source: trunk/MagicSoft/slalib/rcc.c

Last change on this file was 731, checked in by tbretz, 24 years ago
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1#include "slalib.h"
2#include "slamac.h"
3double slaRcc ( double tdb, double ut1, double wl, double u, double v )
4/*
5** - - - - - - -
6** s l a R c c
7** - - - - - - -
8**
9** Relativistic clock correction: the difference between proper time at
10** a point on the surface of the Earth and coordinate time in the Solar
11** System barycentric space-time frame of reference.
12**
13** The proper time is Terrestrial Time TT; the coordinate
14** time is an implementation of the Barycentric Dynamical Time TDB.
15**
16** Given:
17** TDB double coordinate time (MJD: JD-2400000.5)
18** UT1 double universal time (fraction of one day)
19** WL double clock longitude (radians west)
20** U double clock distance from Earth spin axis (km)
21** V double clock distance north of Earth equatorial plane (km)
22**
23** Returned:
24** The clock correction, TDB-TT, in seconds. TDB may be considered
25** to be the coordinate time in the Solar System barycentre frame of
26** reference, and TT is the proper time given by clocks at mean sea
27** level on the Earth.
28**
29** The result has a main (annual) sinusoidal term of amplitude
30** approximately 0.00166 seconds, plus planetary terms up to about
31** 20 microseconds, and lunar and diurnal terms up to 2 microseconds.
32**
33** The variation arises from the transverse Doppler effect and the
34** gravitational red-shift as the observer varies in speed and moves
35** through different gravitational potentials.
36**
37** The argument TDB is, strictly, the barycentric coordinate time;
38** however, the terrestrial proper time (TT) can in practice be used.
39**
40** The geocentric model is that of Fairhead & Bretagnon (1990), in its
41** full form. It was supplied by Fairhead (private communication) as a
42** FORTRAN subroutine. The original Fairhead routine used explicit
43** formulae, in such large numbers that problems were experienced with
44** certain compilers (Microsoft Fortran on PC aborted with stack
45** overflow, Convex compiled successfully but extremely slowly). The
46** present implementation is a complete recoding in C, with the original
47** Fairhead coefficients held in a table. To optimize arithmetic
48** precision, the terms are accumulated in reverse order, smallest
49** first. The numerical results from this C version agree with
50** those from the original Fairhead Fortran code to better than
51** 10^-15 seconds, depending on the machine hardware.
52**
53** The topocentric part of the model is from Moyer (1981) and
54** Murray (1983).
55**
56** During the interval 1950-2050, the absolute accuracy is better
57** than +/- 3 nanoseconds relative to direct numerical integrations
58** using the JPL DE200/LE200 solar system ephemeris.
59**
60** The IAU definition of TDB is that it must differ from TT only by
61** periodic terms. Though practical, this is an imprecise definition
62** which ignores the existence of very long-period and secular effects
63** in the dynamics of the solar system. As a consequence, different
64** implementations of TDB will, in general, differ in zero-point and
65** will drift linearly relative to one other.
66**
67** References:
68** Bretagnon P, 1982 Astron. Astrophys., 114, 278-288.
69** Fairhead L & Bretagnon P, 1990, Astron. Astrophys., 229, 240-247.
70**
71** Meeus J, 1984, l'Astronomie, 348-354.
72** Moyer T D, 1981, Cel. Mech., 23, 33.
73** Murray C A, 1983, Vectorial Astrometry, Adam Hilger.
74**
75** Defined in slamac.h: D2PI, dmod
76**
77** Last revision: 31 December 1999
78**
79** Copyright P.T.Wallace. All rights reserved.
80*/
81{
82/*
83** Fairhead and Bretagnon canonical coefficients
84**
85** 787 sets of three coefficients.
86**
87** Each set is amplitude (microseconds)
88** frequency (radians per Julian millennium since J2000),
89** phase (radians).
90**
91** Sets 1-474 are the T^0 terms,
92** " 475-679 " " T^1 "
93** " 680-764 " " T^2 "
94** " 765-784 " " T^3 "
95** " 785-787 " " T^4 " .
