/
htc20b.cpp
275 lines (246 loc) · 11 KB
/
htc20b.cpp
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
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
/* Copyright (C) 2018, Project Pluto
This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301, USA. */
/* -----------------------------------------------------------------------! */
/* Downloaded from ftp://ftp.imcce.fr/pub/ephem/satel/htc20/htc20.f */
/* translated by f2c (version 20100827), then heavily edited. */
/* A test routine is provided at the end of this file. */
/* */
/* Positions (in astronomical unit) and velocities (in astronomical unit */
/* per day) of Helene, Telesto, and Calypso (Lagrangian satellites of Dione */
/* and Tethys in Saturn's system) referred to the center of Saturn and to */
/* the mean ecliptic and mean equinox of J2000. From: "An upgraded theory */
/* for Helene, Telesto, and Calypso", Oberti P., Vienne A., 2002, A&A */
/* XXX, XXX */
/* Pascal.Oberti@obs-nice.fr / Alain.Vienne@imcce.fr */
/* */
/* WARNING: Comparison to JPL's _Horizons_ ephemerides show errors of */
/* several thousand km for all three objects. I don't really know why. */
/* I think it may just be due to the fact that modelling objects at */
/* libration points could require more terms than are given below. Also, */
/* HTC20 does predate the arrival of Cassini at Jupiter, and was based */
/* entirely on twenty years of ground-based observations. */
/* */
/* Input: jd, a Saturnian time in Julian day (TT) */
/* sat_no: the satellite's number (0: Helene, 1: Telesto, 2: Calypso) */
/* Output: xyz(3) (real*8 array); VXYZ(3) (real*8 array) */
/* xyz: the 3 Cartesian coordinates of the satellite's position (a.u.) */
/* vxyz: the 3 Cartesian coordinates of the satellite's velocity (a.u./day) */
/* (may be NULL to indicate no interest in the velocity) */
/* Return value is non-zero if sat_no is invalid (i.e., not 0, 1, or 2) */
/* -----------------------------------------------------------------------! */
/* Sample output from the test code below for 'htc20b 2451590':
Helen -351737.078 126965.254 -33017.275 -289321.532 -705652.257 396448.135
Teles 222550.256 -182154.616 71289.412 640383.150 632265.407 -391213.715
Calyp -278795.483 -66349.449 64265.081 292171.217 -836964.572 420403.505
*/
int htc20( const double jd, const int sat_no, double *xyz, double *vxyz);
#include <math.h>
#include <stdint.h>
#define HTC2_HELENE 0
#define HTC2_TELESTO 1
#define HTC2_CALYPSO 2
int htc20( const double jd, const int sat_no, double *xyz, double *vxyz)
{
/* Initialized data */
static const double rnu1[3] = { 2.29427177,3.32489098,-3.32489617 };
static const double rnu2[3] = { -.00802443,-.00948045,.00946761 };
static const double rnu3[3] = { 2.29714724,3.33170385,-3.33170262 };
static const double rlamda[3] = { 2.29571726,3.32830561,3.32830561 };
static const double phi1[3] = { 3.27342548,6.2423359,5.4138476 };
static const double phi2[3] = { 1.30770422,4.62624497,1.36874776 };
static const double phi3[3] = { .77232982,.04769409,5.64157287 };
static const double theta[3] = { 3.07410251,3.24465053,3.2507488 };
static const int8_t ih[48] /* was [4][12] */ = {
0, 0, 0, 1,
0, 0, 1, 0,
0, 1, 0, -1,
0, 1, 0, 1,
0, 2, 0, -1,
0, 2, 0, 1,
0, 3, 0, -1,
0, 3, 0, 1,
1, -1, 0, 1,
1, 0, 0, -1,
1, 0, 0, 1,
1, 1, 0, 1 };
static const int16_t rh[144] = {
-2396, -399, 442, 1278, -4939, 2466,
557, -2152, 1074, 5500, 916, -1015,
0, 0, 0, 0, 5, 10,
0, 5, 10, 0, 0, 0,
