1994 * * Copyright (C) 1995 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., 51 Franklin Street, Fifth Floor, * Boston, MA 02110-1301 USA * *- IMPLICIT NONE DOUBLE PRECISION UTC DOUBLE PRECISION sla_DAT sla_DTT=32.184D0+sla_DAT(UTC) END SUBROUTINE sla_ECMAT (DATE, RMAT) *+ * - - - - - - * E C M A T * - - - - - - * * Form the equatorial to ecliptic rotation matrix - IAU 1980 theory * (double precision) * * Given: * DATE dp TDB (loosely ET) as Modified Julian Date * (JD-2400000.5) * Returned: * RMAT dp(3,3) matrix * * Reference: * Murray,C.A., Vectorial Astrometry, section 4.3. * * Note: * The matrix is in the sense V(ecl) = RMAT * V(equ); the * equator, equinox and ecliptic are mean of date. * * Called: sla_DEULER * * P.T.Wallace Starlink 23 August 1996 * * Copyright (C) 1996 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., 51 Franklin Street, Fifth Floor, * Boston, MA 02110-1301 USA * *- IMPLICIT NONE DOUBLE PRECISION DATE,RMAT(3,3) * Arc seconds to radians DOUBLE PRECISION AS2R PARAMETER (AS2R=0.484813681109535994D-5) DOUBLE PRECISION T,EPS0 * Interval between basic epoch J2000.0 and current epoch (JC) T = (DATE-51544.5D0)/36525D0 * Mean obliquity EPS0 = AS2R* : (84381.448D0+(-46.8150D0+(-0.00059D0+0.001813D0*T)*T)*T) * Matrix CALL sla_DEULER('X',EPS0,0D0,0D0,RMAT) END DOUBLE PRECISION FUNCTION sla_EPJ (DATE) *+ * - - - - * E P J * - - - - * * Conversion of Modified Julian Date to Julian Epoch (double precision) * * Given: * DATE dp Modified Julian Date (JD - 2400000.5) * * The result is the Julian Epoch. * * Reference: * Lieske,J.H., 1979. Astron.Astrophys.,73,282. * * P.T.Wallace Starlink February 1984 * * Copyright (C) 1995 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., 51 Franklin Street, Fifth Floor, * Boston, MA 02110-1301 USA * *- IMPLICIT NONE DOUBLE PRECISION DATE sla_EPJ = 2000D0 + (DATE-51544.5D0)/365.25D0 END SUBROUTINE sla_EQECL (DR, DD, DATE, DL, DB) *+ * - - - - - - * E Q E C L * - - - - - - * * Transformation from J2000.0 equatorial coordinates to * ecliptic coordinates (double precision) * * Given: * DR,DD dp J2000.0 mean RA,Dec (radians) * DATE dp TDB (loosely ET) as Modified Julian Date * (JD-2400000.5) * Returned: * DL,DB dp ecliptic longitude and latitude * (mean of date, IAU 1980 theory, radians) * * Called: * sla_DCS2C, sla_PREC, sla_EPJ, sla_DMXV, sla_ECMAT, sla_DCC2S, * sla_DRANRM, sla_DRANGE * * P.T.Wallace Starlink March 1986 * * Copyright (C) 1995 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., 51 Franklin Street, Fifth Floor, * Boston, MA 02110-1301 USA * *- IMPLICIT NONE DOUBLE PRECISION DR,DD,DATE,DL,DB DOUBLE PRECISION sla_EPJ,sla_DRANRM,sla_DRANGE DOUBLE PRECISION RMAT(3,3),V1(3),V2(3) * Spherical to Cartesian CALL sla_DCS2C(DR,DD,V1) * Mean J2000 to mean of date CALL sla_PREC(2000D0,sla_EPJ(DATE),RMAT) CALL sla_DMXV(RMAT,V1,V2) * Equatorial to ecliptic CALL sla_ECMAT(DATE,RMAT) CALL sla_DMXV(RMAT,V2,V1) * Cartesian to spherical CALL sla_DCC2S(V1,DL,DB) * Express in conventional