96*/
97 static double fairhd[2361] = {
98 1656.674564e-6, 6283.075849991, 6.240054195,
99 22.417471e-6, 5753.384884897, 4.296977442,
100 13.839792e-6, 12566.151699983, 6.196904410,
101 4.770086e-6, 529.690965095, 0.444401603,
102 4.676740e-6, 6069.776754553, 4.021195093,
103 2.256707e-6, 213.299095438, 5.543113262,
104 1.694205e-6, -3.523118349, 5.025132748,
105 1.554905e-6, 77713.771467920, 5.198467090,
106 1.276839e-6, 7860.419392439, 5.988822341,
107 1.193379e-6, 5223.693919802, 3.649823730,
108 1.115322e-6, 3930.209696220, 1.422745069,
109 0.794185e-6, 11506.769769794, 2.322313077,
110 0.447061e-6, 26.298319800, 3.615796498,
111 0.435206e-6, -398.149003408, 4.349338347,
112 0.600309e-6, 1577.343542448, 2.678271909,
113 0.496817e-6, 6208.294251424, 5.696701824,
114 0.486306e-6, 5884.926846583, 0.520007179,
115 0.432392e-6, 74.781598567, 2.435898309,
116 0.468597e-6, 6244.942814354, 5.866398759,
117 0.375510e-6, 5507.553238667, 4.103476804,
118 0.243085e-6, -775.522611324, 3.651837925,
119 0.173435e-6, 18849.227549974, 6.153743485,
120 0.230685e-6, 5856.477659115, 4.773852582,
121 0.203747e-6, 12036.460734888, 4.333987818,
122 0.143935e-6, -796.298006816, 5.957517795,
123 0.159080e-6, 10977.078804699, 1.890075226,
124 0.119979e-6, 38.133035638, 4.551585768,
125 0.118971e-6, 5486.777843175, 1.914547226,
126 0.116120e-6, 1059.381930189, 0.873504123,
127 0.137927e-6, 11790.629088659, 1.135934669,
128 0.098358e-6, 2544.314419883, 0.092793886,
129 0.101868e-6, -5573.142801634, 5.984503847,
130 0.080164e-6, 206.185548437, 2.095377709,
131 0.079645e-6, 4694.002954708, 2.949233637,
132 0.062617e-6, 20.775395492, 2.654394814,
133 0.075019e-6, 2942.463423292, 4.980931759,
134 0.064397e-6, 5746.271337896, 1.280308748,
135 0.063814e-6, 5760.498431898, 4.167901731,
136 0.048042e-6, 2146.165416475, 1.495846011,
137 0.048373e-6, 155.420399434, 2.251573730,
138 0.058844e-6, 426.598190876, 4.839650148,
139 0.046551e-6, -0.980321068, 0.921573539,
140 0.054139e-6, 17260.154654690, 3.411091093,
141 0.042411e-6, 6275.962302991, 2.869567043,
142 0.040184e-6, -7.113547001, 3.565975565,
143 0.036564e-6, 5088.628839767, 3.324679049,
144 0.040759e-6, 12352.852604545, 3.981496998,
145 0.036507e-6, 801.820931124, 6.248866009,
146 0.036955e-6, 3154.687084896, 5.071801441,
147 0.042732e-6, 632.783739313, 5.720622217,
148 0.042560e-6, 161000.685737473, 1.270837679,
149 0.040480e-6, 15720.838784878, 2.546610123,
150 0.028244e-6, -6286.598968340, 5.069663519,
151 0.033477e-6, 6062.663207553, 4.144987272,
152 0.034867e-6, 522.577418094, 5.210064075,
153 0.032438e-6, 6076.890301554, 0.749317412,
154 0.030215e-6, 7084.896781115, 3.389610345,
155 0.029247e-6, -71430.695617928, 4.183178762,
156 0.033529e-6, 9437.762934887, 2.404714239,
157 0.032423e-6, 8827.390269875, 5.541473556,
158 0.027567e-6, 6279.552731642, 5.040846034,
159 0.029862e-6, 12139.553509107, 1.770181024,
160 0.022509e-6, 10447.387839604, 1.460726241,
161 0.020937e-6, 8429.241266467, 0.652303414,
162 0.020322e-6, 419.484643875, 3.735430632,
163 0.024816e-6, -1194.447010225, 1.087136918,
164 0.025196e-6, 1748.016413067, 2.901883301,
165 0.021691e-6, 14143.495242431, 5.952658009,
166 0.017673e-6, 6812.766815086, 3.186129845,
167 0.022567e-6, 6133.512652857, 3.307984806,
168 0.016155e-6, 10213.285546211, 1.331103168,
169 0.014751e-6, 1349.867409659, 4.308933301,
170 0.015949e-6, -220.412642439, 4.005298270,
171 0.015974e-6, -2352.866153772, 6.145309371,
172 0.014223e-6, 17789.845619785, 2.104551349,
173 0.017806e-6, 73.297125859, 3.475975097,
