/
ElpMpp02.h
executable file
·510 lines (478 loc) · 20.7 KB
/
ElpMpp02.h
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
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
// ----------------------------------------------------------------
// This code calculates the ELP/MPP02 series.
//
// ELP/MPP02 is a semi-analytic solution for the lunar motion developed by
// J. Chapront and G. Francou in 2002. It is an improvement of the ELP2000-82B
// lunar theory.
//
// Source paper:
// The lunar theory ELP revisited. Introduction of new planetary perturbations
// by J. Chapront and G. Francou, Astronomy and Astrophysics, v.404, p.735-742 (2003)
// http://adsabs.harvard.edu/abs/2003A%26A...404..735C
//
// This code and data files are based on the authors' FORTRAN code and data files on
// ftp://cyrano-se.obspm.fr/pub/2_lunar_solutions/2_elpmpp02/
//
// The following 14 data files are required:
// elp_main.long, elp_main.lat, elp_main.dist,
// elp_pert.longT0, elp_pert.longT1, elp_pert.longT2, elp_pert.longT3,
// elp_pert.latT0, elp_pert.latT1, elp_pert.latT2,
// elp_pert.distT0, elp_pert.distT1, elp_pert.distT2, elp_pert.distT3
//
// Usage:
// 1. Set the parameter corr: corr=0 uses parameters fitted
// to the lunar laser ranging (LLR) observation data, corr=1 uses
// parameters fitted to JPL's DE405/DE406 ephemerides.
// 2. Call the function setup_parameters() to set up parameters
// corresponding to the choice of corr. There are two sets of
// parameters: a) parameters for adjusting the lunar and
// planetary arguments, stored in the struct Elp_paras;
// b) parameters for adjusting the coefficeients in
// the Elp/MPP02 series for the main problem, stored in the struct
// Elp_facs.
// 3. Call the function setup_Elp_coefs() to set up the coefficients
// for the ELP/MPP02 series. The coefficients are stored in the struct
// Elp_coefs.
// 4. Call getX2000() to compute the rectangular geocentric coordinates
// of the Moon's position with respect to the mean ecliptic and
// equinox of J2000.0.
//
// See example.cpp for an example of using this code.
//----------------------------------------------------------------
#include <cmath>
#include <cstdlib>
#include <iostream>
#include <fstream>
#include <string>
using namespace std;
#define PI 3.14159265358979323846
// Arguments for ELP/MPP02 series
struct Elp_args {
double W1, D, F, L, Lp, zeta, Me, Ve, EM, Ma, Ju, Sa, Ur, Ne;
};
// Factors multiplied by B1-B5 for longitude and latitude
struct Elp_facs {
double fA, fB1, fB2, fB3, fB4, fB5;
};
// parameters for adjusting the lunar and planetary arguments
struct Elp_paras {
// parameters adjusted to fit data
double Dw1_0, Dw2_0, Dw3_0, Deart_0, Dperi, Dw1_1, Dgam, De, Deart_1, Dep,
Dw2_1, Dw3_1, Dw1_2, Dw1_3, Dw1_4, Dw2_2, Dw2_3, Dw3_2, Dw3_3;
// parameters derived from the previous parameters
double Cw2_1, Cw3_1;
};
// Coefficients for the ELP/MPP02 series
struct Elp_coefs {
// Main problem
int n_main_long, n_main_lat, n_main_dist;
int **i_main_long, **i_main_lat, **i_main_dist;
