| 1 | #include "slalib.h"
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| 2 | #include "slamac.h"
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| 3 | void slaAopqk ( double rap, double dap, double aoprms[14],
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| 4 | double *aob, double *zob, double *hob,
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| 5 | double *dob, double *rob )
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| 6 | /*
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| 7 | ** - - - - - - - - -
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| 8 | ** s l a A o p q k
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| 9 | ** - - - - - - - - -
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| 10 | **
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| 11 | ** Quick apparent to observed place (but see note 8, below, for
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| 12 | ** remarks about speed).
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| 13 | **
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| 14 | ** Given:
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| 15 | ** rap double geocentric apparent right ascension
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| 16 | ** dap double geocentric apparent declination
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| 17 | ** aoprms double[14] star-independent apparent-to-observed parameters:
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| 18 | **
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| 19 | ** (0) geodetic latitude (radians)
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| 20 | ** (1,2) sine and cosine of geodetic latitude
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| 21 | ** (3) magnitude of diurnal aberration vector
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| 22 | ** (4) height (hm)
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| 23 | ** (5) ambient temperature (t)
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| 24 | ** (6) pressure (p)
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| 25 | ** (7) relative humidity (rh)
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| 26 | ** (8) wavelength (wl)
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| 27 | ** (9) lapse rate (tlr)
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| 28 | ** (10,11) refraction constants A and B (radians)
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| 29 | ** (12) longitude + eqn of equinoxes + sidereal DUT (radians)
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| 30 | ** (13) local apparent sidereal time (radians)
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| 31 | **
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| 32 | ** Returned:
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| 33 | ** *aob double observed azimuth (radians: N=0,E=90)
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| 34 | ** *zob double observed zenith distance (radians)
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| 35 | ** *hob double observed hour angle (radians)
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| 36 | ** *dob double observed declination (radians)
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| 37 | ** *rob double observed right ascension (radians)
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| 38 | **
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| 39 | ** Notes:
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| 40 | **
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| 41 | ** 1) This routine returns zenith distance rather than elevation
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| 42 | ** in order to reflect the fact that no allowance is made for
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| 43 | ** depression of the horizon.
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| 44 | **
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| 45 | ** 2) The accuracy of the result is limited by the corrections for
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| 46 | ** refraction. Providing the meteorological parameters are
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| 47 | ** known accurately and there are no gross local effects, the
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| 48 | ** observed RA,Dec predicted by this routine should be within
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| 49 | ** about 0.1 arcsec for a zenith distance of less than 70 degrees.
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| 50 | ** Even at a topocentric zenith distance of 90 degrees, the
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| 51 | ** accuracy in elevation should be better than 1 arcmin; useful
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| 52 | ** results are available for a further 3 degrees, beyond which
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| 53 | ** the slaRefro routine returns a fixed value of the refraction.
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| 54 | ** The complementary routines slaAop (or slaAopqk) and slaOap
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| 55 | ** (or slaOapqk) are self-consistent to better than 1 micro-
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| 56 | ** arcsecond all over the celestial sphere.
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| 57 | **
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| 58 | ** 3) It is advisable to take great care with units, as even
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| 59 | ** unlikely values of the input parameters are accepted and
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| 60 | ** processed in accordance with the models used.
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| 61 | **
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| 62 | ** 4) "Apparent" place means the geocentric apparent right ascension
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| 63 | ** and declination, which is obtained from a catalogue mean place
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| 64 | ** by allowing for space motion, parallax, precession, nutation,
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| 65 | ** annual aberration, and the Sun's gravitational lens effect. For
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| 66 | ** star positions in the FK5 system (i.e. J2000), these effects can
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| 67 | ** be applied by means of the slaMap etc routines. Starting from
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| 68 | ** other mean place systems, additional transformations will be
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| 69 | ** needed; for example, FK4 (i.e. B1950) mean places would first
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| 70 | ** have to be converted to FK5, which can be done with the
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| 71 | ** slaFk425 etc routines.
