1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
|
#include "erfa.h"
void eraAtioq(double ri, double di, eraASTROM *astrom,
double *aob, double *zob,
double *hob, double *dob, double *rob)
/*
** - - - - - - - - -
** e r a 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 eraApio[13] or eraApco[13].
**
** Given:
** ri double CIRS right ascension
** di double CIRS declination
** astrom eraASTROM* 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 eraAtioq and
** eraAtoiq 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 eraAtci13 (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 eraApio[13] or eraApco[13]. If nothing has
** changed significantly except the time, eraAper[13] may be used to
** perform the requisite adjustment to the astrom structure.
**
** Called:
** eraS2c spherical coordinates to unit vector
** eraC2s p-vector to spherical
** eraAnp normalize angle into range 0 to 2pi
**
** Copyright (C) 2013-2016, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
/* 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, 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. */
eraS2c(ri-astrom->eral, di, v);
x = v[0];
y = v[1];
z = v[2];
/* Polar motion. */
xhd = x + astrom->xpl*z;
yhd = y - astrom->ypl*z;
zhd = z - astrom->xpl*x + astrom->ypl*y;
/* 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. */
eraC2s ( v, &hmobs, &dcobs );
/* Right ascension (with respect to CIO). */
raobs = astrom->eral + hmobs;
/* Return the results. */
*aob = eraAnp(azobs);
*zob = zdobs;
*hob = -hmobs;
*dob = dcobs;
*rob = eraAnp(raobs);
/* Finished. */
}
/*----------------------------------------------------------------------
**
**
** Copyright (C) 2013-2016, NumFOCUS Foundation.
** All rights reserved.
**
** This library is derived, with permission, from the International
** Astronomical Union's "Standards of Fundamental Astronomy" library,
** available from http://www.iausofa.org.
**
** The ERFA version is intended to retain identical functionality to
** the SOFA library, but made distinct through different function and
** file names, as set out in the SOFA license conditions. The SOFA
** original has a role as a reference standard for the IAU and IERS,
** and consequently redistribution is permitted only in its unaltered
** state. The ERFA version is not subject to this restriction and
** therefore can be included in distributions which do not support the
** concept of "read only" software.
**
** Although the intent is to replicate the SOFA API (other than
** replacement of prefix names) and results (with the exception of
** bugs; any that are discovered will be fixed), SOFA is not
** responsible for any errors found in this version of the library.
**
** If you wish to acknowledge the SOFA heritage, please acknowledge
** that you are using a library derived from SOFA, rather than SOFA
** itself.
**
**
** TERMS AND CONDITIONS
**
** Redistribution and use in source and binary forms, with or without
** modification, are permitted provided that the following conditions
** are met:
**
** 1 Redistributions of source code must retain the above copyright
** notice, this list of conditions and the following disclaimer.
**
** 2 Redistributions in binary form must reproduce the above copyright
** notice, this list of conditions and the following disclaimer in
** the documentation and/or other materials provided with the
** distribution.
**
** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
** the International Astronomical Union nor the names of its
** contributors may be used to endorse or promote products derived
** from this software without specific prior written permission.
**
** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
** POSSIBILITY OF SUCH DAMAGE.
**
*/
|
