1 /*
2  *  This library is free software; you can redistribute it and/or
3  *  modify it under the terms of the GNU Lesser General Public
4  *  License as published by the Free Software Foundation; either
5  *  version 2 of the License, or (at your option) any later version.
6  *
7  *  This library is distributed in the hope that it will be useful,
8  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
9  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
10  *  Lesser General Public License for more details.
11  *
12  *  You should have received a copy of the GNU General Public License
13  *  along with this program; if not, write to the Free Software
14  *  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
15  *
16  *  Some functions in this file use the VSOP87 solution by
17  *  Messrs. Bretagnon and Francou.
18  *
19  *  Copyright (C) 2000 - 2005 Liam Girdwood <lgirdwood@gmail.com>
20  */
21 
22 module nova.mars;
23 
24 import std.math;
25 import nova.vsop87;
26 import nova.solar;
27 import nova.earth;
28 import nova.transform;
29 import nova.rise_set;
30 import nova.utility;
31 
32 enum LONG_L0 = 1409;
33 enum LONG_L1 = 891;
34 enum LONG_L2 = 442;
35 enum LONG_L3 = 194;
36 enum LONG_L4 = 75;
37 enum LONG_L5 = 24;
38 enum LAT_B0 = 441;
39 enum LAT_B1 = 291;
40 enum LAT_B2 = 161;
41 enum LAT_B3 = 64;
42 enum LAT_B4 = 18;
43 enum LAT_B5 = 9;
44 enum RADIUS_R0 = 1107;
45 enum RADIUS_R1 = 672;
46 enum RADIUS_R2 = 368;
47 enum RADIUS_R3 = 160;
48 enum RADIUS_R4 = 57;
49 enum RADIUS_R5 = 17;
50 
51 /* cache variables */
52 static double cJD = 0.0, cL = 0.0, cB = 0.0, cR = 0.0;
53 
54 
55 static const ln_vsop[LONG_L0] mars_longitude_l0 = [
56     {     6.20347711581,  0.00000000000,        0.00000000000},
57     {     0.18656368093,  5.05037100270,     3340.61242669980},
58     {     0.01108216816,  5.40099836344,     6681.22485339960},
59     {     0.00091798406,  5.75478744667,    10021.83728009940},
60     {     0.00027744987,  5.97049513147,        3.52311834900},
61     {     0.00010610235,  2.93958560338,     2281.23049651060},
62     {     0.00012315897,  0.84956094002,     2810.92146160520},
63     {     0.00008926784,  4.15697846427,        0.01725365220},
64     {     0.00008715691,  6.11005153139,    13362.44970679920},
65     {     0.00006797556,  0.36462229657,      398.14900340820},
66     {     0.00007774872,  3.33968761376,     5621.84292321040},
67     {     0.00003575078,  1.66186505710,     2544.31441988340},
68     {     0.00004161108,  0.22814971327,     2942.46342329160},
69     {     0.00003075252,  0.85696614132,      191.44826611160},
70     {     0.00002628117,  0.64806124465,     3337.08930835080},
71     {     0.00002937546,  6.07893711402,        0.06731030280},
72     {     0.00002389414,  5.03896442664,      796.29800681640},
73     {     0.00002579844,  0.02996736156,     3344.13554504880},
74     {     0.00001528141,  1.14979301996,     6151.53388830500},
75     {     0.00001798806,  0.65634057445,      529.69096509460},
76     {     0.00001264357,  3.62275122593,     5092.15195811580},
77     {     0.00001286228,  3.06796065034,     2146.16541647520},
78     {     0.00001546404,  2.91579701718,     1751.53953141600},
79     {     0.00001024902,  3.69334099279,     8962.45534991020},
80     {     0.00000891566,  0.18293837498,    16703.06213349900},
81     {     0.00000858759,  2.40093811940,     2914.01423582380},
82     {     0.00000832715,  2.46418619474,     3340.59517304760},
83     {     0.00000832720,  4.49495782139,     3340.62968035200},
84     {     0.00000712902,  3.66335473479,     1059.38193018920},
85     {     0.00000748723,  3.82248614017,      155.42039943420},
86     {     0.00000723861,  0.67497311481,     3738.76143010800},
87     {     0.00000635548,  2.92182225127,     8432.76438481560},
88     {     0.00000655162,  0.48864064125,     3127.31333126180},
89     {     0.00000550474,  3.81001042328,        0.98032106820},
90     {     0.00000552750,  4.47479317037,     1748.01641306700},