double *A_main_long, *A_main_lat, *A_main_dist;
// Perturbation, longitude
int n_pert_longT0, n_pert_longT1, n_pert_longT2, n_pert_longT3;
int **i_pert_longT0, **i_pert_longT1, **i_pert_longT2, **i_pert_longT3;
double *A_pert_longT0, *A_pert_longT1, *A_pert_longT2, *A_pert_longT3;
double *ph_pert_longT0, *ph_pert_longT1, *ph_pert_longT2, *ph_pert_longT3;
// Perturbation, latitude
int n_pert_latT0, n_pert_latT1, n_pert_latT2;
int **i_pert_latT0, **i_pert_latT1, **i_pert_latT2;
double *A_pert_latT0, *A_pert_latT1, *A_pert_latT2;
double *ph_pert_latT0, *ph_pert_latT1, *ph_pert_latT2;
// Perturbation, distance
int n_pert_distT0, n_pert_distT1, n_pert_distT2, n_pert_distT3;
int **i_pert_distT0, **i_pert_distT1, **i_pert_distT2, **i_pert_distT3;
double *A_pert_distT0, *A_pert_distT1, *A_pert_distT2, *A_pert_distT3;
double *ph_pert_distT0, *ph_pert_distT1, *ph_pert_distT2, *ph_pert_distT3;
};
// restrict x to [-pi, pi)
double mod2pi(double x) {
const double tpi = 2.0*PI;
return x - tpi*floor((x + PI)/tpi);
}
// Set up adjustable parameters
// corr=0: fit to LLR data, corr=1: fit to DE405
void setup_parameters(int corr, Elp_paras ¶s, Elp_facs &facs) {
// PARAMETERS adjusted to fit data
switch (corr) {
case 0:
paras.Dw1_0 = -0.10525;
paras.Dw2_0 = 0.16826;
paras.Dw3_0 = -0.10760;
paras.Deart_0 = -0.04012;
paras.Dperi = -0.04854;
paras.Dw1_1 = -0.32311;
paras.Dgam = 0.00069;
paras.De = 0.00005;
paras.Deart_1 = 0.01442;
paras.Dep = 0.00226;
paras.Dw2_1 = 0.08017;
paras.Dw3_1 = -0.04317;
paras.Dw1_2 = -0.03794;
paras.Dw1_3 = 0.0;
paras.Dw1_4 = 0.0;
paras.Dw2_2 = 0.0;
paras.Dw2_3 = 0.0;
paras.Dw3_2 = 0.0;
paras.Dw3_3 = 0.0;
break;
case 1:
paras.Dw1_0 = -0.07008;
paras.Dw2_0 = 0.20794;
paras.Dw3_0 = -0.07215;
paras.Deart_0 = -0.00033;
paras.Dperi = -0.00749;
paras.Dw1_1 = -0.35106;
paras.Dgam = 0.00085;
paras.De = -0.00006;
paras.Deart_1 = 0.00732;
paras.Dep = 0.00224;
paras.Dw2_1 = 0.08017;
paras.Dw3_1 = -0.04317;
paras.Dw1_2 = -0.03743;
paras.Dw1_3 = -0.00018865;
paras.Dw1_4 = -0.00001024;
paras.Dw2_2 = 0.00470602;
paras.Dw2_3 = -0.00025213;
paras.Dw3_2 = -0.00261070;
paras.Dw3_3 = -0.00010712;
break;
}
// derived parameters
const double am = 0.074801329;
const double alpha = 0.002571881;
const double dtsm = 2.0*alpha/(3.0*am);
const double xa = 2.0*alpha/3.0;
const double sec = PI/648000.0; // arcsecs -> radians
double bp[5][2] = {{0.311079095, -0.103837907},
{-0.004482398, 0.000668287},
{-0.001102485, -0.001298072},
{0.001056062, -0.000178028},
{0.000050928, -0.000037342}};
double w11 = (1732559343.73604 + paras.Dw1_1)*sec;
double w21 = (14643420.3171 + paras.Dw2_1)*sec;
double w31 = (-6967919.5383 + paras.Dw3_1)*sec;
double x2 = w21/w11;
double x3 = w31/w11;
double y2 = am*bp[0][0] + xa*bp[4][0];
double y3 = am*bp[0][1] + xa*bp[4][1];
double d21 = x2-y2;
double d22 = w11*bp[1][0];
double d23 = w11*bp[2][0];
double d24 = w11*bp[3][0];
double d25 = y2/am;
double d31 = x3-y3;
double d32 = w11*bp[1][1];
double d33 = w11*bp[2][1];
double d34 = w11*bp[3][1];
