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#include "sofa.h"
void iauAe2hd (double az, double el, double phi,
double *ha, double *dec)
/*
** - - - - - - - - -
** i a u A e 2 h d
** - - - - - - - - -
**
** Horizon to equatorial coordinates: transform azimuth and altitude
** to hour angle and declination.
**
** Given:
** az double azimuth
** el double altitude (informally, elevation)
** phi double site latitude
**
** Returned:
** ha double hour angle (local)
** dec double 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: 2017 September 12
**
** SOFA release 2020-07-21
**
** Copyright (C) 2020 IAU SOFA Board. See notes at end.
*/
{
double 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);
/* HA,Dec 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);
*ha = (r != 0.0) ? atan2(y,x) : 0.0;
*dec = atan2(z,r);
/* Finished. */
/*----------------------------------------------------------------------
**
** Copyright (C) 2020
** 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
**
**--------------------------------------------------------------------*/
}