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/*
*+
* Name:
* palAopqk
* Purpose:
* Quick apparent to observed place
* Language:
* Starlink ANSI C
* Type of Module:
* Library routine
* Invocation:
* void palAopqk ( double rap, double dap, const double aoprms[14],
* double *aob, double *zob, double *hob,
* double *dob, double *rob );
* Arguments:
* rap = double (Given)
* Geocentric apparent right ascension
* dap = double (Given)
* Geocentric apparent declination
* aoprms = const double [14] (Given)
* Starindependent apparenttoobserved parameters.
*
* [0] geodetic latitude (radians)
* [1,2] sine and cosine of geodetic latitude
* [3] magnitude of diurnal aberration vector
* [4] height (HM)
* [5] ambient temperature (T)
* [6] pressure (P)
* [7] relative humidity (RH)
* [8] wavelength (WL)
* [9] lapse rate (TLR)
* [10,11] refraction constants A and B (radians)
* [12] longitude + eqn of equinoxes + sidereal DUT (radians)
* [13] local apparent sidereal time (radians)
* aob = double * (Returned)
* Observed azimuth (radians: N=0,E=90)
* zob = double * (Returned)
* Observed zenith distance (radians)
* hob = double * (Returned)
* Observed Hour Angle (radians)
* dob = double * (Returned)
* Observed Declination (radians)
* rob = double * (Returned)
* Observed Right Ascension (radians)
* Description:
* Quick apparent to observed place.
* Authors:
* TIMJ: Tim Jenness (JAC, Hawaii)
* PTW: Patrick T. Wallace
* {enter_new_authors_here}
* Notes:
*  This routine returns zenith distance rather than elevation
* in order to reflect the fact that no allowance is made for
* depression of the horizon.
*
*  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 palRefro routine returns a fixed value of the refraction.
* The complementary routines palAop (or palAopqk) and palOap
* (or palOapqk) are selfconsistent to better than 1 micro
* arcsecond all over the celestial sphere.
*
*  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.
*
*  "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 palMap 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
* palFk425 etc routines.
*
*  "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.
*
*  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 nonperpendicularity 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.
*
*  The starindependent apparenttoobservedplace parameters
* in AOPRMS may be computed by means of the palAoppa routine.
* If nothing has changed significantly except the time, the
* palAoppat routine may be used to perform the requisite
* partial recomputation of AOPRMS.
*
*  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 airpressure; 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.
*
*  The azimuths etc produced by the present routine are with
* respect to the celestial pole. Corrections to the terrestrial
* pole can be computed using palPolmo.
* History:
* 20120825 (TIMJ):
* Initial version, copied from Fortran SLA
* Adapted with permission from the Fortran SLALIB library.
* {enter_further_changes_here}
* Copyright:
* Copyright (C) 2003 Rutherford Appleton Laboratory
* Copyright (C) 2012 Science and Technology Facilities Council.
* All Rights Reserved.
* Licence:
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License as
* published by the Free Software Foundation; either version 3 of
* the License, or (at your option) any later version.
*
* This program is distributed in the hope that it will be
* useful, but WITHOUT ANY WARRANTY; without even the implied
* warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
* PURPOSE. See the GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
* MA 021101301, USA.
* Bugs:
* {note_any_bugs_here}
*
*/
#include <math.h>
#include "pal.h"
void palAopqk ( double rap, double dap, const double aoprms[14],
double *aob, double *zob, double *hob,
double *dob, double *rob ) {
/* Breakpoint for fast/slow refraction algorithm:
* ZD greater than arctan(4), (see palRefco routine)
* or vector Z less than cosine(arctan(Z)) = 1/sqrt(17) */
const double zbreak = 0.242535625;
int i;
double 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;
/* sin, cos of latitude */
sphi = aoprms[1];
cphi = aoprms[2];
/* local apparent sidereal time */
st = aoprms[13];
/* apparent ra,dec to cartesian ha,dec */
palDcs2c( rapst, dap, v );
xhd = v[0];
yhd = v[1];
zhd = v[2];
/* diurnal aberration */
diurab = aoprms[3];
f = (1.0diurab*yhd);
xhdt = f*xhd;
yhdt = f*(yhd+diurab);
zhdt = f*zhd;
/* cartesian ha,dec to cartesian az,el (s=0,e=90) */
xaet = sphi*xhdtcphi*zhdt;
yaet = yhdt;
zaet = cphi*xhdt+sphi*zhdt;
/* azimuth (n=0,e=90) */
if (xaet == 0.0 && yaet == 0.0) {
azobs = 0.0;
} else {
azobs = atan2(yaet,xaet);
}
/* topocentric zenith distance */
zdt = atan2(sqrt(xaet*xaet+yaet*yaet),zaet);
/*
* refraction
*  */
/* fast algorithm using two constant model */
refa = aoprms[10];
refb = aoprms[11];
palRefz(zdt,refa,refb,&zdobs);
/* large zenith distance? */
if (cos(zdobs) < zbreak) {
/* yes: use rigorous algorithm */
/* initialize loop (maximum of 10 iterations) */
i = 1;
dzd = 1.0e1;
while (fabs(dzd) > 1e10 && i <= 10) {
/* compute refraction using current estimate of observed zd */
palRefro(zdobs,aoprms[4],aoprms[5],aoprms[6],
aoprms[7],aoprms[8],aoprms[0],
aoprms[9],1e8,&dref);
/* remaining discrepancy */
dzd = zdobs+drefzdt;
/* update the estimate */
zdobs = zdobsdzd;
/* increment the iteration counter */
i++;
}
}
/* 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[0] = sphi*xaeo+cphi*zaeo;
v[1] = yaeo;
v[2] = cphi*xaeo+sphi*zaeo;
/* to spherical ha,dec */
palDcc2s(v,&hmobs,&dcobs);
/* right ascension */
raobs = palDranrm(st+hmobs);
/* return the results */
*aob = azobs;
*zob = zdobs;
*hob = hmobs;
*dob = dcobs;
*rob = raobs;
}