-67, 264, -132, -677, -110, 123,
294, 48, -53, -154, 608, -304,
-66, 265, -133, -676, -107, 122,
-295, -47, 53, 151, -607, 303,
15, 16, -10, -44, 33, -13,
19, -14, 6, 35, 38, -23,
15, 17, -10, -44, 33, -13,
-19, 14, -6, -35, -38, 23,
2, 0, 0, -2, 4, -2,
0, -2, 0, 4, 2, 0,
2, 0, 0, -2, 4, -2,
0, 2, 0, -4, -2, 0,
0, 0, 0, 0, 3, 0,
0, 0, 0, -3, 0, 0,
-2, 8, -4, 0, 0, 0,
9, 0, -2, 0, 0, 0,
0, 2, 0, -13, -2, 2,
-3, 0, 0, 3, -11, 6,
0, 0, 0, 0, 3, 0,
0, 0, 0, -3, 0, 0 };
static const int8_t it[24] /* was [4][6] */ = {
0, 0, 0, 1,
0, 0, 1, 0,
0, 1, 0, -1,
0, 1, 0, 1,
1, 0, 0, -1,
1, 0, 0, 1 };
static const int16_t rt[72] /* was [6][12] */ = {
-1933, -253, 320, 1237, -5767, 2904,
372, -1733, 873, 6432, 842, -1066,
0, 0, 0, 2, 10, 19,
2, 10, 19, 0, 0, 0,
-6, 29, -15, -108, -14, 18,
32, 4, -5, -21, 97, -49,
-6, 29, -15, -108, -14, 18,
-33, -4, 5, 20, -97, 49,
0, 7, -3, 0, 0, 0,
7, 0, 0, 0, 0, 0,
0, 2, 0, -16, -2, 3,
-2, 0, 0, 3, -14, 7 };
static const int8_t ic[48] /* was [4][12] */ = {
0, 0, 0, 1,
0, 0, 1, 0,
0, 1, -1, 0,
0, 1, 0, -1,
0, 1, 0, 1,
0, 1, 1, 0,
0, 2, 0, -1,
0, 2, 0, 1,
1, -1, 0, -1,
1, 0, 0, -1,
1, 0, 0, 1,
1, 1, 0, -1 };
static const int16_t rc[144] /* was [6][24] */ = {
651, 1615, -910, -6145, 2170, -542,
-1846, 652, -163, -2166, -5375, 3030,
0, 0, 0, 5, 27, 52,
5, 27, 52, 0, 0, 0,
0, 0, -2, 0, 0, 0,
0, 0, 0, 0, 0, -2,
-78, 27, -7, -89, -225, 127,
27, 68, -38, -257, 89, -22,
-77, 28, -7, -92, -225, 127,
-28, -67, 38, 257, -92, 23,
0, 0, -2, 0, 0, 0,
0, 0, 0, 0, 0, 2,
-2, 0, 0, 4, -6, 3,
0, 2, 0, -7, -3, 2,
-2, 0, 0, 4, -6, 3,
0, -2, 0, 7, 3, -2,
0, 0, 0, 2, 0, 0,
0, 0, 0, 0, -2, 0,
-4, 0, 0, -9, -22, 12,
0, 3, -2, -25, 9, -2,
-11, 4, 0, 0, 0, 0,
-4, -10, 6, 0, 0, 0,
0, 0, 0, 2, 0, 0,
0, 0, 0, 0, -2, 0 };
int i, n_terms = (sat_no == HTC2_TELESTO ? 6 : 12);
const int8_t *iptr;
const int16_t *rptr;
double arg1, arg2, arg3, arg4;
const double t = jd - 2451545.;
switch( sat_no)
{
case HTC2_HELENE:
iptr = ih;
rptr = rh;
break;
case HTC2_TELESTO:
iptr = it;
rptr = rt;
break;
case HTC2_CALYPSO:
iptr = ic;
rptr = rc;
break;
default: /* Not a valid satellite */
return( -1);
}
for (i = 0; i < 3; ++i)
{
xyz[i] = 0.;
if( vxyz)
vxyz[i] = 0.;
}
arg1 = rnu1[sat_no] * t + phi1[sat_no];
arg2 = rnu2[sat_no] * t + phi2[sat_no];
arg3 = rnu3[sat_no] * t + phi3[sat_no];
arg4 = rlamda[sat_no] * t + theta[sat_no];
while( n_terms--)
{
const double ang =
iptr[0] * arg1 + iptr[1] * arg2
+ iptr[2] * arg3 + iptr[3] * arg4;
const double cos_ang = cos( ang);
const double sin_ang = sin( ang);
for( i = 0; i < 3; ++i, rptr++)
{
xyz[i] += (double)rptr[0] * cos_ang + (double)rptr[6] * sin_ang;
if( vxyz)
vxyz[i] += (double)rptr[3] * cos_ang + (double)rptr[9] * sin_ang;
}
iptr += 4;
rptr += 9;
}
for( i = 0; i < 3; ++i)
{
*xyz++ *= 1.e-6;
if( vxyz)
*vxyz++ *= 1.e-6;
}
return 0;
} /* htc20 */
#ifdef TEST_MAIN
#ifndef AU_IN_KM
#define AU_IN_KM 1.495978707e+8
#endif
#include <stdlib.h>
#include <stdio.h>
int main( const int argc, const char **argv)
{
double xyz[3], vxyz[3];
int i, idx;
for( idx = 1; idx < argc; idx++)
{
const double jd = atof( argv[idx]);
if( jd != 0.)
for( i = 0; i < 3; i++)
{
static const char *sat_name[3] = { "Helen", "Teles", "Calyp" };
htc20( jd, i, xyz, vxyz);
printf( "%s %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f\n",
sat_name[i],
xyz[0] * AU_IN_KM,
xyz[1] * AU_IN_KM,
xyz[2] * AU_IN_KM,
vxyz[0] * AU_IN_KM,
vxyz[1] * AU_IN_KM,
vxyz[2] * AU_IN_KM);
}
}
return( 0);
}
#endif