ranges DL=sla_DRANRM(DL) DB=sla_DRANGE(DB) END DOUBLE PRECISION FUNCTION sla_EQEQX (DATE) *+ * - - - - - - * E Q E Q X * - - - - - - * * Equation of the equinoxes (IAU 1994, double precision) * * Given: * DATE dp TDB (loosely ET) as Modified Julian Date * (JD-2400000.5) * * The result is the equation of the equinoxes (double precision) * in radians: * * Greenwich apparent ST = GMST + sla_EQEQX * * References: IAU Resolution C7, Recommendation 3 (1994) * Capitaine, N. & Gontier, A.-M., Astron. Astrophys., * 275, 645-650 (1993) * * Called: sla_NUTC * * Patrick Wallace Starlink 23 August 1996 * * Copyright (C) 1996 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., 51 Franklin Street, Fifth Floor, * Boston, MA 02110-1301 USA * *- IMPLICIT NONE DOUBLE PRECISION DATE * Turns to arc seconds and arc seconds to radians DOUBLE PRECISION T2AS,AS2R PARAMETER (T2AS=1296000D0, : AS2R=0.484813681109535994D-5) DOUBLE PRECISION T,OM,DPSI,DEPS,EPS0 * Interval between basic epoch J2000.0 and current epoch (JC) T=(DATE-51544.5D0)/36525D0 * Longitude of the mean ascending node of the lunar orbit on the * ecliptic, measured from the mean equinox of date OM=AS2R*(450160.280D0+(-5D0*T2AS-482890.539D0 : +(7.455D0+0.008D0*T)*T)*T) * Nutation CALL sla_NUTC(DATE,DPSI,DEPS,EPS0) * Equation of the equinoxes sla_EQEQX=DPSI*COS(EPS0)+AS2R*(0.00264D0*SIN(OM)+ : 0.000063D0*SIN(OM+OM)) END SUBROUTINE sla_GEOC (P, H, R, Z) *+ * - - - - - * G E O C * - - - - - * * Convert geodetic position to geocentric (double precision) * * Given: * P dp latitude (geodetic, radians) * H dp height above reference spheroid (geodetic, metres) * * Returned: * R dp distance from Earth axis (AU) * Z dp distance from plane of Earth equator (AU) * * Notes: * * 1 Geocentric latitude can be obtained by evaluating ATAN2(Z,R). * * 2 IAU 1976 constants are used. * * Reference: * * Green,R.M., Spherical Astronomy, CUP 1985, p98. * * Last revision: 22 July 2004 * * 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., 51 Franklin Street, Fifth Floor, * Boston, MA 02110-1301 USA * *- IMPLICIT NONE DOUBLE PRECISION P,H,R,Z * Earth equatorial radius (metres) DOUBLE PRECISION A0 PARAMETER (A0=6378140D0) * Reference spheroid flattening factor and useful function DOUBLE PRECISION F,B PARAMETER (F=1D0/298.257D0,B=(1D0-F)**2) * Astronomical unit in metres DOUBLE PRECISION AU PARAMETER (AU=1.49597870D11) DOUBLE PRECISION SP,CP,C,S * Geodetic to geocentric conversion SP = SIN(P) CP = COS(P) C = 1D0/SQRT(CP*CP+B*SP*SP) S = B*C R = (A0*C+H)*CP/AU Z = (A0*S+H)*SP/AU END DOUBLE PRECISION FUNCTION sla_GMST (UT1) *+ * - - - - - * G M S T * - - - - - * * Conversion from universal time to sidereal time (double precision) * * Given: * UT1 dp universal time (strictly UT1) expressed as * modified Julian Date (JD-2400000.5) * * The result is the Greenwich mean sidereal time (double * precision, radians). * * The IAU 1982 expression (see page S15 of 1984 Astronomical Almanac) * is used, but rearranged to reduce