91     {     0.00000425966,  0.55364317304,     6283.07584999140},
92     {     0.00000415131,  0.49662285038,      213.29909543800},
93     {     0.00000472167,  3.62547124025,     1194.44701022460},
94     {     0.00000306551,  0.38052848348,     6684.74797174860},
95     {     0.00000312141,  0.99853944405,     6677.70173505060},
96     {     0.00000293198,  4.22131299634,       20.77539549240},
97     {     0.00000302375,  4.48618007156,     3532.06069281140},
98     {     0.00000274027,  0.54222167059,     3340.54511639700},
99     {     0.00000281079,  5.88163521788,     1349.86740965880},
100     {     0.00000231183,  1.28242156993,     3870.30339179440},
101     {     0.00000283602,  5.76885434940,     3149.16416058820},
102     {     0.00000236117,  5.75503217933,     3333.49887969900},
103     {     0.00000274033,  0.13372524985,     3340.67973700260},
104     {     0.00000299395,  2.78323740866,     6254.62666252360},
105     {     0.00000204162,  2.82133445874,     1221.84856632140},
106     {     0.00000238866,  5.37153646326,     4136.91043351620},
107     {     0.00000188648,  1.49104066040,     9492.14631500480},
108     {     0.00000221228,  3.50466812198,      382.89653222320},
109     {     0.00000179196,  1.00561962003,      951.71840625060},
110     {     0.00000172117,  0.43943649536,     5486.77784317500},
111     {     0.00000193118,  3.35716641911,        3.59042865180},
112     {     0.00000144304,  1.41874112114,      135.06508003540},
113     {     0.00000160016,  3.94857092451,     4562.46099302120},
114     {     0.00000174072,  2.41361337725,      553.56940284240},
115     {     0.00000130989,  4.04491134956,    12303.06777661000},
116     {     0.00000138243,  4.30145122848,        7.11354700080},
117     {     0.00000128062,  1.80665816220,     5088.62883976680},
118     {     0.00000139898,  3.32595559208,     2700.71514038580},
119     {     0.00000128105,  2.20807538189,     1592.59601363280},
120     {     0.00000116944,  3.12806863456,     7903.07341972100},
121     {     0.00000110378,  1.05194545948,      242.72860397400},
122     {     0.00000113481,  3.70070432339,     1589.07289528380},
123     {     0.00000100099,  3.24340223714,    11773.37681151540},
124     {     0.00000095594,  0.53950648295,    20043.67456019880},
125     {     0.00000098947,  4.84558326403,     6681.24210705180},
126     {     0.00000104542,  0.78532737699,     8827.39026987480},
127     {     0.00000084186,  3.98971116025,     4399.99435688900},
128     {     0.00000086928,  2.20183965407,    11243.68584642080},
129     {     0.00000071438,  2.80307223477,     3185.19202726560},
130     {     0.00000072095,  5.84669532401,     5884.92684658320},
131     {     0.00000073482,  2.18421190324,     8429.24126646660},
132     {     0.00000098946,  2.81481171439,     6681.20759974740},
133     {     0.00000068413,  2.73834597183,     2288.34404351140},
134     {     0.00000086747,  1.02091867465,     7079.37385680780},
135     {     0.00000065316,  2.68114882713,       28.44918746780},
136     {     0.00000083745,  3.20254912006,     4690.47983635860},
137     {     0.00000075031,  0.76647765061,     6467.92575796160},
138     {     0.00000068983,  3.76403440528,     6041.32756708560},
139     {     0.00000066706,  0.73630288873,     3723.50895892300},
140     {     0.00000063313,  4.52771850220,      426.59819087600},
141     {     0.00000061684,  6.16831461502,     2274.11694950980},
142     {     0.00000052260,  0.89938935091,     9623.68827669120},
143     {     0.00000055485,  4.60622447136,     4292.33083295040},
144     {     0.00000051331,  4.14823934301,     3341.59274776800},
145     {     0.00000056633,  5.06250402329,       15.25247118500},
146     {     0.00000063376,  0.91293637746,     3553.91152213780},
147     {     0.00000045822,  0.78790300125,     1990.74501704100},
148     {     0.00000048553,  3.95677994023,     4535.05943692440},
149     {     0.00000041223,  6.02013764154,     3894.18182954220},
