1 #include "erfa.h"
2
eraAtoiq(const char * type,double ob1,double ob2,eraASTROM * astrom,double * ri,double * di)3 void eraAtoiq(const char *type,
4 double ob1, double ob2, eraASTROM *astrom,
5 double *ri, double *di)
6 /*
7 ** - - - - - - - - -
8 ** e r a A t o i q
9 ** - - - - - - - - -
10 **
11 ** Quick observed place to CIRS, given the star-independent astrometry
12 ** parameters.
13 **
14 ** Use of this function is appropriate when efficiency is important and
15 ** where many star positions are all to be transformed for one date.
16 ** The star-independent astrometry parameters can be obtained by
17 ** calling eraApio[13] or eraApco[13].
18 **
19 ** Given:
20 ** type char[] type of coordinates: "R", "H" or "A" (Note 1)
21 ** ob1 double observed Az, HA or RA (radians; Az is N=0,E=90)
22 ** ob2 double observed ZD or Dec (radians)
23 ** astrom eraASTROM* star-independent astrometry parameters:
24 ** pmt double PM time interval (SSB, Julian years)
25 ** eb double[3] SSB to observer (vector, au)
26 ** eh double[3] Sun to observer (unit vector)
27 ** em double distance from Sun to observer (au)
28 ** v double[3] barycentric observer velocity (vector, c)
29 ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor
30 ** bpn double[3][3] bias-precession-nutation matrix
31 ** along double longitude + s' (radians)
32 ** xpl double polar motion xp wrt local meridian (radians)
33 ** ypl double polar motion yp wrt local meridian (radians)
34 ** sphi double sine of geodetic latitude
35 ** cphi double cosine of geodetic latitude
36 ** diurab double magnitude of diurnal aberration vector
37 ** eral double "local" Earth rotation angle (radians)
38 ** refa double refraction constant A (radians)
39 ** refb double refraction constant B (radians)
40 **
41 ** Returned:
42 ** ri double* CIRS right ascension (CIO-based, radians)
43 ** di double* CIRS declination (radians)
44 **
45 ** Notes:
46 **
47 ** 1) "Observed" Az,El means the position that would be seen by a
48 ** perfect geodetically aligned theodolite. This is related to
49 ** the observed HA,Dec via the standard rotation, using the geodetic
50 ** latitude (corrected for polar motion), while the observed HA and
51 ** RA are related simply through the Earth rotation angle and the
52 ** site longitude. "Observed" RA,Dec or HA,Dec thus means the
53 ** position that would be seen by a perfect equatorial with its
54 ** polar axis aligned to the Earth's axis of rotation. By removing
55 ** from the observed place the effects of atmospheric refraction and
56 ** diurnal aberration, the CIRS RA,Dec is obtained.
57 **
58 ** 2) Only the first character of the type argument is significant.
59 ** "R" or "r" indicates that ob1 and ob2 are the observed right
60 ** ascension and declination; "H" or "h" indicates that they are
61 ** hour angle (west +ve) and declination; anything else ("A" or
62 ** "a" is recommended) indicates that ob1 and ob2 are azimuth (north
63 ** zero, east 90 deg) and zenith distance. (Zenith distance is used
64 ** rather than altitude in order to reflect the fact that no
65 ** allowance is made for depression of the horizon.)
66 **
67 ** 3) The accuracy of the result is limited by the corrections for
68 ** refraction, which use a simple A*tan(z) + B*tan^3(z) model.
69 ** Providing the meteorological parameters are known accurately and
70 ** there are no gross local effects, the predicted observed
71 ** coordinates should be within 0.05 arcsec (optical) or 1 arcsec
72 ** (radio) for a zenith distance of less than 70 degrees, better
73 ** than 30 arcsec (optical or radio) at 85 degrees and better than
74 ** 20 arcmin (optical) or 30 arcmin (radio) at the horizon.
75 **
76 ** Without refraction, the complementary functions eraAtioq and
77 ** eraAtoiq are self-consistent to better than 1 microarcsecond all
78 ** over the celestial sphere. With refraction included, consistency
79 ** falls off at high zenith distances, but is still better than
80 ** 0.05 arcsec at 85 degrees.
81 **
82 ** 4) It is advisable to take great care with units, as even unlikely
83 ** values of the input parameters are accepted and processed in
84 ** accordance with the models used.
85 **
86 ** Called:
87 ** eraS2c spherical coordinates to unit vector
88 ** eraC2s p-vector to spherical
89 ** eraAnp normalize angle into range 0 to 2pi
90 **
91 ** Copyright (C) 2013-2020, NumFOCUS Foundation.
92 ** Derived, with permission, from the SOFA library. See notes at end of file.