rounding errors. This expression * is always described as giving the GMST at 0 hours UT. In fact, it * gives the difference between the GMST and the UT, which happens to * equal the GMST (modulo 24 hours) at 0 hours UT each day. In this * routine, the entire UT is used directly as the argument for the * standard formula, and the fractional part of the UT is added * separately. Note that the factor 1.0027379... does not appear in the * IAU 1982 expression explicitly but in the form of the coefficient * 8640184.812866, which is 86400x36525x0.0027379... * * See also the routine sla_GMSTA, which delivers better numerical * precision by accepting the UT date and time as separate arguments. * * Called: sla_DRANRM * * P.T.Wallace Starlink 14 October 2001 * * Copyright (C) 2001 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., 51 Franklin Street, Fifth Floor, * Boston, MA 02110-1301 USA * *- IMPLICIT NONE DOUBLE PRECISION UT1 DOUBLE PRECISION sla_DRANRM DOUBLE PRECISION D2PI,S2R PARAMETER (D2PI=6.283185307179586476925286766559D0, : S2R=7.272205216643039903848711535369D-5) DOUBLE PRECISION TU * Julian centuries from fundamental epoch J2000 to this UT TU=(UT1-51544.5D0)/36525D0 * GMST at this UT sla_GMST=sla_DRANRM(MOD(UT1,1D0)*D2PI+ : (24110.54841D0+ : (8640184.812866D0+ : (0.093104D0-6.2D-6*TU)*TU)*TU)*S2R) END 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., 51 Franklin Street, Fifth Floor, * Boston, MA 02110-1301 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, 0.0D0, : -0.3D0, 93.3D0, 0.0D0, 0.0D0, : -0.1D0, 92.1D0, 0.0D0, 0.0D0, : -0.5D0, 133.6D0, 0.0D0, 0.0D0, : -0.1D0, 81.5D0, 0.0D0, 0.0D0, : 0.0D0, 123.9D0, 0.0D0, 0.0D0 / DATA ( ( PSI(I,J), I=1,4 ), J=91,100 ) / : -0.3D0, 128.1D0, 0.0D0, 0.0D0, : 0.1D0, 74.1D0, 0.0D0, -0.3D0, : -0.2D0, -70.3D0, 0.0D0, 0.0D0, : -0.4D0, 66.6D0, 0.0D0, 0.0D0, : 0.1D0, -66.7D0, 0.0D0, 0.0D0, : -0.7D0, 69.3D0, 0.0D0, -0.3D0, : 0.0D0, -70.4D0, 0.0D0, 0.0D0, : -0.1D0, 101.5D0, 0.0D0, 0.0D0, : 0.5D0, -69.1D0, 0.0D0, 0.0D0, : -0.2D0, 58.5D0, 0.0D0, 0.2D0 / DATA ( ( PSI(I,J), I=1,4 ), J=101,110 ) / : 0.1D0, -94.9D0, 0.0D0, 0.2D0, : 0.0D0, 52.9D0, 0.0D0, -0.2D0, : 0.1D0, 86.7D0, 0.0D0, -0.2D0, : -0.1D0, -59.2D0, 0.0D0, 0.2D0, : 0.3D0, -58.8D0, 0.0D0, 0.1D0, : -0.3D0, 49.0D0, 0.0D0, 0.0D0, : -0.2D0, 56.9D0, 0.0D0, -0.1D0, : 0.3D0, -50.2D0, 0.0D0, 0.0D0, : -0.2D0, 53.4D0, 0.0D0, -0.1D0, : 0.1D0, -76.5D0, 0.0D0, 0.0D0 / DATA ( ( PSI(I,J), I=1,4 ), J=111,120 ) / : -0.2D0, 45.3D0, 0.0D0, 0.0D0, : 0.1D0, -46.8D0, 0.0D0, 0.0D0, : 0.2D0, -44.6D0, 0.0D0, 0.0D0, : 0.2D0, -48.7D0, 0.0D0, 0.0D0, : 0.1D0, -46.8D0, 0.0D0, 0.0D0, : 0.1D0, -42.0D0, 0.0D0, 0.0D0, : 0.0D0, 46.4D0, 0.0D0, -0.1D0, : 0.2D0, -67.3D0, 0.0D0, 0.1D0, : 0.0D0, -65.8D0, 0.0D0, 0.2D0, : -0.1D0, -43.9D0, 0.0D0, 0.3D0 / DATA ( ( PSI(I,J), I=1,4 ), J=121,130 ) / : 0.0D0, -38.9D0, 0.0D0, 0.0D0, : -0.3D0, 63.9D0, 0.0D0, 0.0D0, : -0.2D0, 41.2D0, 0.0D0, 0.0D0, : 0.0D0, -36.1D0, 0.0D0, 0.2D0, : -0.3D0, 58.5D0, 0.0D0, 0.0D0, : -0.1D0, 36.1D0, 0.0D0, 0.0D0, : 