174 0.013671e-6, -536.804512095, 5.971672571,
175 0.011942e-6, 8031.092263058, 2.053414715,
176 0.014318e-6, 16730.463689596, 3.016058075,
177 0.012462e-6, 103.092774219, 1.737438797,
178 0.010962e-6, 3.590428652, 2.196567739,
179 0.015078e-6, 19651.048481098, 3.969480770,
180 0.010396e-6, 951.718406251, 5.717799605,
181 0.011707e-6, -4705.732307544, 2.654125618,
182 0.010453e-6, 5863.591206116, 1.913704550,
183 0.012420e-6, 4690.479836359, 4.734090399,
184 0.011847e-6, 5643.178563677, 5.489005403,
185 0.008610e-6, 3340.612426700, 3.661698944,
186 0.011622e-6, 5120.601145584, 4.863931876,
187 0.010825e-6, 553.569402842, 0.842715011,
188 0.008666e-6, -135.065080035, 3.293406547,
189 0.009963e-6, 149.563197135, 4.870690598,
190 0.009858e-6, 6309.374169791, 1.061816410,
191 0.007959e-6, 316.391869657, 2.465042647,
192 0.010099e-6, 283.859318865, 1.942176992,
193 0.007147e-6, -242.728603974, 3.661486981,
194 0.007505e-6, 5230.807466803, 4.920937029,
195 0.008323e-6, 11769.853693166, 1.229392026,
196 0.007490e-6, -6256.777530192, 3.658444681,
197 0.009370e-6, 149854.400134205, 0.673880395,
198 0.007117e-6, 38.027672636, 5.294249518,
199 0.007857e-6, 12168.002696575, 0.525733528,
200 0.007019e-6, 6206.809778716, 0.837688810,
201 0.006056e-6, 955.599741609, 4.194535082,
202 0.008107e-6, 13367.972631107, 3.793235253,
203 0.006731e-6, 5650.292110678, 5.639906583,
204 0.007332e-6, 36.648562930, 0.114858677,
205 0.006366e-6, 4164.311989613, 2.262081818,
206 0.006858e-6, 5216.580372801, 0.642063318,
207 0.006919e-6, 6681.224853400, 6.018501522,
208 0.006826e-6, 7632.943259650, 3.458654112,
209 0.005308e-6, -1592.596013633, 2.500382359,
210 0.005096e-6, 11371.704689758, 2.547107806,
211 0.004841e-6, 5333.900241022, 0.437078094,
212 0.005582e-6, 5966.683980335, 2.246174308,
213 0.006304e-6, 11926.254413669, 2.512929171,
214 0.006603e-6, 23581.258177318, 5.393136889,
215 0.005123e-6, -1.484472708, 2.999641028,
216 0.004648e-6, 1589.072895284, 1.275847090,
217 0.005119e-6, 6438.496249426, 1.486539246,
218 0.004521e-6, 4292.330832950, 6.140635794,
219 0.005680e-6, 23013.539539587, 4.557814849,
220 0.005488e-6, -3.455808046, 0.090675389,
221 0.004193e-6, 7234.794256242, 4.869091389,
222 0.003742e-6, 7238.675591600, 4.691976180,
223 0.004148e-6, -110.206321219, 3.016173439,
224 0.004553e-6, 11499.656222793, 5.554998314,
225 0.004892e-6, 5436.993015240, 1.475415597,
226 0.004044e-6, 4732.030627343, 1.398784824,
227 0.004164e-6, 12491.370101415, 5.650931916,
228 0.004349e-6, 11513.883316794, 2.181745369,
229 0.003919e-6, 12528.018664345, 5.823319737,
230 0.003129e-6, 6836.645252834, 0.003844094,
231 0.004080e-6, -7058.598461315, 3.690360123,
232 0.003270e-6, 76.266071276, 1.517189902,
233 0.002954e-6, 6283.143160294, 4.447203799,
234 0.002872e-6, 28.449187468, 1.158692983,
235 0.002881e-6, 735.876513532, 0.349250250,
236 0.003279e-6, 5849.364112115, 4.893384368,
237 0.003625e-6, 6209.778724132, 1.473760578,
238 0.003074e-6, 949.175608970, 5.185878737,
239 0.002775e-6, 9917.696874510, 1.030026325,
240 0.002646e-6, 10973.555686350, 3.918259169,
241 0.002575e-6, 25132.303399966, 6.109659023,
242 0.003500e-6, 263.083923373, 1.892100742,
243 0.002740e-6, 18319.536584880, 4.320519510,
244 0.002464e-6, 202.253395174, 4.698203059,
245 0.002409e-6, 2.542797281, 5.325009315,
246 0.003354e-6, -90955.551694697, 1.942656623,
247 0.002296e-6, 6496.374945429, 5.061810696,
248 0.003002e-6, 6172.869528772, 2.797822767,
249 0.003202e-6, 27511.467873537, 0.531673101,
250 0.002954e-6, -6283.008539689, 4.533471191,
