SUBROUTINE sla_AOPQK (RAP, DAP, AOPRMS, AOB, ZOB, HOB, DOB, ROB) *+ * - - - - - - * A O P Q K * - - - - - - * * Quick apparent to observed place (but see note 8, below, for * remarks about speed). * * Given: * RAP d geocentric apparent right ascension * DAP d geocentric apparent declination * AOPRMS d(14) star-independent apparent-to-observed parameters: * * (1) geodetic latitude (radians) * (2,3) sine and cosine of geodetic latitude * (4) magnitude of diurnal aberration vector * (5) height (HM) * (6) ambient temperature (T) * (7) pressure (P) * (8) relative humidity (RH) * (9) wavelength (WL) * (10) lapse rate (TLR) * (11,12) refraction constants A and B (radians) * (13) longitude + eqn of equinoxes + sidereal DUT (radians) * (14) local apparent sidereal time (radians) * * Returned: * AOB d observed azimuth (radians: N=0,E=90) * ZOB d observed zenith distance (radians) * HOB d observed Hour Angle (radians) * DOB d observed Declination (radians) * ROB d observed Right Ascension (radians) * * Notes: * * 1) This routine returns zenith distance rather than elevation * in order to reflect the fact that no allowance is made for * depression of the horizon. * * 2) The accuracy of the result is limited by the corrections for * refraction. Providing the meteorological parameters are * known accurately and there are no gross local effects, the * observed RA,Dec predicted by this routine should be within * about 0.1 arcsec for a zenith distance of less than 70 degrees. * Even at a topocentric zenith distance of 90 degrees, the * accuracy in elevation should be better than 1 arcmin; useful * results are available for a further 3 degrees, beyond which * the slaRefro routine returns a fixed value of the refraction. * The complementary routines slaAop (or slaAopqk) and slaOap * (or slaOapqk) are self-consistent to better than 1 micro- * arcsecond all over the celestial sphere. * * 3) It is advisable to take great care with units, as even * unlikely values of the input parameters are accepted and * processed in accordance with the models used. * * 4) "Apparent" place means the geocentric apparent right ascension * and declination, which is obtained from a catalogue mean place * by allowing for space motion, parallax, precession, nutation, * annual aberration, and the Sun's gravitational lens effect. For * star positions in the FK5 system (i.e. J2000), these effects can * be applied by means of the sla_MAP etc routines. Starting from * other mean place systems, additional transformations will be * needed; for example, FK4 (i.e. B1950) mean places would first * have to be converted to FK5, which can be done with the * sla_FK425 etc routines. * * 5) "Observed" Az,El means the position that would be seen by a * perfect theodolite located at the observer. This is obtained * from the geocentric apparent RA,Dec by allowing for Earth * orientation and diurnal aberration, rotating from equator * to horizon coordinates, and then adjusting for refraction. * The HA,Dec is obtained by rotating back into equatorial * coordinates, using the geodetic latitude corrected for polar * motion, and is the position that would be seen by a perfect * equatorial located at the observer and with its polar axis * aligned to the Earth's axis of rotation (n.b. not to the * refracted pole). Finally, the RA is obtained by subtracting * the HA from the local apparent ST. * * 6) To predict the required setting of a real telescope, the * observed place produced by this routine would have to be * adjusted for the tilt of the azimuth or polar axis of the * mounting (with appropriate corrections for mount flexures), * for non-perpendicularity between the mounting axes, for the * position of the rotator axis and the pointing axis relative * to it, for tube flexure, for gear and encoder errors, and * finally