1 #include "erfa.h"
2
eraStarpv(double ra,double dec,double pmr,double pmd,double px,double rv,double pv[2][3])3 int eraStarpv(double ra, double dec,
4 double pmr, double pmd, double px, double rv,
5 double pv[2][3])
6 /*
7 ** - - - - - - - - - -
8 ** e r a S t a r p v
9 ** - - - - - - - - - -
10 **
11 ** Convert star catalog coordinates to position+velocity vector.
12 **
13 ** Given (Note 1):
14 ** ra double right ascension (radians)
15 ** dec double declination (radians)
16 ** pmr double RA proper motion (radians/year)
17 ** pmd double Dec proper motion (radians/year)
18 ** px double parallax (arcseconds)
19 ** rv double radial velocity (km/s, positive = receding)
20 **
21 ** Returned (Note 2):
22 ** pv double[2][3] pv-vector (au, au/day)
23 **
24 ** Returned (function value):
25 ** int status:
26 ** 0 = no warnings
27 ** 1 = distance overridden (Note 6)
28 ** 2 = excessive speed (Note 7)
29 ** 4 = solution didn't converge (Note 8)
30 ** else = binary logical OR of the above
31 **
32 ** Notes:
33 **
34 ** 1) The star data accepted by this function are "observables" for an
35 ** imaginary observer at the solar-system barycenter. Proper motion
36 ** and radial velocity are, strictly, in terms of barycentric
37 ** coordinate time, TCB. For most practical applications, it is
38 ** permissible to neglect the distinction between TCB and ordinary
39 ** "proper" time on Earth (TT/TAI). The result will, as a rule, be
40 ** limited by the intrinsic accuracy of the proper-motion and
41 ** radial-velocity data; moreover, the pv-vector is likely to be
42 ** merely an intermediate result, so that a change of time unit
43 ** would cancel out overall.
44 **
45 ** In accordance with normal star-catalog conventions, the object's
46 ** right ascension and declination are freed from the effects of
47 ** secular aberration. The frame, which is aligned to the catalog
48 ** equator and equinox, is Lorentzian and centered on the SSB.
49 **
50 ** 2) The resulting position and velocity pv-vector is with respect to
51 ** the same frame and, like the catalog coordinates, is freed from
52 ** the effects of secular aberration. Should the "coordinate
53 ** direction", where the object was located at the catalog epoch, be
54 ** required, it may be obtained by calculating the magnitude of the
55 ** position vector pv[0][0-2] dividing by the speed of light in
56 ** au/day to give the light-time, and then multiplying the space
57 ** velocity pv[1][0-2] by this light-time and adding the result to
58 ** pv[0][0-2].
59 **
60 ** Summarizing, the pv-vector returned is for most stars almost
61 ** identical to the result of applying the standard geometrical
62 ** "space motion" transformation. The differences, which are the
63 ** subject of the Stumpff paper referenced below, are:
64 **
65 ** (i) In stars with significant radial velocity and proper motion,
66 ** the constantly changing light-time distorts the apparent proper
67 ** motion. Note that this is a classical, not a relativistic,
68 ** effect.
69 **
70 ** (ii) The transformation complies with special relativity.
71 **
72 ** 3) Care is needed with units. The star coordinates are in radians
73 ** and the proper motions in radians per Julian year, but the
74 ** parallax is in arcseconds; the radial velocity is in km/s, but
75 ** the pv-vector result is in au and au/day.
76 **
77 ** 4) The RA proper motion is in terms of coordinate angle, not true
78 ** angle. If the catalog uses arcseconds for both RA and Dec proper
79 ** motions, the RA proper motion will need to be divided by cos(Dec)
80 ** before use.
81 **
82 ** 5) Straight-line motion at constant speed, in the inertial frame,
83 ** is assumed.
84 **
85 ** 6) An extremely small (or zero or negative) parallax is interpreted
86 ** to mean that the object is on the "celestial sphere", the radius
87 ** of which is an arbitrary (large) value (see the constant PXMIN).
88 ** When the distance is overridden in this way, the status,
89 ** initially zero, has 1 added to it.
90 **
91 ** 7) If the space velocity is a significant fraction of c (see the
92 ** constant VMAX), it is arbitrarily set to zero. When this action
93 ** occurs, 2 is added to the status.
94 **
95 ** 8) The relativistic adjustment involves an iterative calculation.
96 ** If the process fails to converge within a set number (IMAX) of
97 ** iterations, 4 is added to the status.
98 **
99 ** 9) The inverse transformation is performed by the function
100 ** eraPvstar.
101 **
102 ** Called:
103 ** eraS2pv spherical coordinates to pv-vector
104 ** eraPm modulus of p-vector
105 ** eraZp zero p-vector
106 ** eraPn decompose p-vector into modulus and direction
107 ** eraPdp scalar product of two p-vectors
108 ** eraSxp multiply p-vector by scalar
109 ** eraPmp p-vector minus p-vector
110 ** eraPpp p-vector plus p-vector
111 **
112 ** Reference:
113 **
114 ** Stumpff, P., 1985, Astron.Astrophys. 144, 232-240.
115 **
116 ** Copyright (C) 2013-2020, NumFOCUS Foundation.
117 ** Derived, with permission, from the SOFA library. See notes at end of file.