150     {     0.00000041941,  3.58309124437,     8031.09226305840},
151     {     0.00000056395,  1.68727941626,     6872.67311951120},
152     {     0.00000055907,  3.46261441099,      263.08392337280},
153     {     0.00000051677,  2.81307639242,     3339.63210563160},
154     {     0.00000040669,  3.13838566327,     9595.23908922340},
155     {     0.00000038111,  0.73396370751,    10025.36039844840},
156     {     0.00000039498,  5.63225741360,     3097.88382272579},
157     {     0.00000044175,  3.19530118759,     5628.95647021120},
158     {     0.00000036718,  2.63750919104,      692.15760122680},
159     {     0.00000045905,  0.28717581576,     5614.72937620960},
160     {     0.00000038351,  5.82880639987,     3191.04922956520},
161     {     0.00000038198,  2.34832438823,      162.46663613220},
162     {     0.00000032561,  0.48401318272,     6681.29216370240},
163     {     0.00000037135,  0.68510839331,     2818.03500860600},
164     {     0.00000031169,  3.98160436995,       20.35531939880},
165     {     0.00000032561,  0.89250965753,     6681.15754309680},
166     {     0.00000037749,  4.15481250779,     2803.80791460440},
167     {     0.00000033626,  6.11997987693,     6489.77658728800},
168     {     0.00000029007,  2.42707198395,     3319.83703120740},
169     {     0.00000038794,  1.35194224244,    10018.31416175040},
170     {     0.00000033149,  1.14024195200,        5.52292430740},
171     {     0.00000027583,  1.59721760699,     7210.91581849420},
172     {     0.00000028699,  5.72047550940,     7477.52286021600},
173     {     0.00000034039,  2.59525636978,    11769.85369316640},
174     {     0.00000025380,  0.52092092633,       10.63666534980},
175     {     0.00000026355,  1.34519007001,     3496.03282613400},
176     {     0.00000024555,  4.00321315879,    11371.70468975820},
177     {     0.00000025637,  0.24963503109,      522.57741809380},
178     {     0.00000027275,  4.55649766071,     3361.38782219220},
179     {     0.00000023766,  1.84063759173,    12832.75874170460},
180     {     0.00000022814,  3.52628452806,     1648.44675719740},
181     {     0.00000022272,  0.72111173236,      266.60704172180},
182     {     0.00000021201,  3.11823578369,     2957.71589447660},
183     {     0.00000020156,  3.67147308710,     1758.65307841680},
184     {     0.00000021530,  6.15388673691,     3264.34635542420},
185     {     0.00000020090,  1.08241387913,     7064.12138562280},
186     {     0.00000021344,  4.28178434496,     4032.77002792660},
187     {     0.00000027541,  6.08386421472,     6674.11130639880},
188     {     0.00000019842,  2.37674123073,    10713.99488132620},
189     {     0.00000025518,  3.43241978555,     3443.70520091840},
190     {     0.00000022542,  5.64861441506,     2388.89402044920},
191     {     0.00000024376,  0.97006548518,      632.78373931320},
192     {     0.00000023079,  4.74990771219,     3347.72597370060},
193     {     0.00000017708,  3.69743280195,     3344.20285535160},
194     {     0.00000022658,  3.95447568336,     4989.05918389720},
195     {     0.00000022600,  5.24085203262,     3205.54734666440},
196     {     0.00000016811,  5.48619684184,        3.88133535800},
197     {     0.00000018422,  4.22550249103,     2787.04302385740},
198     {     0.00000022735,  4.98523942294,     7632.94325965020},
199     {     0.00000016638,  2.52822534159,    14584.29827312060},
200     {     0.00000020963,  4.27879531719,     5099.26550511660},
201     {     0.00000016033,  1.76789519365,     3475.67750673520},
202     {     0.00000015814,  3.13241857680,       59.37386191360},
203     {     0.00000018113,  3.25756742113,     3337.02199804800},
204     {     0.00000019295,  3.23912725911,        7.04623669800},
205     {     0.00000016777,  4.39731653353,    15643.68020330980},
206     {     0.00000017554,  4.09198247074,       74.78159856730},
207     {     0.00000013713,  2.54103541653,     4933.20844033260},
208     {     0.00000016007,  1.54673981973,    14054.60730802600},