93 */
94 {
95 int c;
96 double c1, c2, sphi, cphi, ce, xaeo, yaeo, zaeo, v[3],
97 xmhdo, ymhdo, zmhdo, az, sz, zdo, refa, refb, tz, dref,
98 zdt, xaet, yaet, zaet, xmhda, ymhda, zmhda,
99 f, xhd, yhd, zhd, xpl, ypl, w, hma;
100
101
102 /* Coordinate type. */
103 c = (int) type[0];
104
105 /* Coordinates. */
106 c1 = ob1;
107 c2 = ob2;
108
109 /* Sin, cos of latitude. */
110 sphi = astrom->sphi;
111 cphi = astrom->cphi;
112
113 /* Standardize coordinate type. */
114 if ( c == 'r' || c == 'R' ) {
115 c = 'R';
116 } else if ( c == 'h' || c == 'H' ) {
117 c = 'H';
118 } else {
119 c = 'A';
120 }
121
122 /* If Az,ZD, convert to Cartesian (S=0,E=90). */
123 if ( c == 'A' ) {
124 ce = sin(c2);
125 xaeo = - cos(c1) * ce;
126 yaeo = sin(c1) * ce;
127 zaeo = cos(c2);
128
129 } else {
130
131 /* If RA,Dec, convert to HA,Dec. */
132 if ( c == 'R' ) c1 = astrom->eral - c1;
133
134 /* To Cartesian -HA,Dec. */
135 eraS2c ( -c1, c2, v );
136 xmhdo = v[0];
137 ymhdo = v[1];
138 zmhdo = v[2];
139
140 /* To Cartesian Az,El (S=0,E=90). */
141 xaeo = sphi*xmhdo - cphi*zmhdo;
142 yaeo = ymhdo;
143 zaeo = cphi*xmhdo + sphi*zmhdo;
144 }
145
146 /* Azimuth (S=0,E=90). */
147 az = ( xaeo != 0.0 || yaeo != 0.0 ) ? atan2(yaeo,xaeo) : 0.0;
148
149 /* Sine of observed ZD, and observed ZD. */
150 sz = sqrt ( xaeo*xaeo + yaeo*yaeo );
151 zdo = atan2 ( sz, zaeo );
152
153 /*
154 ** Refraction
155 ** ----------
156 */
157
158 /* Fast algorithm using two constant model. */
159 refa = astrom->refa;
160 refb = astrom->refb;
161 tz = sz / zaeo;
162 dref = ( refa + refb*tz*tz ) * tz;
163 zdt = zdo + dref;
164
165 /* To Cartesian Az,ZD. */
166 ce = sin(zdt);
167 xaet = cos(az) * ce;
168 yaet = sin(az) * ce;
169 zaet = cos(zdt);
170
171 /* Cartesian Az,ZD to Cartesian -HA,Dec. */
172 xmhda = sphi*xaet + cphi*zaet;
173 ymhda = yaet;
174 zmhda = - cphi*xaet + sphi*zaet;
175
176 /* Diurnal aberration. */
177 f = ( 1.0 + astrom->diurab*ymhda );
178 xhd = f * xmhda;
179 yhd = f * ( ymhda - astrom->diurab );
180 zhd = f * zmhda;
181
182 /* Polar motion. */
183 xpl = astrom->xpl;
184 ypl = astrom->ypl;
185 w = xpl*xhd - ypl*yhd + zhd;
186 v[0] = xhd - xpl*w;
187 v[1] = yhd + ypl*w;
188 v[2] = w - ( xpl*xpl + ypl*ypl ) * zhd;
189
190 /* To spherical -HA,Dec. */
191 eraC2s(v, &hma, di);
192
193 /* Right ascension. */
194 *ri = eraAnp(astrom->eral + hma);
195
196 /* Finished. */
197
198 }
199 /*----------------------------------------------------------------------
200 **
201 **
202 ** Copyright (C) 2013-2020, NumFOCUS Foundation.
203 ** All rights reserved.
204 **
205 ** This library is derived, with permission, from the International
206 ** Astronomical Union's "Standards of Fundamental Astronomy" library,
207 ** available from http://www.iausofa.org.
208 **
209 ** The ERFA version is intended to retain identical functionality to
210 ** the SOFA library, but made distinct through different function and
211 ** file names, as set out in the SOFA license conditions. The SOFA
212 ** original has a role as a reference standard for the IAU and IERS,
213 ** and consequently redistribution is permitted only in its unaltered
214 ** state. The ERFA version is not subject to this restriction and
215 ** therefore can be included in distributions which do not support the
216 ** concept of "read only" software.
217 **
218 ** Although the intent is to replicate the SOFA API (other than
219 ** replacement of prefix names) and results (with the exception of
220 ** bugs; any that are discovered will be fixed), SOFA is not
221 ** responsible for any errors found in this version of the library.
222 **
223 ** If you wish to acknowledge the SOFA heritage, please acknowledge
224 ** that you are using a library derived from SOFA, rather than SOFA
225 ** itself.
226 **
227 **
228 ** TERMS AND CONDITIONS
229 **
230 ** Redistribution and use in source and binary forms, with or without
231 ** modification, are permitted provided that the following conditions
232 ** are met:
233 **
234 ** 1 Redistributions of source code must retain the above copyright
235 ** notice, this list of conditions and the following disclaimer.
236 **
237 ** 2 Redistributions in binary form must reproduce the above copyright
238 ** notice, this list of conditions and the following disclaimer in
239 ** the documentation and/or other materials provided with the
240 ** distribution.
241 **
242 ** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
243 ** the International Astronomical Union nor the names of its
244 ** contributors may be used to endorse or promote products derived
245 ** from this software without specific prior written permission.
246 **
247 ** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
248 ** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
249 ** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
250 ** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
251 ** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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253 ** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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261