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| 72 | **
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| 73 | ** 5) "Observed" Az,El means the position that would be seen by a
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| 74 | ** perfect theodolite located at the observer. This is obtained
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| 75 | ** from the geocentric apparent RA,Dec by allowing for Earth
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| 76 | ** orientation and diurnal aberration, rotating from equator
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| 77 | ** to horizon coordinates, and then adjusting for refraction.
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| 78 | ** The HA,Dec is obtained by rotating back into equatorial
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| 79 | ** coordinates, using the geodetic latitude corrected for polar
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| 80 | ** motion, and is the position that would be seen by a perfect
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| 81 | ** equatorial located at the observer and with its polar axis
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| 82 | ** aligned to the Earth's axis of rotation (n.b. not to the
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| 83 | ** refracted pole). Finally, the RA is obtained by subtracting
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| 84 | ** the HA from the local apparent ST.
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| 85 | **
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| 86 | ** 6) To predict the required setting of a real telescope, the
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| 87 | ** observed place produced by this routine would have to be
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| 88 | ** adjusted for the tilt of the azimuth or polar axis of the
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| 89 | ** mounting (with appropriate corrections for mount flexures),
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| 90 | ** for non-perpendicularity between the mounting axes, for the
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| 91 | ** position of the rotator axis and the pointing axis relative
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| 92 | ** to it, for tube flexure, for gear and encoder errors, and
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| 93 | ** finally for encoder zero points. Some telescopes would, of
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| 94 | ** course, exhibit other properties which would need to be
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| 95 | ** accounted for at the appropriate point in the sequence.
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| 96 | **
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| 97 | ** 7) The star-independent apparent-to-observed-place parameters
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| 98 | ** in aoprms may be computed by means of the slaAoppa routine.
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| 99 | ** If nothing has changed significantly except the time, the
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| 100 | ** slaAoppat routine may be used to perform the requisite
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| 101 | ** partial recomputation of aoprms.
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| 102 | **
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| 103 | ** 8) At zenith distances beyond about 76 degrees, the need for
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| 104 | ** special care with the corrections for refraction causes a
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| 105 | ** marked increase in execution time. Moreover, the effect
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| 106 | ** gets worse with increasing zenith distance. Adroit
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| 107 | ** programming in the calling application may allow the
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| 108 | ** problem to be reduced. Prepare an alternative aoprms array,
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| 109 | ** computed for zero air-pressure; this will disable the
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| 110 | ** refraction corrections and cause rapid execution. Using
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| 111 | ** this aoprms array, a preliminary call to the present routine
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| 112 | ** will, depending on the application, produce a rough position
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| 113 | ** which may be enough to establish whether the full, slow
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| 114 | ** calculation (using the real aoprms array) is worthwhile.
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| 115 | ** For example, there would be no need for the full calculation
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| 116 | ** if the preliminary call had already established that the
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| 117 | ** source was well below the elevation limits for a particular
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| 118 | ** telescope.
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| 119 | **
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| 120 | ** 9) The azimuths etc produced by the present routine are with
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| 121 | ** respect to the celestial pole. Corrections to the terrestrial
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| 122 | ** pole can be computed using slaPolmo.
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| 123 | **
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| 124 | ** Called: slaDcs2c, slaRefz, slaRefro, slaDcc2s, slaDranrm
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| 125 | **
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| 126 | ** Last revision: 22 February 1996
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| 127 | **
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| 128 | ** Copyright P.T.Wallace. All rights reserved.