209     {     0.00000014603,  3.45689862899,     7373.38245462640},
210     {     0.00000013547,  4.04141743525,     4929.68532198360},
211     {     0.00000014222,  0.59967781578,       23.87843774780},
212     {     0.00000013876,  5.40880274251,    10973.55568635000},
213     {     0.00000014026,  1.44210504015,    10404.73381232260},
214     {     0.00000016055,  3.79399064336,     2118.76386037840},
215     {     0.00000013717,  3.59037690181,    15113.98923821520},
216     {     0.00000018040,  4.25416134565,     2487.41604494780},
217     {     0.00000015846,  0.56902641445,      103.09277421860},
218     {     0.00000013402,  5.16918481175,    10213.28554621100},
219     {     0.00000016068,  2.36894092837,     3265.83082813250},
220     {     0.00000012773,  0.10474161940,     7234.79425624200},
221     {     0.00000012197,  1.73028863618,       36.02786667740},
222     {     0.00000012283,  5.19941258642,    10021.85453375160},
223     {     0.00000011947,  5.47980574430,     2921.12778282460},
224     {     0.00000011890,  4.76587196145,     5828.02847164760},
225     {     0.00000012283,  3.16864076359,    10021.82002644720},
226     {     0.00000013269,  6.17851484916,     1744.42598441520},
227     {     0.00000011749,  5.72731481869,        0.42007609361},
228     {     0.00000012340,  2.52148348822,     2906.90068882300},
229     {     0.00000014458,  4.38011275876,      316.39186965660},
230     {     0.00000010640,  3.44997335322,      639.89728631400},
231     {     0.00000010925,  0.60402475795,     5085.03841111500},
232     {     0.00000010646,  5.47663096745,      419.48464387520},
233     {     0.00000010795,  1.37204952026,    10419.98628350760},
234     {     0.00000010573,  1.09027262515,    12168.00269657460},
235     {     0.00000009578,  4.89483638811,     3230.40610548040},
236     {     0.00000009805,  5.83614893022,    14314.16811304980},
237     {     0.00000009718,  0.00011311901,     9225.53927328300},
238     {     0.00000009146,  1.10288559040,     9808.53818466140},
239     {     0.00000009779,  3.60055224203,      206.18554843720},
240     {     0.00000012732,  1.79880344270,    13745.34623902240},
241     {     0.00000012156,  4.42292535673,    14712.31711645800},
242     {     0.00000008805,  3.97132756722,      170.67287061920},
243     {     0.00000010682,  4.33907151559,     7740.60678358880},
244     {     0.00000010040,  1.38291942087,     3583.34103067380},
245     {     0.00000009961,  2.69116597350,       36.60536530420},
246     {     0.00000008473,  4.29275471153,        0.42988312670},
247     {     0.00000010584,  0.89643083679,    23384.28698689860},
248     {     0.00000009597,  4.33289499954,      131.54196168640},
249     {     0.00000008477,  2.86885079661,     9381.93999378540},
250     {     0.00000008436,  3.15234316178,     6525.80445396540},
251     {     0.00000007518,  1.24474332957,     6894.52394883760},
252     {     0.00000006746,  1.58828730801,     6836.64525283380},
253     {     0.00000006722,  4.38897665506,       66.48740891440},
254     {     0.00000006738,  5.77292945138,     5202.35827933520},
255     {     0.00000006243,  1.57847357313,     3325.35995551480},
256     {     0.00000008446,  2.90692880268,       43.71891230500},
257     {     0.00000006482,  6.03333628981,      574.34479833480},
258     {     0.00000006348,  0.06986409522,     1964.83862685400},
259     {     0.00000006193,  5.43709781754,     1861.74585263540},
260     {     0.00000008246,  0.44145777409,     2707.82868738660},
261     {     0.00000005987,  4.22748552841,     4459.36821880260},
262     {     0.00000006530,  1.24945509771,    12964.30070339100},
263     {     0.00000005949,  0.77228459543,     2699.73481931760},
264     {     0.00000007339,  4.95735130126,     3767.21061757580},
265     {     0.00000006135,  3.16322568315,     6680.24453233140},
266     {     0.00000006027,  3.01298246255,     3369.06161416760},