251 0.002353e-6, 639.897286314, 3.734548088,
252 0.002401e-6, 16200.772724501, 2.605547070,
253 0.003053e-6, 233141.314403759, 3.029030662,
254 0.003024e-6, 83286.914269554, 2.355556099,
255 0.002863e-6, 17298.182327326, 5.240963796,
256 0.002103e-6, -7079.373856808, 5.756641637,
257 0.002303e-6, 83996.847317911, 2.013686814,
258 0.002303e-6, 18073.704938650, 1.089100410,
259 0.002381e-6, 63.735898303, 0.759188178,
260 0.002493e-6, 6386.168624210, 0.645026535,
261 0.002366e-6, 3.932153263, 6.215885448,
262 0.002169e-6, 11015.106477335, 4.845297676,
263 0.002397e-6, 6243.458341645, 3.809290043,
264 0.002183e-6, 1162.474704408, 6.179611691,
265 0.002353e-6, 6246.427287062, 4.781719760,
266 0.002199e-6, -245.831646229, 5.956152284,
267 0.001729e-6, 3894.181829542, 1.264976635,
268 0.001896e-6, -3128.388765096, 4.914231596,
269 0.002085e-6, 35.164090221, 1.405158503,
270 0.002024e-6, 14712.317116458, 2.752035928,
271 0.001737e-6, 6290.189396992, 5.280820144,
272 0.002229e-6, 491.557929457, 1.571007057,
273 0.001602e-6, 14314.168113050, 4.203664806,
274 0.002186e-6, 454.909366527, 1.402101526,
275 0.001897e-6, 22483.848574493, 4.167932508,
276 0.001825e-6, -3738.761430108, 0.545828785,
277 0.001894e-6, 1052.268383188, 5.817167450,
278 0.001421e-6, 20.355319399, 2.419886601,
279 0.001408e-6, 10984.192351700, 2.732084787,
280 0.001847e-6, 10873.986030480, 2.903477885,
281 0.001391e-6, -8635.942003763, 0.593891500,
282 0.001388e-6, -7.046236698, 1.166145902,
283 0.001810e-6, -88860.057071188, 0.487355242,
284 0.001288e-6, -1990.745017041, 3.913022880,
285 0.001297e-6, 23543.230504682, 3.063805171,
286 0.001335e-6, -266.607041722, 3.995764039,
287 0.001376e-6, 10969.965257698, 5.152914309,
288 0.001745e-6, 244287.600007027, 3.626395673,
289 0.001649e-6, 31441.677569757, 1.952049260,
290 0.001416e-6, 9225.539273283, 4.996408389,
291 0.001238e-6, 4804.209275927, 5.503379738,
292 0.001472e-6, 4590.910180489, 4.164913291,
293 0.001169e-6, 6040.347246017, 5.841719038,
294 0.001039e-6, 5540.085789459, 2.769753519,
295 0.001004e-6, -170.672870619, 0.755008103,
296 0.001284e-6, 10575.406682942, 5.306538209,
297 0.001278e-6, 71.812653151, 4.713486491,
298 0.001321e-6, 18209.330263660, 2.624866359,
299 0.001297e-6, 21228.392023546, 0.382603541,
300 0.000954e-6, 6282.095528923, 0.882213514,
301 0.001145e-6, 6058.731054289, 1.169483931,
302 0.000979e-6, 5547.199336460, 5.448375984,
303 0.000987e-6, -6262.300454499, 2.656486959,
304 0.001070e-6, -154717.609887482, 1.827624012,
305 0.000991e-6, 4701.116501708, 4.387001801,
306 0.001155e-6, -14.227094002, 3.042700750,
307 0.001176e-6, 277.034993741, 3.335519004,
308 0.000890e-6, 13916.019109642, 5.601498297,
309 0.000884e-6, -1551.045222648, 1.088831705,
310 0.000876e-6, 5017.508371365, 3.969902609,
311 0.000806e-6, 15110.466119866, 5.142876744,
312 0.000773e-6, -4136.910433516, 0.022067765,
313 0.001077e-6, 175.166059800, 1.844913056,
314 0.000954e-6, -6284.056171060, 0.968480906,
315 0.000737e-6, 5326.786694021, 4.923831588,
316 0.000845e-6, -433.711737877, 4.749245231,
317 0.000819e-6, 8662.240323563, 5.991247817,
318 0.000852e-6, 199.072001436, 2.189604979,
319 0.000723e-6, 17256.631536341, 6.068719637,
320 0.000940e-6, 6037.244203762, 6.197428148,
321 0.000885e-6, 11712.955318231, 3.280414875,
322 0.000706e-6, 12559.038152982, 2.824848947,
323 0.000732e-6, 2379.164473572, 2.501813417,
324 0.000764e-6, -6127.655450557, 2.236346329,
325 0.000908e-6, 131.541961686, 2.521257490,
326 0.000907e-6, 35371.887265976, 3.370195967,
327 0.000673e-6, 1066.495477190, 3.876512374,