double d35 = y3/am;
paras.Cw2_1 = d21*paras.Dw1_1 + d25*paras.Deart_1 + d22*paras.Dgam +
d23*paras.De + d24*paras.Dep;
paras.Cw3_1 = d31*paras.Dw1_1 + d35*paras.Deart_1 + d32*paras.Dgam +
d33*paras.De + d34*paras.Dep;
// factors multipled by B1-B5 for longitude and latitude
double delnu_nu = (0.55604 + paras.Dw1_1)*sec/w11;
double dele = (0.01789 + paras.De)*sec;
double delg = (-0.08066 + paras.Dgam)*sec;
double delnp_nu = (-0.06424 + paras.Deart_1)*sec/w11;
double delep = (-0.12879 + paras.Dep)*sec;
// factors multipled by B1-B5 for longitude and latitude
facs.fB1 = -am*delnu_nu + delnp_nu;
facs.fB2 = delg;
facs.fB3 = dele;
facs.fB4 = delep;
facs.fB5 = -xa*delnu_nu + dtsm*delnp_nu;
// factor multiplie A_i for distance
facs.fA = 1.0 - 2.0/3.0*delnu_nu;
}
// Read main problem file
// n is the number of terms in the series, which is stored in the
// first line of the data file
void read_main_problem_file(const char *infile, int &n, int ** &i_main, double * &A_main,
double fA, Elp_facs facs) {
double A,B1,B2,B3,B4,B5,B6;
int i;
ifstream file(infile, ios::in);
if (!file) {
cerr << "Error in opening " << infile << endl;
exit(1);
}
file >> n;
i_main = new int *[n];
A_main = new double[n];
for (i=0; i<n; i++) i_main[i] = new int[4];
for (i=0; i<n; i++) {
if (file.eof()) {
cerr << "Reached the end of the file " << infile
<< " before reading all data!" << endl;
exit(1);
}
file >> i_main[i][0] >> i_main[i][1] >> i_main[i][2] >> i_main[i][3]
>> A >> B1 >> B2 >> B3 >> B4 >> B5 >> B6;
A_main[i] = fA*A + facs.fB1*B1 + facs.fB2*B2 + facs.fB3*B3 +
facs.fB4*B4 + facs.fB5*B5;
}
file.close();
}
// Read perturbation file
// n is the number of terms in the series, which is stored in the
// first line of the data file
void read_perturbation_file(const char *infile, int &n, int ** &i_pert, double * &A_pert,
double * &phase) {
int i;
ifstream file(infile);
if (!file) {
cerr << "Error in opening " << infile << endl;
exit(1);
}
file >> n;
i_pert = new int *[n];
A_pert = new double[n];
phase = new double[n];
for (i=0; i<n; i++) i_pert[i] = new int[13];
for (i=0; i<n; i++) {
if (file.eof()) {
cerr << "Reached the end of the file " << infile
<< " before reading all data!" << endl;
exit(1);
}
file >> i_pert[i][0] >> i_pert[i][1] >> i_pert[i][2] >> i_pert[i][3]
>> i_pert[i][4] >> i_pert[i][5] >> i_pert[i][6] >> i_pert[i][7]
>> i_pert[i][8] >> i_pert[i][9] >> i_pert[i][10] >> i_pert[i][11]
>> i_pert[i][12] >> A_pert[i] >> phase[i];
}
file.close();
}
// set up coefficients for the ELP/MPP02 series
void setup_Elp_coefs(Elp_coefs &coefs, Elp_facs facs) {
string infile;
// Main problem
infile = "elp_main.long";
read_main_problem_file(infile.c_str(), coefs.n_main_long, coefs.i_main_long,
coefs.A_main_long, 1.0, facs);
infile = "elp_main.lat";
read_main_problem_file(infile.c_str(), coefs.n_main_lat, coefs.i_main_lat,
coefs.A_main_lat, 1.0, facs);
infile = "elp_main.dist";
read_main_problem_file(infile.c_str(), coefs.n_main_dist, coefs.i_main_dist,
coefs.A_main_dist, facs.fA, facs);
