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
|
#include "erfa.h"
void eraPmpx(double rc, double dc, double pr, double pd,
double px, double rv, double pmt, double pob[3],
double pco[3])
/*
** - - - - - - - -
** e r a P m p x
** - - - - - - - -
**
** Proper motion and parallax.
**
** Given:
** rc,dc double ICRS RA,Dec at catalog epoch (radians)
** pr double RA proper motion (radians/year; Note 1)
** pd double Dec proper motion (radians/year)
** px double parallax (arcsec)
** rv double radial velocity (km/s, +ve if receding)
** pmt double proper motion time interval (SSB, Julian years)
** pob double[3] SSB to observer vector (au)
**
** Returned:
** pco double[3] coordinate direction (BCRS unit vector)
**
** Notes:
**
** 1) The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
**
** 2) The proper motion time interval is for when the starlight
** reaches the solar system barycenter.
**
** 3) To avoid the need for iteration, the Roemer effect (i.e. the
** small annual modulation of the proper motion coming from the
** changing light time) is applied approximately, using the
** direction of the star at the catalog epoch.
**
** References:
**
** 1984 Astronomical Almanac, pp B39-B41.
**
** Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to
** the Astronomical Almanac, 3rd ed., University Science Books
** (2013), Section 7.2.
**
** Called:
** eraPdp scalar product of two p-vectors
** eraPn decompose p-vector into modulus and direction
**
** Copyright (C) 2013-2016, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
/* Km/s to au/year */
const double VF = ERFA_DAYSEC*ERFA_DJM/ERFA_DAU;
/* Light time for 1 au, Julian years */
const double AULTY = ERFA_AULT/ERFA_DAYSEC/ERFA_DJY;
int i;
double sr, cr, sd, cd, x, y, z, p[3], dt, pxr, w, pdz, pm[3];
/* Spherical coordinates to unit vector (and useful functions). */
sr = sin(rc);
cr = cos(rc);
sd = sin(dc);
cd = cos(dc);
p[0] = x = cr*cd;
p[1] = y = sr*cd;
p[2] = z = sd;
/* Proper motion time interval (y) including Roemer effect. */
dt = pmt + eraPdp(p,pob)*AULTY;
/* Space motion (radians per year). */
pxr = px * ERFA_DAS2R;
w = VF * rv * pxr;
pdz = pd * z;
pm[0] = - pr*y - pdz*cr + w*x;
pm[1] = pr*x - pdz*sr + w*y;
pm[2] = pd*cd + w*z;
/* Coordinate direction of star (unit vector, BCRS). */
for (i = 0; i < 3; i++) {
p[i] += dt*pm[i] - pxr*pob[i];
}
eraPn(p, &w, pco);
/* 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.
**
*/
|