0.0D0, -39.7D0, 0.0D0, 0.0D0, : 0.1D0, -57.7D0, 0.0D0, 0.0D0, : -0.2D0, 33.4D0, 0.0D0, 0.0D0, : 36.4D0, 0.0D0, 0.0D0, 0.0D0 / DATA ( ( PSI(I,J), I=1,4 ), J=131,140 ) / : -0.1D0, 55.7D0, 0.0D0, -0.1D0, : 0.1D0, -35.4D0, 0.0D0, 0.0D0, : 0.1D0, -31.0D0, 0.0D0, 0.0D0, : -0.1D0, 30.1D0, 0.0D0, 0.0D0, : -0.3D0, 49.2D0, 0.0D0, 0.0D0, : -0.2D0, 49.1D0, 0.0D0, 0.0D0, : -0.1D0, 33.6D0, 0.0D0, 0.0D0, : 0.1D0, -33.5D0, 0.0D0, 0.0D0, : 0.1D0, -31.0D0, 0.0D0, 0.0D0, : -0.1D0, 28.0D0, 0.0D0, 0.0D0 / DATA ( ( 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, 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-3.9D0, 20.5D0, 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, 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), J=51,60 ) / : -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 SUBROUTINE sla_NUT (DATE, RMATN) *+ * - - - - * N U T * - - - - * * Form the matrix of nutation for a given date - Shirai & Fukushima * 2001 theory (double precision) * * Reference: * Shirai, T. & Fukushima, T., Astron.J. 121, 3270-3283 (2001). * * Given: * DATE d TDB (loosely ET) as Modified Julian Date * (=JD-2400000.5) * Returned: * RMATN d(3,3) nutation matrix * * Notes: * * 1 The matrix is in the sense v(true) = rmatn * v(mean) . * where v(true) is the star vector relative to the true equator and * equinox of date and v(mean) is the star vector relative to the * mean equator and equinox of date. * * 2 The matrix represents forced nutation (but not free core * nutation) plus corrections to the IAU~1976 precession model. * * 3 Earth attitude predictions made by combining the present nutation * matrix with IAU~1976 precession are accurate to 1~mas (with * respect to the ICRS) for a few decades around 2000. * * 4 The distinction between the required TDB and TT is always * negligible. Moreover, for all but the most critical applications * UTC is adequate. * * Called: sla_NUTC, sla_DEULER * * Last revision: 1 December 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., 51 Franklin Street, Fifth Floor, * Boston, MA 02110-1301 USA * *- IMPLICIT NONE DOUBLE PRECISION DATE,RMATN(3,3) DOUBLE PRECISION DPSI,DEPS,EPS0 * Nutation components and mean obliquity CALL sla_NUTC(DATE,DPSI,DEPS,EPS0) * Rotation matrix CALL sla_DEULER('XZX',EPS0,-DPSI,-(EPS0+DEPS),RMATN) END SUBROUTINE sla_PREBN (BEP0, BEP1, RMATP) *+ * - - - - - - * P R E B N * - - - - - - * * Generate the matrix of precession between two epochs, * using the old, pre-IAU1976, Bessel-Newcomb model, using * Kinoshita's formulation (double precision) * * Given: * BEP0 dp beginning Besselian epoch * BEP1 dp ending Besselian epoch * * Returned: * RMATP dp(3,3) precession matrix * * The matrix is in the sense V(BEP1) = RMATP * V(BEP0) * * Reference: * Kinoshita, H. (1975) 'Formulas for precession', SAO Special * Report No. 364, Smithsonian Institution Astrophysical * Observatory, Cambridge, Massachusetts. * * Called: sla_DEULER * * P.T.Wallace Starlink 23 August 1996 * * Copyright (C) 1996 