328 0.000814e-6, 17654.780539750, 4.627122566,
329 0.000630e-6, 36.027866677, 0.156368499,
330 0.000798e-6, 515.463871093, 5.151962502,
331 0.000798e-6, 148.078724426, 5.909225055,
332 0.000806e-6, 309.278322656, 6.054064447,
333 0.000607e-6, -39.617508346, 2.839021623,
334 0.000601e-6, 412.371096874, 3.984225404,
335 0.000646e-6, 11403.676995575, 3.852959484,
336 0.000704e-6, 13521.751441591, 2.300991267,
337 0.000603e-6, -65147.619767937, 4.140083146,
338 0.000609e-6, 10177.257679534, 0.437122327,
339 0.000631e-6, 5767.611978898, 4.026532329,
340 0.000576e-6, 11087.285125918, 4.760293101,
341 0.000674e-6, 14945.316173554, 6.270510511,
342 0.000726e-6, 5429.879468239, 6.039606892,
343 0.000710e-6, 28766.924424484, 5.672617711,
344 0.000647e-6, 11856.218651625, 3.397132627,
345 0.000678e-6, -5481.254918868, 6.249666675,
346 0.000618e-6, 22003.914634870, 2.466427018,
347 0.000738e-6, 6134.997125565, 2.242668890,
348 0.000660e-6, 625.670192312, 5.864091907,
349 0.000694e-6, 3496.032826134, 2.668309141,
350 0.000531e-6, 6489.261398429, 1.681888780,
351 0.000611e-6, -143571.324284214, 2.424978312,
352 0.000575e-6, 12043.574281889, 4.216492400,
353 0.000553e-6, 12416.588502848, 4.772158039,
354 0.000689e-6, 4686.889407707, 6.224271088,
355 0.000495e-6, 7342.457780181, 3.817285811,
356 0.000567e-6, 3634.621024518, 1.649264690,
357 0.000515e-6, 18635.928454536, 3.945345892,
358 0.000486e-6, -323.505416657, 4.061673868,
359 0.000662e-6, 25158.601719765, 1.794058369,
360 0.000509e-6, 846.082834751, 3.053874588,
361 0.000472e-6, -12569.674818332, 5.112133338,
362 0.000461e-6, 6179.983075773, 0.513669325,
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676 0.000465e-6, 10969.965257698, 0.476681802,
677 0.000424e-6, -7079.373856808, 1.112242763,
678 0.000427e-6, 735.876513532, 1.994214480,
679 0.000478e-6, -6127.655450557, 3.778025483,
680 0.000414e-6, 10973.555686350, 5.441088327,
681 0.000512e-6, 1589.072895284, 0.107123853,
682 0.000378e-6, 10984.192351700, 0.915087231,
683 0.000402e-6, 11371.704689758, 4.107281715,
684 0.000453e-6, 9917.696874510, 1.917490952,
685 0.000395e-6, 149.563197135, 2.763124165,
686 0.000371e-6, 5739.157790895, 3.112111866,
687 0.000350e-6, 11790.629088659, 0.440639857,
688 0.000356e-6, 6133.512652857, 5.444568842,
689 0.000344e-6, 412.371096874, 5.676832684,
690 0.000383e-6, 955.599741609, 5.559734846,
691 0.000333e-6, 6496.374945429, 0.261537984,
692 0.000340e-6, 6055.549660552, 5.975534987,
693 0.000334e-6, 1066.495477190, 2.335063907,
694 0.000399e-6, 11506.769769794, 5.321230910,
695 0.000314e-6, 18319.536584880, 2.313312404,
696 0.000424e-6, 1052.268383188, 1.211961766,
697 0.000307e-6, 63.735898303, 3.169551388,
698 0.000329e-6, 29.821438149, 6.106912080,
699 0.000357e-6, 6309.374169791, 4.223760346,
700 0.000312e-6, -3738.761430108, 2.180556645,
701 0.000301e-6, 309.278322656, 1.499984572,
702 0.000268e-6, 12043.574281889, 2.447520648,
703 0.000257e-6, 12491.370101415, 3.662331761,
704 0.000290e-6, 625.670192312, 1.272834584,
705 0.000256e-6, 5429.879468239, 1.913426912,
706 0.000339e-6, 3496.032826134, 4.165930011,
707 0.000283e-6, 3930.209696220, 4.325565754,
708 0.000241e-6, 12528.018664345, 3.832324536,
709 0.000304e-6, 4686.889407707, 1.612348468,
710 0.000259e-6, 16200.772724501, 3.470173146,
711 0.000238e-6, 12139.553509107, 1.147977842,
712 0.000236e-6, 6172.869528772, 3.776271728,
713 0.000296e-6, -7058.598461315, 0.460368852,
714 0.000306e-6, 10575.406682942, 0.554749016,
715 0.000251e-6, 17298.182327326, 0.834332510,
716 0.000290e-6, 4732.030627343, 4.759564091,
