c/src/atioq.c

#include "sofa.h"

void iauAtioq(double ri, double di, iauASTROM *astrom,
              double *aob, double *zob,
              double *hob, double *dob, double *rob)
/*
**  - - - - - - - - -
**   i a u A t i o q
**  - - - - - - - - -
**
**  Quick CIRS to observed place transformation.
**
**  Use of this function 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 iauApio[13] or iauApco[13].
**
**  This function is part of the International Astronomical Union's
**  SOFA (Standards of Fundamental Astronomy) software collection.
**
**  Status:  support function.
**
**  Given:
**     ri     double     CIRS right ascension
**     di     double     CIRS declination
**     astrom iauASTROM* star-independent astrometry parameters:
**      pmt    double       PM time interval (SSB, Julian years)
**      eb     double[3]    SSB to observer (vector, au)
**      eh     double[3]    Sun to observer (unit vector)
**      em     double       distance from Sun to observer (au)
**      v      double[3]    barycentric observer velocity (vector, c)
**      bm1    double       sqrt(1-|v|^2): reciprocal of Lorenz factor
**      bpn    double[3][3] bias-precession-nutation matrix
**      along  double       longitude + s' (radians)
**      xpl    double       polar motion xp wrt local meridian (radians)
**      ypl    double       polar motion yp wrt local meridian (radians)
**      sphi   double       sine of geodetic latitude
**      cphi   double       cosine of geodetic latitude
**      diurab double       magnitude of diurnal aberration vector
**      eral   double       "local" Earth rotation angle (radians)
**      refa   double       refraction constant A (radians)
**      refb   double       refraction constant B (radians)
**
**  Returned:
**     aob    double*    observed azimuth (radians: N=0,E=90)
**     zob    double*    observed zenith distance (radians)
**     hob    double*    observed hour angle (radians)
**     dob    double*    observed declination (radians)
**     rob    double*    observed right ascension (CIO-based, radians)
**
**  Notes:
**
**  1) This function 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 20 arcmin (optical) or 30 arcmin (radio) at the horizon.
**
**     Without refraction, the complementary functions iauAtioq and
**     iauAtoiq 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 iauAtci13 (etc.) functions.  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 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 iauApio[13] or iauApco[13].  If nothing has
**     changed significantly except the time, iauAper[13] may be used to
**     perform the requisite adjustment to the astrom structure.
**
**  Called:
**     iauS2c       spherical coordinates to unit vector
**     iauC2s       p-vector to spherical
**     iauAnp       normalize angle into range 0 to 2pi
**
**  This revision:   2020 December 7
**
**  SOFA release 2021-05-12
**
**  Copyright (C) 2021 IAU SOFA Board.  See notes at end.
*/
{
/* Minimum cos(alt) and sin(alt) for refraction purposes */
   const double CELMIN = 1e-6;
   const double SELMIN = 0.05;

   double 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;


/* CIRS RA,Dec to Cartesian -HA,Dec. */
   iauS2c(ri-astrom->eral, di, v);
   x = v[0];
   y = v[1];
   z = v[2];

/* Polar motion. */
   sx = sin(astrom->xpl);
   cx = cos(astrom->xpl);
   sy = sin(astrom->ypl);
   cy = cos(astrom->ypl);
   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 = ( 1.0 - astrom->diurab*yhd );
   xhdt = f * xhd;
   yhdt = f * ( yhd + astrom->diurab );
   zhdt = f * zhd;

/* Cartesian -HA,Dec to Cartesian Az,El (S=0,E=90). */
   xaet = astrom->sphi*xhdt - astrom->cphi*zhdt;
   yaet = yhdt;
   zaet = astrom->cphi*xhdt + astrom->sphi*zhdt;

/* Azimuth (N=0,E=90). */
   azobs = ( xaet != 0.0 || yaet != 0.0 ) ? atan2(yaet,-xaet) : 0.0;

/* ---------- */
/* Refraction */
/* ---------- */

/* Cosine and sine of altitude, with precautions. */
   r = sqrt(xaet*xaet + yaet*yaet);
   r = r > CELMIN ? r : CELMIN;
   z = zaet > SELMIN ? zaet : SELMIN;

/* A*tan(z)+B*tan^3(z) model, with Newton-Raphson correction. */
   tz = r/z;
   w = astrom->refb*tz*tz;
   del = ( astrom->refa + w ) * tz /
         ( 1.0 + ( astrom->refa + 3.0*w ) / ( z*z ) );

/* Apply the change, giving observed vector. */
   cosdel = 1.0 - del*del/2.0;
   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[0] = astrom->sphi*xaeo + astrom->cphi*zaeo;
   v[1] = yaeo;
   v[2] = - astrom->cphi*xaeo + astrom->sphi*zaeo;

/* To spherical -HA,Dec. */
   iauC2s ( v, &hmobs, &dcobs );

/* Right ascension (with respect to CIO). */
   raobs = astrom->eral + hmobs;

/* Return the results. */
   *aob = iauAnp(azobs);
   *zob = zdobs;
   *hob = -hmobs;
   *dob = dcobs;
   *rob = iauAnp(raobs);

/* 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
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**        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.
**
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**
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**
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*
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**
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**--------------------------------------------------------------------*/
}