SUBROUTINE iau_ATIOQ ( RI, DI, ASTROM, AOB, ZOB, HOB, DOB, ROB ) *+ * - - - - - - - - - - * i a u _ A T I O Q * - - - - - - - - - - * * Quick CIRS to observed place transformation. * * Use of this routine is appropriate when efficiency is important and * where many star positions are all to be transformed for one date. * The star-independent astrometry parameters can be obtained by * calling iau_APIO[13] or iau_APCO[13]. * * This routine is part of the International Astronomical Union's * SOFA (Standards of Fundamental Astronomy) software collection. * * Status: support routine. * * Given: * RI d CIRS right ascension * DI d CIRS declination * ASTROM d(30) star-independent astrometry parameters: * (1) PM time interval (SSB, Julian years) * (2-4) SSB to observer (vector, au) * (5-7) Sun to observer (unit vector) * (8) distance from Sun to observer (au) * (9-11) v: barycentric observer velocity (vector, c) * (12) sqrt(1-|v|^2): reciprocal of Lorenz factor * (13-21) bias-precession-nutation matrix * (22) longitude + s' (radians) * (23) polar motion xp wrt local meridian (radians) * (24) polar motion yp wrt local meridian (radians) * (25) sine of geodetic latitude * (26) cosine of geodetic latitude * (27) magnitude of diurnal aberration vector * (28) "local" Earth rotation angle (radians) * (29) refraction constant A (radians) * (30) refraction constant B (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 (CIO-based, radians) * ROB d observed right ascension (CIO-based, radians) * * Notes: * * 1) This routine returns zenith distance rather than altitude 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, which use a simple A*tan(z) + B*tan^3(z) model. * Providing the meteorological parameters are known accurately and * there are no gross local effects, the predicted observed * coordinates should be within 0.05 arcsec (optical) or 1 arcsec * (radio) for a zenith distance of less than 70 degrees, better * than 30 arcsec (optical or radio) at 85 degrees and better than * 25 arcmin (optical) or 35 arcmin (radio) at the horizon. * * Without refraction, the complementary routines iau_ATIOQ and * iau_ATOIQ are self-consistent to better than 1 microarcsecond all * over the celestial sphere. With refraction included, consistency * falls off at high zenith distances, but is still better than * 0.05 arcsec at 85 degrees. * * 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) The CIRS RA,Dec is obtained from a star catalog mean place by * allowing for space motion, parallax, the Sun's gravitational lens * effect, annual aberration and precession-nutation. For star * positions in the ICRS, these effects can be applied by means of * the iau_ATCI13 (etc.) routines. Starting from classical "mean * place" systems, additional transformations will be needed first. * * 5) "Observed" Az,El means the position that would be seen by a * perfect geodetically aligned theodolite. This is obtained from * the CIRS 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, and is the position that would be * seen by a perfect equatorial with its polar axis aligned to the * Earth's axis of rotation. Finally, the (CIO-based) RA is obtained * by subtracting the HA from the local ERA. * * 6) The star-independent CIRS-to-observed-place parameters in ASTROM * may be computed with iau_APIO[13] or iau_APCO[13]. If nothing has * changed significantly except the time, iau_APER[13] may be used * to perform the requisite adjustment to the ASTROM array. * * Called: * iau_S2C spherical coordinates to unit vector * iau_C2S p-vector to spherical * iau_ANP normalize angle into range 0 to 2pi * * This revision: 2022 August 30 * * SOFA release 2023-10-11 * * Copyright (C) 2023 IAU SOFA Board. See notes