267     {     0.00000005857,  4.30341888951,     7875.67186362420},
268     {     0.00000006360,  1.77803516211,     2178.13772229200},
269     {     0.00000005771,  0.96116030741,    13916.01910964160},
270     {     0.00000006100,  4.49881794524,     6682.20517446780},
271     {     0.00000005777,  4.92993290350,     2384.32327072920},
272     {     0.00000007647,  6.16291591270,     6531.66165626500},
273     {     0.00000007242,  0.52885257496,    10575.40668294180},
274     {     0.00000005311,  4.51564606382,     6144.42034130420},
275     {     0.00000005212,  3.49017198482,    12935.85151592320},
276     {     0.00000006680,  3.48192412858,     1118.75579210280},
277     {     0.00000005226,  3.25464016223,     2391.43681773000},
278     {     0.00000005215,  0.01031380055,      533.21408344360},
279     {     0.00000005534,  3.42311181658,     3134.42687826260},
280     {     0.00000005437,  6.18510783147,     8425.65083781480},
281     {     0.00000005774,  3.55189251089,     8969.56889691100},
282     {     0.00000005093,  0.60862188744,     8955.34180290940},
283     {     0.00000004840,  4.63233532160,     4569.57454002200},
284     {     0.00000005828,  5.92311700172,      640.87760738220},
285     {     0.00000005686,  0.76212811066,     3120.19978426100},
286     {     0.00000004912,  1.70752765226,    13358.92658845020},
287     {     0.00000005490,  4.29423846802,     3503.07906283200},
288     {     0.00000004676,  3.34239248969,     3116.26763099790},
289     {     0.00000005858,  2.38460385828,     3302.47939106200},
290     {     0.00000005098,  1.12472834482,     5331.35744374080},
291     {     0.00000004412,  1.38574902846,    17256.63153634140},
292     {     0.00000004261,  1.69359026235,    13524.91634293140},
293     {     0.00000004191,  0.19115182648,     9830.38901398780},
294     {     0.00000004164,  0.43810126153,     1066.49547719000},
295     {     0.00000005192,  3.63498024808,      536.80451209540},
296     {     0.00000005664,  0.50444427941,     5305.45105355380},
297     {     0.00000005477,  5.96812391483,     3074.00538497800},
298     {     0.00000005303,  5.40010329848,     3355.86489788480},
299     {     0.00000004043,  0.83846792979,    10021.90459040220},
300     {     0.00000004153,  3.14489443759,     8439.87793181640},
301     {     0.00000004818,  1.08987352671,    13365.97282514820},
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1377     {     0.00000000045,  2.28393936160,    22986.13798349040},
1378     {     0.00000000049,  2.14605615000,    19830.37546476080},
1379     {     0.00000000047,  4.12536462391,    23009.94911093539},
1380     {     0.00000000049,  5.16525026592,     3774.32416457660},
1381     {     0.00000000045,  3.89882558892,    12988.11183083600},
1382     {     0.00000000048,  4.74927850843,      529.67371144240},
1383     {     0.00000000055,  4.19502260708,    20043.65730654660},
1384     {     0.00000000057,  1.14903860224,     7747.72033058960},
1385     {     0.00000000044,  0.79186614799,    26357.67508463600},
1386     {     0.00000000044,  3.13459824792,    13951.51453380740},
1387     {     0.00000000043,  2.23439626313,     1987.22189869200},
1388     {     0.00000000058,  2.28159262648,    10006.58480891440},
1389     {     0.00000000046,  0.16036583144,    18763.87998757080},
1390     {     0.00000000045,  1.72302046270,    17402.33328172660},
1391     {     0.00000000043,  5.75831854990,    25298.29315444680},
1392     {     0.00000000047,  5.27437932280,      423.07507252700},
1393     {     0.00000000060,  3.50233382826,     6511.64467026660},
1394     {     0.00000000043,  1.82217346876,    10017.95594474140},
1395     {     0.00000000049,  4.64906795465,     6251.10354417460},
1396     {     0.00000000042,  5.31789294983,    11368.18157140920},
1397     {     0.00000000048,  0.49685981802,      529.70821874680},
1398     {     0.00000000051,  0.63985050945,    17499.36014031540},
1399     {     0.00000000048,  0.19901251387,     1905.46476494040},