717 0.000261e-6, 5884.926846583, 0.298259862,
718 0.000249e-6, 5547.199336460, 3.749366406,
719 0.000213e-6, 11712.955318231, 5.415666119,
720 0.000223e-6, 4701.116501708, 2.703203558,
721 0.000268e-6, -640.877607382, 0.283670793,
722 0.000209e-6, 5636.065016677, 1.238477199,
723 0.000193e-6, 10177.257679534, 1.943251340,
724 0.000182e-6, 6283.143160294, 2.456157599,
725 0.000184e-6, -227.526189440, 5.888038582,
726 0.000182e-6, -6283.008539689, 0.241332086,
727 0.000228e-6, -6284.056171060, 2.657323816,
728 0.000166e-6, 7238.675591600, 5.930629110,
729 0.000167e-6, 3097.883822726, 5.570955333,
730 0.000159e-6, -323.505416657, 5.786670700,
731 0.000154e-6, -4136.910433516, 1.517805532,
732 0.000176e-6, 12029.347187887, 3.139266834,
733 0.000167e-6, 12132.439962106, 3.556352289,
734 0.000153e-6, 202.253395174, 1.463313961,
735 0.000157e-6, 17267.268201691, 1.586837396,
736 0.000142e-6, 83996.847317911, 0.022670115,
737 0.000152e-6, 17260.154654690, 0.708528947,
738 0.000144e-6, 6084.003848555, 5.187075177,
739 0.000135e-6, 5756.566278634, 1.993229262,
740 0.000134e-6, 5750.203491159, 3.457197134,
741 0.000144e-6, 5326.786694021, 6.066193291,
742 0.000160e-6, 11015.106477335, 1.710431974,
743 0.000133e-6, 3634.621024518, 2.836451652,
744 0.000134e-6, 18073.704938650, 5.453106665,
745 0.000134e-6, 1162.474704408, 5.326898811,
746 0.000128e-6, 5642.198242609, 2.511652591,
747 0.000160e-6, 632.783739313, 5.628785365,
748 0.000132e-6, 13916.019109642, 0.819294053,
749 0.000122e-6, 14314.168113050, 5.677408071,
750 0.000125e-6, 12359.966151546, 5.251984735,
751 0.000121e-6, 5749.452731634, 2.210924603,
752 0.000136e-6, -245.831646229, 1.646502367,
753 0.000120e-6, 5757.317038160, 3.240883049,
754 0.000134e-6, 12146.667056108, 3.059480037,
755 0.000137e-6, 6206.809778716, 1.867105418,
756 0.000141e-6, 17253.041107690, 2.069217456,
757 0.000129e-6, -7477.522860216, 2.781469314,
758 0.000116e-6, 5540.085789459, 4.281176991,
759 0.000116e-6, 9779.108676125, 3.320925381,
760 0.000129e-6, 5237.921013804, 3.497704076,
761 0.000113e-6, 5959.570433334, 0.983210840,
762 0.000122e-6, 6282.095528923, 2.674938860,
763 0.000140e-6, -11.045700264, 4.957936982,
764 0.000108e-6, 23543.230504682, 1.390113589,
765 0.000106e-6, -12569.674818332, 0.429631317,
766 0.000110e-6, -266.607041722, 5.501340197,
767 0.000115e-6, 12559.038152982, 4.691456618,
768 0.000134e-6, -2388.894020449, 0.577313584,
769 0.000109e-6, 10440.274292604, 6.218148717,
770 0.000102e-6, -543.918059096, 1.477842615,
771 0.000108e-6, 21228.392023546, 2.237753948,
772 0.000101e-6, -4535.059436924, 3.100492232,
773 0.000103e-6, 76.266071276, 5.594294322,
774 0.000104e-6, 949.175608970, 5.674287810,
775 0.000101e-6, 13517.870106233, 2.196632348,
776 0.000100e-6, 11933.367960670, 4.056084160,
777 4.322990e-6, 6283.075849991, 2.642893748,
778 0.406495e-6, 0.000000000, 4.712388980,
779 0.122605e-6, 12566.151699983, 2.438140634,
780 0.019476e-6, 213.299095438, 1.642186981,
781 0.016916e-6, 529.690965095, 4.510959344,
782 0.013374e-6, -3.523118349, 1.502210314,
783 0.008042e-6, 26.298319800, 0.478549024,
784 0.007824e-6, 155.420399434, 5.254710405,
785 0.004894e-6, 5746.271337896, 4.683210850,
786 0.004875e-6, 5760.498431898, 0.759507698,
787 0.004416e-6, 5223.693919802, 6.028853166,
788 0.004088e-6, -7.113547001, 0.060926389,
789 0.004433e-6, 77713.771467920, 3.627734103,
790 0.003277e-6, 18849.227549974, 2.327912542,
791 0.002703e-6, 6062.663207553, 1.271941729,
792 0.003435e-6, -775.522611324, 0.747446224,
793 0.002618e-6, 6076.890301554, 3.633715689,
