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
|
#include "erfa.h"
void eraHfk5z(double rh, double dh, double date1, double date2,
double *r5, double *d5, double *dr5, double *dd5)
/*
** - - - - - - - - -
** e r a H f k 5 z
** - - - - - - - - -
**
** Transform a Hipparcos star position into FK5 J2000.0, assuming
** zero Hipparcos proper motion.
**
** Given:
** rh double Hipparcos RA (radians)
** dh double Hipparcos Dec (radians)
** date1,date2 double TDB date (Note 1)
**
** Returned (all FK5, equinox J2000.0, date date1+date2):
** r5 double RA (radians)
** d5 double Dec (radians)
** dr5 double FK5 RA proper motion (rad/year, Note 4)
** dd5 double Dec proper motion (rad/year, Note 4)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
**
** 3) The FK5 to Hipparcos transformation is modeled as a pure rotation
** and spin; zonal errors in the FK5 catalogue are not taken into
** account.
**
** 4) It was the intention that Hipparcos should be a close
** approximation to an inertial frame, so that distant objects have
** zero proper motion; such objects have (in general) non-zero
** proper motion in FK5, and this function returns those fictitious
** proper motions.
**
** 5) The position returned by this function is in the FK5 J2000.0
** reference system but at date date1+date2.
**
** 6) See also eraFk52h, eraH2fk5, eraFk5zhz.
**
** Called:
** eraS2c spherical coordinates to unit vector
** eraFk5hip FK5 to Hipparcos rotation and spin
** eraRxp product of r-matrix and p-vector
** eraSxp multiply p-vector by scalar
** eraRxr product of two r-matrices
** eraTrxp product of transpose of r-matrix and p-vector
** eraPxp vector product of two p-vectors
** eraPv2s pv-vector to spherical
** eraAnp normalize angle into range 0 to 2pi
**
** Reference:
**
** F.Mignard & M.Froeschle, 2000, Astron.Astrophys. 354, 732-739.
**
** Copyright (C) 2013-2016, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double t, ph[3], r5h[3][3], s5h[3], sh[3], vst[3],
rst[3][3], r5ht[3][3], pv5e[2][3], vv[3],
w, r, v;
/* Time interval from fundamental epoch J2000.0 to given date (JY). */
t = ((date1 - ERFA_DJ00) + date2) / ERFA_DJY;
/* Hipparcos barycentric position vector (normalized). */
eraS2c(rh, dh, ph);
/* FK5 to Hipparcos orientation matrix and spin vector. */
eraFk5hip(r5h, s5h);
/* Rotate the spin into the Hipparcos system. */
eraRxp(r5h, s5h, sh);
/* Accumulated Hipparcos wrt FK5 spin over that interval. */
eraSxp(t, s5h, vst);
/* Express the accumulated spin as a rotation matrix. */
eraRv2m(vst, rst);
/* Rotation matrix: accumulated spin, then FK5 to Hipparcos. */
eraRxr(r5h, rst, r5ht);
/* De-orient & de-spin the Hipparcos position into FK5 J2000.0. */
eraTrxp(r5ht, ph, pv5e[0]);
/* Apply spin to the position giving a space motion. */
eraPxp(sh, ph, vv);
/* De-orient & de-spin the Hipparcos space motion into FK5 J2000.0. */
eraTrxp(r5ht, vv, pv5e[1]);
/* FK5 position/velocity pv-vector to spherical. */
eraPv2s(pv5e, &w, d5, &r, dr5, dd5, &v);
*r5 = eraAnp(w);
return;
}
/*----------------------------------------------------------------------
**
**
** 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.
**
*/
|