1400     {     0.00000000055,  1.08536866814,     1059.36467653700},
1401     {     0.00000000056,  4.31837960167,    13358.85927814740},
1402     {     0.00000000046,  3.71161153699,     8958.52319664710},
1403     {     0.00000000042,  3.41202446638,     7788.36365908440},
1404     {     0.00000000050,  2.27112469625,     3427.92063123960},
1405     {     0.00000000055,  5.25814691818,    12808.88030395680},
1406     {     0.00000000048,  0.28684868478,    11935.84344764760},
1407     {     0.00000000050,  0.30214747846,     3358.42494881780},
1408     {     0.00000000043,  5.05297177364,     3229.42578441220},
1409     {     0.00000000041,  4.11754654123,     6553.20601006220},
1410     {     0.00000000043,  1.90603004116,     3451.79906898740},
1411     {     0.00000000046,  4.45432031146,     3707.83675566220},
1412     {     0.00000000041,  2.88427064230,      927.83996850280},
1413     {     0.00000000040,  5.10715968924,    14715.84023480700},
1414     {     0.00000000050,  5.23088101452,     2373.64154926420},
1415     {     0.00000000039,  3.58038785427,     9124.92198604240},
1416     {     0.00000000052,  4.06208791228,    17660.30346405700},
1417     {     0.00000000043,  0.22819734412,    10025.71861545740},
1418     {     0.00000000040,  2.65434458508,     3341.79306935190},
1419     {     0.00000000049,  5.40078097720,    17762.44406368820},
1420     {     0.00000000039,  0.41453755531,     5096.08411137890},
1421     {     0.00000000052,  2.59285184666,     2538.24850425360},
1422     {     0.00000000045,  4.19179574727,    37057.57749256620},
1423     {     0.00000000043,  4.02858922778,     6258.14978087260},
1424     {     0.00000000041,  1.71920640714,    10507.80933288900},
1425     {     0.00000000038,  2.11769718484,     8123.48606215980},
1426     {     0.00000000049,  2.41908302484,    20441.82356360700},
1427     {     0.00000000046,  3.05701386187,     2324.94940881560},
1428     {     0.00000000045,  5.57751456016,    15423.26756087100},
1429     {     0.00000000040,  2.80315795515,     7520.19414115000},
1430     {     0.00000000050,  3.42753416123,    52566.19261584059},
1431     {     0.00000000049,  2.11653605140,    22189.83997667400},
1432     {     0.00000000043,  3.04326197275,    41592.63692949060},
1433     {     0.00000000039,  3.58098532394,      867.93366407760},
1434     {     0.00000000040,  3.20381465754,    29428.51556827400},
1435     {     0.00000000038,  3.65843764774,    13341.67431130680},
1436     {     0.00000000037,  3.99759212306,    12725.45343477500},
1437     {     0.00000000042,  4.13817253189,     8336.78515759780},
1438     {     0.00000000038,  0.58099499580,     8966.38750317330},
1439     {     0.00000000049,  2.27415271613,     3123.79021291280},
1440     {     0.00000000037,  3.14802303104,     5466.42252377620},
1441     {     0.00000000046,  1.23573182695,    11787.60390551700},
1442     {     0.00000000037,  5.60013944614,     8123.50331581200},
1443     {     0.00000000039,  2.12359970883,    23387.81010524760},
1444     {     0.00000000037,  5.00181395644,    17810.20093918380},
1445     {     0.00000000038,  6.00950016545,     4295.85395129940},
1446     {     0.00000000040,  6.05295156557,     6151.55114195720},
1447     {     0.00000000036,  0.42674900890,     9997.95884235160},
1448     {     0.00000000044,  4.13342515647,    12192.86145539060},
1449     {     0.00000000037,  2.57249437155,     9815.13654280280},
1450     {     0.00000000036,  0.30459710615,    10618.01565410840},
1451     {     0.00000000039,  1.53352233747,     6683.97636401060},
1452     {     0.00000000050,  5.87136225569,     4396.47123854000},
1453     {     0.00000000040,  4.58209614492,     8294.17618643120},
1454     {     0.00000000036,  3.26497387820,    16269.35039562219},
1455     {     0.00000000040,  4.17543231683,     9962.46341818580},
1456     {     0.00000000036,  1.95918123970,      360.11078196160},
1457     {     0.00000000038,  2.38454082948,    24093.27678917520},
