SUBROUTINE iau_AE2HD (AZ, EL, PHI, HA, DEC) *+ * - - - - - - - - - - * i a u _ A E 2 H D * - - - - - - - - - - * * Horizon to equatorial coordinates: transform azimuth and altitude * to hour angle and declination. * * This routine is part of the International Astronomical Union's * SOFA (Standards of Fundamental Astronomy) software collection. * * Status: support routine. * * Given: * AZ d azimuth * EL d elevation * PHI d observatory latitude * * Returned: * HA d hour angle * DEC d declination * * Notes: * * 1) All the arguments are angles in radians. * * 2) The sign convention for azimuth is north zero, east +pi/2. * * 3) HA is returned in the range +/-pi. Declination is returned in * the range +/-pi/2. * * 4) The latitude PHI is pi/2 minus the angle between the Earth's * rotation axis and the adopted zenith. In many applications it * will be sufficient to use the published geodetic latitude of the * site. In very precise (sub-arcsecond) applications, PHI can be * corrected for polar motion. * * 5) The azimuth AZ must be with respect to the rotational north pole, * as opposed to the ITRS pole, and an azimuth with respect to north * on a map of the Earth's surface will need to be adjusted for * polar motion if sub-arcsecond accuracy is required. * * 6) Should the user wish to work with respect to the astronomical * zenith rather than the geodetic zenith, PHI will need to be * adjusted for deflection of the vertical (often tens of * arcseconds), and the zero point of HA will also be affected. * * 7) The transformation is the same as Ve = Ry(phi-pi/2)*Rz(pi)*Vh, * where Ve and Vh are lefthanded unit vectors in the (ha,dec) and * (az,el) systems respectively and Rz and Ry are rotations about * first the z-axis and then the y-axis. (n.b. Rz(pi) simply * reverses the signs of the x and y components.) For efficiency, * the algorithm is written out rather than calling other utility * functions. For applications that require even greater * efficiency, additional savings are possible if constant terms * such as functions of latitude are computed once and for all. * * 8) Again for efficiency, no range checking of arguments is carried * out. * * Last revision: 2018 January 2 * * SOFA release 2021-05-12 * * Copyright (C) 2021 IAU SOFA Board. See notes at end. * *----------------------------------------------------------------------- IMPLICIT NONE DOUBLE PRECISION AZ, EL, PHI, HA, DEC DOUBLE PRECISION SA, CA, SE, CE, SP, CP, X, Y, Z, R * Useful trig functions. SA = SIN(AZ) CA = COS(AZ) SE = SIN(EL) CE = COS(EL) SP = SIN(PHI) CP = COS(PHI) * Az,Alt unit vector. X = - CA*CE*SP + SE*CP Y = - SA*CE Z = CA*CE*CP + SE*SP * To spherical. R = SQRT(X*X + Y*Y) IF ( R.EQ.0D0 ) THEN HA = 0D0 ELSE HA = ATAN2(Y,X) END IF DEC = ATAN2(Z,R) * Finished. *+---------------------------------------------------------------------- * * Copyright (C) 2021 * 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. That portion of your * distribution that does not consist of intact and unchanged copies * of SOFA source code files is a "derived work" that must comply * with the following requirements: * * a) Your work shall be marked or carry a statement that it * (i) uses routines and computations derived by you from * software provided by SOFA under license to you; and * (ii) does not itself constitute software provided by and/or * endorsed by SOFA. * * b) The source code of your derived work must contain descriptions * of how the derived work is based upon, contains and/or differs * from the original SOFA software. * * c) The names of all routines in your derived work shall not * include the prefix "iau" or "sofa" or trivial modifications * thereof such as changes of case. * * d) The origin of the SOFA components of your derived work must * not be misrepresented; you must not claim that you wrote the * original software, nor file a patent application for SOFA * software or algorithms embedded in the SOFA software. * * e) These requirements must be reproduced intact in any source * distribution and shall apply to anyone to whom you have * granted a further right to modify the source code of your * derived work. * * Note that, as originally distributed, the SOFA software is * intended to be a definitive implementation of the IAU standards, * and consequently third-party modifications are discouraged. All * variations, no matter how minor, must be explicitly marked as * such, as explained above. * * 4. You shall not cause the SOFA software to be brought into * disrepute, either by misuse, or use for inappropriate tasks, or * by inappropriate modification. * * 5. The SOFA software is provided "as is" and SOFA makes no warranty * as to its use or performance. SOFA does not and cannot warrant * the performance or results which the user may obtain by using the * SOFA software. SOFA makes no warranties, express or implied, as * to non-infringement of third party rights, merchantability, or * fitness for any particular purpose. In no event will SOFA be * liable to the user for any consequential, incidental, or special * damages, including any lost profits or lost savings, even if a * SOFA representative has been advised of such damages, or for any * claim by any third party. * * 6. 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