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| 129 | */
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| 130 | {
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| 131 | /*
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| 132 | ** Breakpoint for fast/slow refraction algorithm:
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| 133 | ** ZD greater than arctan(4), (see slaRefco routine)
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| 134 | ** or vector z less than cosine(arctan(z)) = 1/sqrt(17)
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| 135 | */
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| 136 | static double zbreak = 0.242535625;
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| 137 |
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| 138 | int i;
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| 139 |
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| 140 | double sphi, cphi, st, v[3], xhd, yhd, zhd, diurab, f,
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| 141 | xhdt, yhdt, zhdt, xaet, yaet, zaet, azobs,
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| 142 | zdt, refa, refb, zdobs, dzd, dref, ce,
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| 143 | xaeo, yaeo, zaeo, hmobs, dcobs, raobs;
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| 144 |
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| 145 | /* Sin, cos of latitude */
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| 146 | sphi = aoprms[1];
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| 147 | cphi = aoprms[2];
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| 148 |
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| 149 | /* Local apparent sidereal time */
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| 150 | st = aoprms[13];
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| 151 |
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| 152 | /* Apparent RA,Dec to Cartesian -HA,Dec */
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| 153 | slaDcs2c(rap - st, dap, v);
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| 154 | xhd = v[0];
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| 155 | yhd = v[1];
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| 156 | zhd = v[2];
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| 157 |
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| 158 | /* Diurnal aberration */
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| 159 | diurab = aoprms[3];
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| 160 | f = 1.0 - diurab * yhd;
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| 161 | xhdt = f * xhd;
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| 162 | yhdt = f * ( yhd + diurab );
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| 163 | zhdt = f * zhd;
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| 164 |
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| 165 | /* Cartesian -HA,Dec to Cartesian az,el (S=0,E=90) */
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| 166 | xaet = sphi * xhdt - cphi * zhdt;
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| 167 | yaet = yhdt;
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| 168 | zaet = cphi * xhdt + sphi * zhdt;
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| 169 |
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| 170 | /* Azimuth (N=0,E=90) */
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| 171 | azobs = ( (xaet == 0.0) && (yaet == 0.0) ) ?
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| 172 | 0.0 : atan2 ( yaet, -xaet );
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| 173 |
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| 174 | /* Topocentric zenith distance */
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| 175 | zdt = atan2 ( sqrt ( xaet * xaet + yaet * yaet ), zaet );
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| 176 |
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| 177 | /*
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| 178 | ** Refraction
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| 179 | ** ----------
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| 180 | */
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| 181 |
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| 182 | /* Fast algorithm using two constant model */
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| 183 | refa = aoprms[10];
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| 184 | refb = aoprms[11];
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| 185 | slaRefz ( zdt, refa, refb, &zdobs );
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| 186 |
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| 187 | /* Large zenith distance? */
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| 188 | if ( cos ( zdobs ) < zbreak ) {
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| 189 |
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| 190 | /* Yes: use rigorous algorithm */
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| 191 |
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| 192 | /* Initialize loop (maximum of 10 iterations) */
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| 193 | i = 1;
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| 194 | do {
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| 195 |
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| 196 | /* Compute refraction using current estimate of observed ZD */
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| 197 | slaRefro ( zdobs, aoprms[4], aoprms[5], aoprms[6],
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| 198 | aoprms[7], aoprms[8], aoprms[0],
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| 199 | aoprms[9], 1e-8, &dref );
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| 200 |
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| 201 | /* Remaining discrepancy */
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| 202 | dzd = zdobs + dref - zdt;
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| 203 |
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| 204 | /* Update the estimate */
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| 205 | zdobs -= dzd;
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| 206 |
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| 207 | /* Increment the iteration counter */
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| 208 | i++;
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| 209 |
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| 210 | } while ( fabs ( dzd ) > 1e-10 && i <= 10 );
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| 211 | }
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| 212 |
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| 213 | /* To Cartesian az/ZD */
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| 214 | ce = sin ( zdobs );
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| 215 | xaeo = -cos ( azobs ) * ce;
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| 216 | yaeo = sin ( azobs ) * ce;
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| 217 | zaeo = cos ( zdobs );
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| 218 |
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| 219 | /* Cartesian az/ZD to Cartesian -HA,Dec */
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| 220 | v[0] = sphi * xaeo + cphi * zaeo;
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| 221 | v[1] = yaeo;
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| 222 | v[2] = -cphi * xaeo + sphi * zaeo;
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| 223 |
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| 224 | /* To spherical -HA,dec */
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| 225 | slaDcc2s ( v, &hmobs, &dcobs );
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| 226 |
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| 227 | /* Right ascension */
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| 228 | raobs = slaDranrm ( st + hmobs );
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| 229 |
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| 230 | /* Return the results */
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| 231 | *aob = azobs;
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| 232 | *zob = zdobs;
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| 233 | *hob = -hmobs;
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| 234 | *dob = dcobs;
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| 235 | *rob = raobs;
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| 236 | }
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