at end. * *----------------------------------------------------------------------- IMPLICIT NONE DOUBLE PRECISION RI, DI, ASTROM(30), AOB, ZOB, HOB, DOB, ROB * Minimum sine and cosine of altitude for refraction purposes DOUBLE PRECISION SELMIN, CELMIN PARAMETER ( SELMIN = 0.05D0, CELMIN = 1D-6 ) DOUBLE PRECISION V(3), X, Y, Z, SX, CX, SY, CY, XHD, YHD, ZHD, F, : XHDT, YHDT, ZHDT, XAET, YAET, ZAET, AZOBS, : R, TZ, W, DEL, COSDEL, XAEO, YAEO, ZAEO, : ZDOBS, HMOBS, DCOBS, RAOBS DOUBLE PRECISION iau_ANP * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * CIRS RA,Dec to Cartesian -HA,Dec. CALL iau_S2C ( RI-ASTROM(28), DI, V ) X = V(1) Y = V(2) Z = V(3) * Polar motion. SX = SIN(ASTROM(23)) CX = COS(ASTROM(23)) SY = SIN(ASTROM(24)) CY = COS(ASTROM(24)) XHD = CX*X + SX*Z YHD = SX*SY*X + CY*Y - CX*SY*Z ZHD = -SX*CY*X + SY*Y + CX*CY*Z * Diurnal aberration. F = ( 1D0 - ASTROM(27)*YHD ) XHDT = F * XHD YHDT = F * ( YHD + ASTROM(27) ) ZHDT = F * ZHD * Cartesian -HA,Dec to Cartesian Az,El (S=0,E=90). XAET = ASTROM(25)*XHDT - ASTROM(26)*ZHDT YAET = YHDT ZAET = ASTROM(26)*XHDT + ASTROM(25)*ZHDT * Azimuth (N=0,E=90). IF ( XAET.NE.0D0 .OR. YAET.NE.0D0 ) THEN AZOBS = ATAN2 ( YAET, -XAET ) ELSE AZOBS = 0D0 END IF * ---------- * Refraction * ---------- * Cosine and sine of altitude, with precautions. R = MAX ( SQRT ( XAET*XAET + YAET*YAET ), CELMIN) Z = MAX ( ZAET, SELMIN ) * A*tan(z)+B*tan^3(z) model, with Newton-Raphson correction. TZ = R/Z W = ASTROM(30)*TZ*TZ DEL = ( ASTROM(29) + W ) * TZ / : ( 1D0 + ( ASTROM(29) + 3D0*W ) / ( Z*Z ) ) * Apply the change, giving observed vector. COSDEL = 1D0 - DEL*DEL/2D0 F = COSDEL - DEL*Z/R XAEO = XAET*F YAEO = YAET*F ZAEO = COSDEL*ZAET + DEL*R * Observed ZD. ZDOBS = ATAN2 ( SQRT ( XAEO*XAEO + YAEO*YAEO ), ZAEO ) * Az/El vector to HA,Dec vector (both right-handed). V(1) = ASTROM(25)*XAEO + ASTROM(26)*ZAEO V(2) = YAEO V(3) = - ASTROM(26)*XAEO + ASTROM(25)*ZAEO * To spherical -HA,Dec. CALL iau_C2S ( V, HMOBS, DCOBS ) * Right ascension (with respect to CIO). RAOBS = ASTROM(28) + HMOBS * Return the results. AOB = iau_ANP(AZOBS) ZOB = ZDOBS HOB = -HMOBS DOB = DCOBS ROB = iau_ANP(RAOBS) * Finished. *+---------------------------------------------------------------------- * * Copyright (C) 2023 * Standards of Fundamental Astronomy Board * of the International Astronomical Union. * * ===================== * SOFA Software License * ===================== * * NOTICE TO USER: * * BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND * CONDITIONS WHICH APPLY TO ITS USE. * * 1. The Software is owned by the IAU SOFA Board ("SOFA"). * * 2. Permission is granted to anyone to use the SOFA software for any * purpose, including commercial applications, free of charge and * without payment of royalties, subject to the conditions and * restrictions listed below. * * 3. You (the user) may copy and distribute SOFA source code to others, * and use and adapt its code and algorithms in your own software, * on a world-wide, royalty-free basis. 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The provision of any version of the SOFA software under the terms * and conditions specified herein does not imply that future * versions will also be made available under the same terms and * conditions. * * In any published work or commercial product which uses the SOFA * software directly, acknowledgement (see www.iausofa.org) is * appreciated. * * Correspondence concerning SOFA software should be addressed as * follows: * * By email: sofa@ukho.gov.uk * By post: IAU SOFA Center * HM Nautical Almanac Office * UK Hydrographic Office * Admiralty Way, Taunton * Somerset, TA1 2DN * United Kingdom * *----------------------------------------------------------------------- END