// perturbation, longitude
infile = "elp_pert.longT0";
read_perturbation_file(infile.c_str(), coefs.n_pert_longT0, coefs.i_pert_longT0,
coefs.A_pert_longT0, coefs.ph_pert_longT0);
infile = "elp_pert.longT1";
read_perturbation_file(infile.c_str(), coefs.n_pert_longT1, coefs.i_pert_longT1,
coefs.A_pert_longT1, coefs.ph_pert_longT1);
infile = "elp_pert.longT2";
read_perturbation_file(infile.c_str(), coefs.n_pert_longT2, coefs.i_pert_longT2,
coefs.A_pert_longT2, coefs.ph_pert_longT2);
infile = "elp_pert.longT3";
read_perturbation_file(infile.c_str(), coefs.n_pert_longT3, coefs.i_pert_longT3,
coefs.A_pert_longT3, coefs.ph_pert_longT3);
// perturbation, latitude
infile = "elp_pert.latT0";
read_perturbation_file(infile.c_str(), coefs.n_pert_latT0, coefs.i_pert_latT0,
coefs.A_pert_latT0, coefs.ph_pert_latT0);
infile = "elp_pert.latT1";
read_perturbation_file(infile.c_str(), coefs.n_pert_latT1, coefs.i_pert_latT1,
coefs.A_pert_latT1, coefs.ph_pert_latT1);
infile = "elp_pert.latT2";
read_perturbation_file(infile.c_str(), coefs.n_pert_latT2, coefs.i_pert_latT2,
coefs.A_pert_latT2, coefs.ph_pert_latT2);
// perturbation, distance
infile = "elp_pert.distT0";
read_perturbation_file(infile.c_str(), coefs.n_pert_distT0, coefs.i_pert_distT0,
coefs.A_pert_distT0, coefs.ph_pert_distT0);
infile = "elp_pert.distT1";
read_perturbation_file(infile.c_str(), coefs.n_pert_distT1, coefs.i_pert_distT1,
coefs.A_pert_distT1, coefs.ph_pert_distT1);
infile = "elp_pert.distT2";
read_perturbation_file(infile.c_str(), coefs.n_pert_distT2, coefs.i_pert_distT2,
coefs.A_pert_distT2, coefs.ph_pert_distT2);
infile = "elp_pert.distT3";
read_perturbation_file(infile.c_str(), coefs.n_pert_distT3, coefs.i_pert_distT3,
coefs.A_pert_distT3, coefs.ph_pert_distT3);
}
// Compute the lunar and planetary arguments used in the ELP/MPP02 series
void compute_Elp_arguments(double T, Elp_paras paras, Elp_args &args) {
const double deg = PI/180.0; // degrees -> radians
const double sec = PI/648000.0; // arcsecs -> radians
double T2 = T*T;
double T3 = T*T2;
double T4 = T2*T2;
double w10 = (-142.0 + 18.0/60.0 +(59.95571 + paras.Dw1_0)/3600.0)*deg;
double w11 = mod2pi((1732559343.73604 + paras.Dw1_1)*T*sec);
double w12 = mod2pi((-6.8084 + paras.Dw1_2)*T2*sec);
double w13 = mod2pi((0.006604 + paras.Dw1_3)*T3*sec);
double w14 = mod2pi((-3.169e-5 + paras.Dw1_4)*T4*sec);
double w20 = (83.0 + 21.0/60.0 + (11.67475 + paras.Dw2_0)/3600.0)*deg;
double w21 = mod2pi((14643420.3171 + paras.Dw2_1 + paras.Cw2_1)*T*sec);
double w22 = mod2pi((-38.2631 + paras.Dw2_2)*T2*sec);
double w23 = mod2pi((-0.045047+ paras.Dw2_3)*T3*sec);
double w24 = mod2pi(0.00021301*T4*sec);
double w30 = (125.0 + 2.0/60.0 + (40.39816 + paras.Dw3_0)/3600.0)*deg;
double w31 = mod2pi((-6967919.5383 + paras.Dw3_1 + paras.Cw3_1)*T*sec);
double w32 = mod2pi((6.359 + paras.Dw3_2)*T2*sec);
double w33 = mod2pi((0.007625 + paras.Dw3_3)*T3*sec);
double w34 = mod2pi(-3.586e-5*T4*sec);
double Ea0 = (100.0 + 27.0/60.0 + (59.13885 + paras.Deart_0)/3600.0)*deg;