794 0.003146e-6, 206.185548437, 5.647874613,
795 0.002544e-6, 1577.343542448, 6.232904270,
796 0.002218e-6, -220.412642439, 1.309509946,
797 0.002197e-6, 5856.477659115, 2.407212349,
798 0.002897e-6, 5753.384884897, 5.863842246,
799 0.001766e-6, 426.598190876, 0.754113147,
800 0.001738e-6, -796.298006816, 2.714942671,
801 0.001695e-6, 522.577418094, 2.629369842,
802 0.001584e-6, 5507.553238667, 1.341138229,
803 0.001503e-6, -242.728603974, 0.377699736,
804 0.001552e-6, -536.804512095, 2.904684667,
805 0.001370e-6, -398.149003408, 1.265599125,
806 0.001889e-6, -5573.142801634, 4.413514859,
807 0.001722e-6, 6069.776754553, 2.445966339,
808 0.001124e-6, 1059.381930189, 5.041799657,
809 0.001258e-6, 553.569402842, 3.849557278,
810 0.000831e-6, 951.718406251, 2.471094709,
811 0.000767e-6, 4694.002954708, 5.363125422,
812 0.000756e-6, 1349.867409659, 1.046195744,
813 0.000775e-6, -11.045700264, 0.245548001,
814 0.000597e-6, 2146.165416475, 4.543268798,
815 0.000568e-6, 5216.580372801, 4.178853144,
816 0.000711e-6, 1748.016413067, 5.934271972,
817 0.000499e-6, 12036.460734888, 0.624434410,
818 0.000671e-6, -1194.447010225, 4.136047594,
819 0.000488e-6, 5849.364112115, 2.209679987,
820 0.000621e-6, 6438.496249426, 4.518860804,
821 0.000495e-6, -6286.598968340, 1.868201275,
822 0.000456e-6, 5230.807466803, 1.271231591,
823 0.000451e-6, 5088.628839767, 0.084060889,
824 0.000435e-6, 5643.178563677, 3.324456609,
825 0.000387e-6, 10977.078804699, 4.052488477,
826 0.000547e-6, 161000.685737473, 2.841633844,
827 0.000522e-6, 3154.687084896, 2.171979966,
828 0.000375e-6, 5486.777843175, 4.983027306,
829 0.000421e-6, 5863.591206116, 4.546432249,
830 0.000439e-6, 7084.896781115, 0.522967921,
831 0.000309e-6, 2544.314419883, 3.172606705,
832 0.000347e-6, 4690.479836359, 1.479586566,
833 0.000317e-6, 801.820931124, 3.553088096,
834 0.000262e-6, 419.484643875, 0.606635550,
835 0.000248e-6, 6836.645252834, 3.014082064,
836 0.000245e-6, -1592.596013633, 5.519526220,
837 0.000225e-6, 4292.330832950, 2.877956536,
838 0.000214e-6, 7234.794256242, 1.605227587,
839 0.000205e-6, 5767.611978898, 0.625804796,
840 0.000180e-6, 10447.387839604, 3.499954526,
841 0.000229e-6, 199.072001436, 5.632304604,
842 0.000214e-6, 639.897286314, 5.960227667,
843 0.000175e-6, -433.711737877, 2.162417992,
844 0.000209e-6, 515.463871093, 2.322150893,
845 0.000173e-6, 6040.347246017, 2.556183691,
846 0.000184e-6, 6309.374169791, 4.732296790,
847 0.000227e-6, 149854.400134205, 5.385812217,
848 0.000154e-6, 8031.092263058, 5.120720920,
849 0.000151e-6, 5739.157790895, 4.815000443,
850 0.000197e-6, 7632.943259650, 0.222827271,
851 0.000197e-6, 74.781598567, 3.910456770,
852 0.000138e-6, 6055.549660552, 1.397484253,
853 0.000149e-6, -6127.655450557, 5.333727496,
854 0.000137e-6, 3894.181829542, 4.281749907,
855 0.000135e-6, 9437.762934887, 5.979971885,
856 0.000139e-6, -2352.866153772, 4.715630782,
857 0.000142e-6, 6812.766815086, 0.513330157,
858 0.000120e-6, -4705.732307544, 0.194160689,
859 0.000131e-6, -71430.695617928, 0.000379226,
860 0.000124e-6, 6279.552731642, 2.122264908,
861 0.000108e-6, -6256.777530192, 0.883445696,
862 0.143388e-6, 6283.075849991, 1.131453581,
863 0.006671e-6, 12566.151699983, 0.775148887,
864 0.001480e-6, 155.420399434, 0.480016880,
865 0.000934e-6, 213.299095438, 6.144453084,
866 0.000795e-6, 529.690965095, 2.941595619,
867 0.000673e-6, 5746.271337896, 0.120415406,
868 0.000672e-6, 5760.498431898, 5.317009738,
869 0.000389e-6, -220.412642439, 3.090323467,
870 0.000373e-6, 6062.663207553, 3.003551964,