118 */
119 {
120 /* Smallest allowed parallax */
121 static const double PXMIN = 1e-7;
122
123 /* Largest allowed speed (fraction of c) */
124 static const double VMAX = 0.5;
125
126 /* Maximum number of iterations for relativistic solution */
127 static const int IMAX = 100;
128
129 int i, iwarn;
130 double w, r, rd, rad, decd, v, x[3], usr[3], ust[3],
131 vsr, vst, betst, betsr, bett, betr,
132 dd, ddel, ur[3], ut[3],
133 d = 0.0, del = 0.0, /* to prevent */
134 odd = 0.0, oddel = 0.0, /* compiler */
135 od = 0.0, odel = 0.0; /* warnings */
136
137
138 /* Distance (au). */
139 if (px >= PXMIN) {
140 w = px;
141 iwarn = 0;
142 } else {
143 w = PXMIN;
144 iwarn = 1;
145 }
146 r = ERFA_DR2AS / w;
147
148 /* Radial velocity (au/day). */
149 rd = ERFA_DAYSEC * rv * 1e3 / ERFA_DAU;
150
151 /* Proper motion (radian/day). */
152 rad = pmr / ERFA_DJY;
153 decd = pmd / ERFA_DJY;
154
155 /* To pv-vector (au,au/day). */
156 eraS2pv(ra, dec, r, rad, decd, rd, pv);
157
158 /* If excessive velocity, arbitrarily set it to zero. */
159 v = eraPm(pv[1]);
160 if (v / ERFA_DC > VMAX) {
161 eraZp(pv[1]);
162 iwarn += 2;
163 }
164
165 /* Isolate the radial component of the velocity (au/day). */
166 eraPn(pv[0], &w, x);
167 vsr = eraPdp(x, pv[1]);
168 eraSxp(vsr, x, usr);
169
170 /* Isolate the transverse component of the velocity (au/day). */
171 eraPmp(pv[1], usr, ust);
172 vst = eraPm(ust);
173
174 /* Special-relativity dimensionless parameters. */
175 betsr = vsr / ERFA_DC;
176 betst = vst / ERFA_DC;
177
178 /* Determine the inertial-to-observed relativistic correction terms. */
179 bett = betst;
180 betr = betsr;
181 for (i = 0; i < IMAX; i++) {
182 d = 1.0 + betr;
183 w = betr*betr + bett*bett;
184 del = - w / (sqrt(1.0 - w) + 1.0);
185 betr = d * betsr + del;
186 bett = d * betst;
187 if (i > 0) {
188 dd = fabs(d - od);
189 ddel = fabs(del - odel);
190 if ((i > 1) && (dd >= odd) && (ddel >= oddel)) break;
191 odd = dd;
192 oddel = ddel;
193 }
194 od = d;
195 odel = del;
196 }
197 if (i >= IMAX) iwarn += 4;
198
199 /* Replace observed radial velocity with inertial value. */
200 w = (betsr != 0.0) ? d + del / betsr : 1.0;
201 eraSxp(w, usr, ur);
202
203 /* Replace observed tangential velocity with inertial value. */
204 eraSxp(d, ust, ut);
205
206 /* Combine the two to obtain the inertial space velocity. */
207 eraPpp(ur, ut, pv[1]);
208
209 /* Return the status. */
210 return iwarn;
211
212 }
213 /*----------------------------------------------------------------------
214 **
215 **
216 ** Copyright (C) 2013-2020, NumFOCUS Foundation.
217 ** All rights reserved.
218 **
219 ** This library is derived, with permission, from the International
220 ** Astronomical Union's "Standards of Fundamental Astronomy" library,
221 ** available from http://www.iausofa.org.
222 **
223 ** The ERFA version is intended to retain identical functionality to
224 ** the SOFA library, but made distinct through different function and
225 ** file names, as set out in the SOFA license conditions. The SOFA
226 ** original has a role as a reference standard for the IAU and IERS,
227 ** and consequently redistribution is permitted only in its unaltered
228 ** state. The ERFA version is not subject to this restriction and
229 ** therefore can be included in distributions which do not support the
230 ** concept of "read only" software.
231 **
232 ** Although the intent is to replicate the SOFA API (other than
233 ** replacement of prefix names) and results (with the exception of
234 ** bugs; any that are discovered will be fixed), SOFA is not
235 ** responsible for any errors found in this version of the library.
236 **
237 ** If you wish to acknowledge the SOFA heritage, please acknowledge
238 ** that you are using a library derived from SOFA, rather than SOFA
239 ** itself.
240 **
241 **
242 ** TERMS AND CONDITIONS
243 **
244 ** Redistribution and use in source and binary forms, with or without
245 ** modification, are permitted provided that the following conditions
246 ** are met:
247 **
248 ** 1 Redistributions of source code must retain the above copyright
249 ** notice, this list of conditions and the following disclaimer.
250 **
251 ** 2 Redistributions in binary form must reproduce the above copyright
252 ** notice, this list of conditions and the following disclaimer in
253 ** the documentation and/or other materials provided with the
254 ** distribution.
255 **
256 ** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
257 ** the International Astronomical Union nor the names of its
258 ** contributors may be used to endorse or promote products derived
259 ** from this software without specific prior written permission.
260 **
261 ** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
262 ** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
263 ** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
264 ** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
265 ** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
266 ** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
267 ** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
268 ** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
269 ** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
270 ** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
271 ** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
272 ** POSSIBILITY OF SUCH DAMAGE.
273 **
274 */
275