double Ea1 = mod2pi((129597742.293 + paras.Deart_1)*T*sec);
double Ea2 = mod2pi(-0.0202*T2*sec);
double Ea3 = mod2pi(9e-6*T3*sec);
double Ea4 = mod2pi(1.5e-7*T4*sec);
double p0 = (102.0 + 56.0/60.0 + (14.45766 + paras.Dperi)/3600.0)*deg;
double p1 = mod2pi(1161.24342*T*sec);
double p2 = mod2pi(0.529265*T2*sec);
double p3 = mod2pi(-1.1814e-4*T3*sec);
double p4 = mod2pi(1.1379e-5*T4*sec);
double Me = (-108.0 + 15.0/60.0 + 3.216919/3600.0)*deg;
Me += mod2pi(538101628.66888*T*sec);
double Ve = (-179.0 + 58.0/60.0 + 44.758419/3600.0)*deg;
Ve += mod2pi(210664136.45777*T*sec);
double EM = (100.0 + 27.0/60.0 + 59.13885/3600.0)*deg;
EM += mod2pi(129597742.293*T*sec);
double Ma = (-5.0 + 26.0/60.0 + 3.642778/3600.0)*deg;
Ma += mod2pi(68905077.65936*T*sec);
double Ju = (34.0 + 21.0/60.0 + 5.379392/3600.0)*deg;
Ju += mod2pi(10925660.57335*T*sec);
double Sa = (50.0 + 4.0/60.0 + 38.902495/3600.0)*deg;
Sa += mod2pi(4399609.33632*T*sec);
double Ur = (-46.0 + 3.0/60.0 + 4.354234/3600.0)*deg;
Ur += mod2pi(1542482.57845*T*sec);
double Ne = (-56.0 + 20.0/60.0 + 56.808371/3600.0)*deg;
Ne += mod2pi(786547.897*T*sec);
double W1 = w10+w11+w12+w13+w14;
double W2 = w20+w21+w22+w23+w24;
double W3 = w30+w31+w32+w33+w34;
double Ea = Ea0+Ea1+Ea2+Ea3+Ea4;
double pomp = p0+p1+p2+p3+p4;
// Mean longitude of the Moon
args.W1 = mod2pi(W1);
// Arguments of Delaunay
args.D = mod2pi(W1-Ea + PI);
args.F = mod2pi(W1-W3);
args.L = mod2pi(W1-W2);
args.Lp = mod2pi(Ea-pomp);
// zeta
args.zeta = mod2pi(W1 + 0.02438029560881907*T);
// Planetary arguments (mean longitudes and mean motions)
args.Me = mod2pi(Me);
args.Ve = mod2pi(Ve);
args.EM = mod2pi(EM);
args.Ma = mod2pi(Ma);
args.Ju = mod2pi(Ju);
args.Sa = mod2pi(Sa);
args.Ur = mod2pi(Ur);
args.Ne = mod2pi(Ne);
}
// Sum the ELP/MPP02 series for the main problem
// dist = 0: sine series; dist != 0: cosine series
double Elp_main_sum(int n, int ** &i_main, double * &A_main, Elp_args &args, int dist) {
int i;
double sum = 0.0;
double phase;
if (dist==0) {
// sine series
for (i=0; i<n; i++) {
phase = i_main[i][0]*args.D + i_main[i][1]*args.F + i_main[i][2]*args.L +
i_main[i][3]*args.Lp;
sum += A_main[i]*sin(phase);
}
} else {
// cosine series
for (i=0; i<n; i++) {
phase = i_main[i][0]*args.D + i_main[i][1]*args.F + i_main[i][2]*args.L +
i_main[i][3]*args.Lp;
sum += A_main[i]*cos(phase);
}
}
return sum;
}
// Sum the ELP/MPP02 series for perturbations
double Elp_perturbation_sum(int n, int ** &i_pert, double * &A_pert, double * &ph_pert,
Elp_args &args) {
int i;
double sum = 0.0;
double phase;
for (i=0; i<n; i++) {
phase = ph_pert[i] + i_pert[i][0]*args.D + i_pert[i][1]*args.F +
i_pert[i][2]*args.L + i_pert[i][3]*args.Lp + i_pert[i][4]*args.Me +
i_pert[i][5]*args.Ve + i_pert[i][6]*args.EM + i_pert[i][7]*args.Ma +
i_pert[i][8]*args.Ju + i_pert[i][9]*args.Sa + i_pert[i][10]*args.Ur +
i_pert[i][11]*args.Ne + i_pert[i][12]*args.zeta;
sum += A_pert[i]*sin(phase);
}
return sum;
}
// Calculate the Moon's geocentric X,Y,Z coordinates with respect to
// J2000.0 mean ecliptic and equinox.