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., 51 Franklin Street, Fifth Floor, * Boston, MA 02110-1301 USA * *- IMPLICIT NONE DOUBLE PRECISION BEP0,BEP1,RMATP(3,3) * Arc seconds to radians DOUBLE PRECISION AS2R PARAMETER (AS2R=0.484813681109535994D-5) DOUBLE PRECISION BIGT,T,TAS2R,W,ZETA,Z,THETA * Interval between basic epoch B1850.0 and beginning epoch in TC BIGT = (BEP0-1850D0)/100D0 * Interval over which precession required, in tropical centuries T = (BEP1-BEP0)/100D0 * Euler angles TAS2R = T*AS2R W = 2303.5548D0+(1.39720D0+0.000059D0*BIGT)*BIGT ZETA = (W+(0.30242D0-0.000269D0*BIGT+0.017996D0*T)*T)*TAS2R Z = (W+(1.09478D0+0.000387D0*BIGT+0.018324D0*T)*T)*TAS2R THETA = (2005.1125D0+(-0.85294D0-0.000365D0*BIGT)*BIGT+ : (-0.42647D0-0.000365D0*BIGT-0.041802D0*T)*T)*TAS2R * Rotation matrix CALL sla_DEULER('ZYZ',-ZETA,THETA,-Z,RMATP) END SUBROUTINE sla_PRECES (SYSTEM, EP0, EP1, RA, DC) *+ * - - - - - - - * P R E C E S * - - - - - - - * * Precession - either FK4 (Bessel-Newcomb, pre IAU 1976) or * FK5 (Fricke, post IAU 1976) as required. * * Given: * SYSTEM char precession to be applied: 'FK4' or 'FK5' * EP0,EP1 dp starting and ending epoch * RA,DC dp RA,Dec, mean equator & equinox of epoch EP0 * * Returned: * RA,DC dp RA,Dec, mean equator & equinox of epoch EP1 * * Called: sla_DRANRM, sla_PREBN, sla_PREC, sla_DCS2C, * sla_DMXV, sla_DCC2S * * Notes: * * 1) Lowercase characters in SYSTEM are acceptable. * * 2) The epochs are Besselian if SYSTEM='FK4' and Julian if 'FK5'. * For example, to precess coordinates in the old system from * equinox 1900.0 to 1950.0 the call would be: * CALL sla_PRECES ('FK4', 1900D0, 1950D0, RA, DC) * * 3) This routine will NOT correctly convert between the old and * the new systems - for example conversion from B1950 to J2000. * For these purposes see sla_FK425, sla_FK524, sla_FK45Z and * sla_FK54Z. * * 4) If an invalid SYSTEM is supplied, values of -99D0,-99D0 will * be returned for both RA and DC. * * P.T.Wallace Starlink 20 April 1990 * * Copyright (C) 1995 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., 51 Franklin Street, Fifth Floor, * Boston, MA 02110-1301 USA * *- IMPLICIT NONE CHARACTER SYSTEM*(*) DOUBLE PRECISION EP0,EP1,RA,DC DOUBLE PRECISION PM(3,3),V1(3),V2(3) CHARACTER SYSUC*3 DOUBLE PRECISION sla_DRANRM * Convert to uppercase and validate SYSTEM SYSUC=SYSTEM IF (SYSUC(1:1).EQ.'f') SYSUC(1:1)='F' IF (SYSUC(2:2).EQ.'k') SYSUC(2:2)='K' IF (SYSUC.NE.'FK4'.AND.SYSUC.NE.'FK5') THEN RA=-99D0 DC=-99D0 ELSE * Generate appropriate precession matrix IF (SYSUC.EQ.'FK4') THEN CALL sla_PREBN(EP0,EP1,PM) ELSE CALL sla_PREC(EP0,EP1,PM) END IF * Convert RA,Dec to x,y,z CALL sla_DCS2C(RA,DC,V1) * Precess CALL sla_DMXV(PM,V1,V2) * Back to RA,Dec CALL sla_DCC2S(V2,RA,DC) RA=sla_DRANRM(RA) END IF END SUBROUTINE sla_PREC (EP0, EP1, RMATP) *+ * - - - - - * P R E C * - - - - - * * Form the matrix of precession between two epochs (IAU 1976, FK5) * (double precision) * * Given: * EP0 dp beginning epoch * EP1 dp ending