for encoder zero points. Some telescopes would, of * course, exhibit other properties which would need to be * accounted for at the appropriate point in the sequence. * * 7) The star-independent apparent-to-observed-place parameters * in AOPRMS may be computed by means of the sla_AOPPA routine. * If nothing has changed significantly except the time, the * sla_AOPPAT routine may be used to perform the requisite * partial recomputation of AOPRMS. * * 8) At zenith distances beyond about 76 degrees, the need for * special care with the corrections for refraction causes a * marked increase in execution time. Moreover, the effect * gets worse with increasing zenith distance. Adroit * programming in the calling application may allow the * problem to be reduced. Prepare an alternative AOPRMS array, * computed for zero air-pressure; this will disable the * refraction corrections and cause rapid execution. Using * this AOPRMS array, a preliminary call to the present routine * will, depending on the application, produce a rough position * which may be enough to establish whether the full, slow * calculation (using the real AOPRMS array) is worthwhile. * For example, there would be no need for the full calculation * if the preliminary call had already established that the * source was well below the elevation limits for a particular * telescope. * * 9) The azimuths etc produced by the present routine are with * respect to the celestial pole. Corrections to the terrestrial * pole can be computed using sla_POLMO. * * Called: sla_DCS2C, sla_REFZ, sla_REFRO, sla_DCC2S, sla_DRANRM * * P.T.Wallace Starlink 22 February 1996 * * Copyright (C) 1996 Rutherford Appleton Laboratory *- IMPLICIT NONE DOUBLE PRECISION RAP,DAP,AOPRMS(14),AOB,ZOB,HOB,DOB,ROB * Breakpoint for fast/slow refraction algorithm: * ZD greater than arctan(4), (see sla_REFCO routine) * or vector Z less than cosine(arctan(Z)) = 1/sqrt(17) DOUBLE PRECISION ZBREAK PARAMETER (ZBREAK=0.242535625D0) INTEGER I DOUBLE PRECISION SPHI,CPHI,ST,V(3),XHD,YHD,ZHD,DIURAB,F, : XHDT,YHDT,ZHDT,XAET,YAET,ZAET,AZOBS, : ZDT,REFA,REFB,ZDOBS,DZD,DREF,CE, : XAEO,YAEO,ZAEO,HMOBS,DCOBS,RAOBS DOUBLE PRECISION sla_DRANRM * Sin, cos of latitude SPHI = AOPRMS(2) CPHI = AOPRMS(3) * Local apparent sidereal time ST = AOPRMS(14) * Apparent RA,Dec to Cartesian -HA,Dec CALL sla_DCS2C(RAP-ST,DAP,V) XHD = V(1) YHD = V(2) ZHD = V(3) * Diurnal aberration DIURAB = AOPRMS(4) F = (1D0-DIURAB*YHD) XHDT = F*XHD YHDT = F*(YHD+DIURAB) ZHDT = F*ZHD * Cartesian -HA,Dec to Cartesian Az,El (S=0,E=90) XAET = SPHI*XHDT-CPHI*ZHDT YAET = YHDT ZAET = CPHI*XHDT+SPHI*ZHDT * Azimuth (N=0,E=90) IF (XAET.EQ.0D0.AND.YAET.EQ.0D0) THEN AZOBS = 0D0 ELSE AZOBS = ATAN2(YAET,-XAET) END IF * Topocentric zenith distance ZDT = ATAN2(SQRT(XAET*XAET+YAET*YAET),ZAET) * * Refraction * ---------- * Fast algorithm using two constant model REFA = AOPRMS(11) REFB = AOPRMS(12) CALL sla_REFZ(ZDT,REFA,REFB,ZDOBS) * Large zenith distance? IF (COS(ZDOBS).LT.ZBREAK) THEN * Yes: use rigorous algorithm * Initialize loop (maximum of 10 iterations) I = 1 DZD = 1D1 DO WHILE (ABS(DZD).GT.1D-10.AND.I.LE.10) * Compute refraction using current estimate of observed ZD CALL sla_REFRO(ZDOBS,AOPRMS(5),AOPRMS(6),AOPRMS(7), : AOPRMS(8),AOPRMS(9),AOPRMS(1), : AOPRMS(10),1D-8,DREF) * Remaining discrepancy DZD = ZDOBS+DREF-ZDT * Update the estimate ZDOBS = ZDOBS-DZD * Increment the iteration counter I = I+1 END DO END IF * To Cartesian Az/ZD CE = SIN(ZDOBS) XAEO = -COS(AZOBS)*CE YAEO = SIN(AZOBS)*CE ZAEO = COS(ZDOBS) * Cartesian Az/ZD to Cartesian -HA,Dec V(1) = SPHI*XAEO+CPHI*ZAEO V(2) = YAEO V(3) = -CPHI*XAEO+SPHI*ZAEO * To spherical -HA,Dec CALL sla_DCC2S(V,HMOBS,DCOBS) * Right Ascension RAOBS = sla_DRANRM(ST+HMOBS) * Return the results AOB = AZOBS ZOB = ZDOBS HOB = -HMOBS DOB = DCOBS ROB = RAOBS END