871 0.000360e-6, 6076.890301554, 1.918913041,
872 0.000316e-6, -21.340641002, 5.545798121,
873 0.000315e-6, -242.728603974, 1.884932563,
874 0.000278e-6, 206.185548437, 1.266254859,
875 0.000238e-6, -536.804512095, 4.532664830,
876 0.000185e-6, 522.577418094, 4.578313856,
877 0.000245e-6, 18849.227549974, 0.587467082,
878 0.000180e-6, 426.598190876, 5.151178553,
879 0.000200e-6, 553.569402842, 5.355983739,
880 0.000141e-6, 5223.693919802, 1.336556009,
881 0.000104e-6, 5856.477659115, 4.239842759,
882 0.003826e-6, 6283.075849991, 5.705257275,
883 0.000303e-6, 12566.151699983, 5.407132842,
884 0.000209e-6, 155.420399434, 1.989815753
885 };
886
887 double tsol;
888 int i, i3;
889 double t, w0, w1, w2, w3, w4, wf, wj, wt, rdmoon, rge, rle, rtj, rts;
890
891
892/* Time since J2000.0 in Julian millennia */
893 t = ( tdb - 51544.5 ) / 365250.0;
894
895/* -------------------- Topocentric terms ------------------------------- */
896
897/* Convert UT1 to local solar time in radians */
898 tsol = dmod ( ut1, 1.0 ) * D2PI - wl;
899
900/* Planetary arguments: taken or derived from Bretagnon 1982
901** RLp = mean longitude, mean equinox of date
902** RGp = mean anomaly
903** RTp = mean longitude difference, EMB minus planet */
904
905/* EMB */
906 rle = dmod ( t * 6283.3196666635 + 1.75347031435, D2PI );
907 rge = dmod ( t * 6283.019551285 + 6.24005997418, D2PI );
908
909/* Jupiter */
910 rtj = dmod ( t * 5753.3848591241 + 1.15392381696, D2PI );
911
912/* Saturn */
913 rts = dmod ( t * 6069.7767103654 + .87945355785, D2PI );
914
915/* Lunar mean elongation: derived from Meeus 1984 */
916 rdmoon = dmod ( t * 77713.77144 + 5.198468, D2PI );
917
918/* Topocentric terms (Moyer 1981 and Murray 1983) */
919 wt = u * 2.9e-14 * sin ( tsol + rts )
920 + u * 1e-13 * sin ( tsol - 2.0 * rge )
921 + u * 1.33e-13 * sin ( tsol - rdmoon )
922 + u * 1.33e-13 * sin ( tsol + rtj )
923 - u * 2.29e-13 * sin ( tsol + 2.0 * rle + rge )
924 - v * 2.2e-12 * sin ( rle + rge )
925 + u * 5.312e-12 * sin ( tsol - rge )
926 - u * 1.3677e-11 * sin ( tsol + 2.0 * rle )
927 - v * 1.3184e-10 * cos ( rle )
928 + u * 3.17679e-10 * sin ( tsol );
929
930/* --------------- Fairhead model --------------------------------------- */
931
932/* T^0 */
933 w0 = 0.0;
934 for ( i = 474; i >= 1; --i ) {
935 i3 = i * 3;
936 w0 += fairhd[i3-3] * sin ( fairhd[i3-2] * t + fairhd[i3-1] );
937 }
938
939/* T^1 */
940 w1 = 0.0;
941 for ( i = 679; i >= 475; --i ) {
942 i3 = i * 3;
943 w1 += fairhd[i3-3] * sin ( fairhd[i3-2] * t + fairhd[i3-1] );
944 }
945
946/* T^2 */
947 w2 = 0.0;
948 for ( i = 764; i >= 680; --i ) {
949 i3 = i * 3;
950 w2 += fairhd[i3-3] * sin ( fairhd[i3-2] * t + fairhd[i3-1] );
951 }
952
953/* T^3 */
954 w3 = 0.0;
955 for ( i = 784; i >= 765; --i ) {
956 i3 = i * 3;
957 w3 += fairhd[i3-3] * sin ( fairhd[i3-2] * t + fairhd[i3-1] );
958 }
959
960/* T^4 */
961 w4 = 0.0;
962 for ( i = 787; i >= 785; --i ) {
963 i3 = i * 3;
964 w4 += fairhd[i3-3] * sin ( fairhd[i3-2] * t + fairhd[i3-1] );
965 }
966
967/* Multiply by powers of T and combine */
968 wf = t * ( t * ( t * ( t * w4 + w3 ) + w2 ) + w1 ) + w0;
969
970/* Adjustments to use JPL planetary masses instead of IAU */
971 wj = sin ( t * 6069.776754 + 4.021194 ) * 6.5e-10
972 + sin ( t * 213.299095 + 5.543132 ) * 3.3e-10
973 + sin ( t * 6208.294251 + 5.696701 ) * -1.96e-9
974 + sin ( t * 74.781599 + 2.4359 ) * -1.73e-9
975 + 3.638e-8 * t * t;
976
977/* Final result: TDB-TT in seconds */
978 return wt + wf + wj;
979}
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