epoch * * Returned: * RMATP dp(3,3) precession matrix * * Notes: * * 1) The epochs are TDB (loosely ET) Julian epochs. * * 2) The matrix is in the sense V(EP1) = RMATP * V(EP0) * * 3) Though the matrix method itself is rigorous, the precession * angles are expressed through canonical polynomials which are * valid only for a limited time span. There are also known * errors in the IAU precession rate. The absolute accuracy * of the present formulation is better than 0.1 arcsec from * 1960AD to 2040AD, better than 1 arcsec from 1640AD to 2360AD, * and remains below 3 arcsec for the whole of the period * 500BC to 3000AD. The errors exceed 10 arcsec outside the * range 1200BC to 3900AD, exceed 100 arcsec outside 4200BC to * 5600AD and exceed 1000 arcsec outside 6800BC to 8200AD. * The SLALIB routine sla_PRECL implements a more elaborate * model which is suitable for problems spanning several * thousand years. * * References: * Lieske,J.H., 1979. Astron.Astrophys.,73,282. * equations (6) & (7), p283. * Kaplan,G.H., 1981. USNO circular no. 163, pA2. * * Called: sla_DEULER * * P.T.Wallace Starlink 23 August 1996 * * Copyright (C) 1996 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., 51 Franklin Street, Fifth Floor, * Boston, MA 02110-1301 USA * *- IMPLICIT NONE DOUBLE PRECISION EP0,EP1,RMATP(3,3) * Arc seconds to radians DOUBLE PRECISION AS2R PARAMETER (AS2R=0.484813681109535994D-5) DOUBLE PRECISION T0,T,TAS2R,W,ZETA,Z,THETA * Interval between basic epoch J2000.0 and beginning epoch (JC) T0 = (EP0-2000D0)/100D0 * Interval over which precession required (JC) T = (EP1-EP0)/100D0 * Euler angles TAS2R = T*AS2R W = 2306.2181D0+(1.39656D0-0.000139D0*T0)*T0 ZETA = (W+((0.30188D0-0.000344D0*T0)+0.017998D0*T)*T)*TAS2R Z = (W+((1.09468D0+0.000066D0*T0)+0.018203D0*T)*T)*TAS2R THETA = ((2004.3109D0+(-0.85330D0-0.000217D0*T0)*T0) : +((-0.42665D0-0.000217D0*T0)-0.041833D0*T)*T)*TAS2R * Rotation matrix CALL sla_DEULER('ZYZ',-ZETA,THETA,-Z,RMATP) END SUBROUTINE sla_PVOBS (P, H, STL, PV) *+ * - - - - - - * P V O B S * - - - - - - * * Position and velocity of an observing station (double precision) * * Given: * P dp latitude (geodetic, radians) * H dp height above reference spheroid (geodetic, metres) * STL dp local apparent sidereal time (radians) * * Returned: * PV dp(6) position/velocity 6-vector (AU, AU/s, true equator * and equinox of date) * * Called: sla_GEOC * * IAU 1976 constants are used. * * P.T.Wallace Starlink 14 November 1994 * * Copyright (C) 1995 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., 51 Franklin Street, Fifth Floor, * Boston, MA 02110-1301 USA * *- IMPLICIT NONE DOUBLE PRECISION P,H,STL,PV(6) DOUBLE PRECISION R,Z,S,C,V * Mean sidereal rate (at J2000) in radians per (UT1) second DOUBLE PRECISION SR PARAMETER (SR=7.292115855306589D-5) * Geodetic to geocentric conversion CALL sla_GEOC(P,H,R,Z) * Functions of ST S=SIN(STL) C=COS(STL) * Speed V=SR*R * Position PV(1)=R*C PV(2)=R*S PV(3)=Z * Velocity PV(4)=-V*S PV(5)=V*C PV(6)=0D0 END