// T is the TDB Julian century from J2000.0 = (TBD JD - 2451545)/36525
void getX2000(double T, Elp_paras ¶s, Elp_coefs &coefs,
double &X, double &Y, double &Z) {
double T2 = T*T;
double T3 = T*T2;
double T4 = T2*T2;
double T5 = T2*T3;
Elp_args args;
compute_Elp_arguments(T, paras, args);
// Sum the ELP/MPP02 series
// main problem series
double main_long = Elp_main_sum(coefs.n_main_long, coefs.i_main_long,
coefs.A_main_long, args, 0);
double main_lat = Elp_main_sum(coefs.n_main_lat, coefs.i_main_lat,
coefs.A_main_lat, args, 0);
double main_dist = Elp_main_sum(coefs.n_main_dist, coefs.i_main_dist,
coefs.A_main_dist, args, 1);
// perturbation, longitude
double pert_longT0 = Elp_perturbation_sum(coefs.n_pert_longT0, coefs.i_pert_longT0,
coefs.A_pert_longT0, coefs.ph_pert_longT0, args);
double pert_longT1 = Elp_perturbation_sum(coefs.n_pert_longT1, coefs.i_pert_longT1,
coefs.A_pert_longT1, coefs.ph_pert_longT1, args);
double pert_longT2 = Elp_perturbation_sum(coefs.n_pert_longT2, coefs.i_pert_longT2,
coefs.A_pert_longT2, coefs.ph_pert_longT2, args);
double pert_longT3 = Elp_perturbation_sum(coefs.n_pert_longT3, coefs.i_pert_longT3,
coefs.A_pert_longT3, coefs.ph_pert_longT3, args);
// perturbation, latitude
double pert_latT0 = Elp_perturbation_sum(coefs.n_pert_latT0, coefs.i_pert_latT0,
coefs.A_pert_latT0, coefs.ph_pert_latT0, args);
double pert_latT1 = Elp_perturbation_sum(coefs.n_pert_latT1, coefs.i_pert_latT1,
coefs.A_pert_latT1, coefs.ph_pert_latT1, args);
double pert_latT2 = Elp_perturbation_sum(coefs.n_pert_latT2, coefs.i_pert_latT2,
coefs.A_pert_latT2, coefs.ph_pert_latT2, args);
// perturbation, distance
double pert_distT0 = Elp_perturbation_sum(coefs.n_pert_distT0, coefs.i_pert_distT0,
coefs.A_pert_distT0, coefs.ph_pert_distT0, args);
double pert_distT1 = Elp_perturbation_sum(coefs.n_pert_distT1, coefs.i_pert_distT1,
coefs.A_pert_distT1, coefs.ph_pert_distT1, args);
double pert_distT2 = Elp_perturbation_sum(coefs.n_pert_distT2, coefs.i_pert_distT2,
coefs.A_pert_distT2, coefs.ph_pert_distT2, args);
double pert_distT3 = Elp_perturbation_sum(coefs.n_pert_distT3, coefs.i_pert_distT3,
coefs.A_pert_distT3, coefs.ph_pert_distT3, args);
// Moon's longitude, latitude and distance
double longM = args.W1 + main_long + pert_longT0 + mod2pi(pert_longT1*T) +
mod2pi(pert_longT2*T2) + mod2pi(pert_longT3*T3);
double latM = main_lat + pert_latT0 + mod2pi(pert_latT1*T) + mod2pi(pert_latT2*T2);
const double ra0 = 384747.961370173/384747.980674318;
double r = ra0*(main_dist + pert_distT0 + pert_distT1*T + pert_distT2*T2 + pert_distT3*T3);
double x0 = r*cos(longM)*cos(latM);
double y0 = r*sin(longM)*cos(latM);
double z0 = r*sin(latM);
// Precession matrix
double P = 0.10180391e-4*T + 0.47020439e-6*T2 - 0.5417367e-9*T3
- 0.2507948e-11*T4 + 0.463486e-14*T5;
double Q = -0.113469002e-3*T + 0.12372674e-6*T2 + 0.12654170e-8*T3
- 0.1371808e-11*T4 - 0.320334e-14*T5;
double sq = sqrt(1 - P*P - Q*Q);
double p11 = 1 - 2*P*P;
double p12 = 2*P*Q;
double p13 = 2*P*sq;
double p21 = 2*P*Q;
double p22 = 1-2*Q*Q;
double p23 = -2*Q*sq;
double p31 = -2*P*sq;
double p32 = 2*Q*sq;
double p33 = 1 - 2*P*P - 2*Q*Q;
// Finally, components of position vector wrt J2000.0 mean ecliptic and equinox
X = p11*x0 + p12*y0 + p13*z0;
Y = p21*x0 + p22*y0 + p23*z0;
Z = p31*x0 + p32*y0 + p33*z0;
}