1458     {     0.00000000036,  2.85429847882,     6549.68289171320},
1459     {     0.00000000038,  3.54096291728,    19683.56377823720},
1460     {     0.00000000037,  3.74762124247,     1045.15483618760},
1461     {     0.00000000043,  5.45850357191,    17608.51883016380},
1462     {     0.00000000039,  5.88001746710,     4709.27267954480},
1463     {     0.00000000040,  4.23855320433,     3339.43178404770},
1464     {     0.00000000042,  3.73781410726,     7593.79509706520},
1465 ];
1466 
1467 
1468 static const ln_vsop[LONG_L1] mars_longitude_l1 = [
1469     {  3340.61242700512,  0.00000000000,        0.00000000000},
1470     {     0.01457554523,  3.60433733236,     3340.61242669980},
1471     {     0.00168414711,  3.92318567804,     6681.22485339960},
1472     {     0.00020622975,  4.26108844583,    10021.83728009940},
1473     {     0.00003452392,  4.73210393190,        3.52311834900},
1474     {     0.00002586332,  4.60670058555,    13362.44970679920},
1475     {     0.00000841535,  4.45864030426,     2281.23049651060},
1476     {     0.00000537567,  5.01581256923,      398.14900340820},
1477     {     0.00000520948,  4.99428054039,     3344.13554504880},
1478     {     0.00000432635,  2.56070853083,      191.44826611160},
1479     {     0.00000429655,  5.31645299471,      155.42039943420},
1480     {     0.00000381751,  3.53878166043,      796.29800681640},
1481     {     0.00000328530,  4.95632685192,    16703.06213349900},
1482     {     0.00000282795,  3.15966768785,     2544.31441988340},
1483     {     0.00000205657,  4.56889279932,     2146.16541647520},
1484     {     0.00000168866,  1.32936559060,     3337.08930835080},
1485     {     0.00000157593,  4.18519540728,     1751.53953141600},
1486     {     0.00000133686,  2.23327245555,        0.98032106820},
1487     {     0.00000116965,  2.21414273762,     1059.38193018920},
1488     {     0.00000117503,  6.02411290806,     6151.53388830500},
1489     {     0.00000113718,  5.42753341019,     3738.76143010800},
1490     {     0.00000133565,  5.97420357518,     1748.01641306700},
1491     {     0.00000091099,  1.09626613064,     1349.86740965880},
1492     {     0.00000084256,  5.29330740437,     6684.74797174860},
1493     {     0.00000113886,  2.12863726524,     1194.44701022460},
1494     {     0.00000080823,  4.42818326716,      529.69096509460},
1495     {     0.00000079847,  2.24822372859,     8962.45534991020},
1496     {     0.00000072505,  5.84203374239,      242.72860397400},
1497     {     0.00000072945,  2.50193599662,      951.71840625060},
1498     {     0.00000071490,  3.85645759558,     2914.01423582380},
1499     {     0.00000085340,  3.90856932983,      553.56940284240},
1500     {     0.00000067580,  5.02334895070,      382.89653222320},
1501     {     0.00000065060,  1.01810963274,     3340.59517304760},
1502     {     0.00000065061,  3.04888114328,     3340.62968035200},
1503     {     0.00000061478,  4.15185188249,     3149.16416058820},
1504     {     0.00000048482,  4.87339233007,      213.29909543800},
1505     {     0.00000046581,  1.31461442691,     3185.19202726560},
1506     {     0.00000056642,  3.88772102421,     4136.91043351620},
1507     {     0.00000047615,  1.18228660215,     3333.49887969900},
1508     {     0.00000042052,  5.30826745759,    20043.67456019880},
1509     {     0.00000041330,  0.71392238704,     1592.59601363280},
1510     {     0.00000040280,  2.72571311592,        7.11354700080},
1511     {     0.00000033040,  5.40823104809,     6283.07584999140},
1512     {     0.00000028676,  0.04305323493,     9492.14631500480},
1513     {     0.00000022322,  5.86718681699,     3870.30339179440},
1514     {     0.00000022432,  5.46596961275,       20.35531939880},
1515     {     0.00000022606,  0.83782540818,     3097.88382272579},
1516     {     0.00000021416,  5.37936489667,     3340.54511639700},
1517     {     0.00000023347,  6.16774433900,     3532.06069281140},
1518     {     0.00000026573,  3.89000631130,     1221.84856632140},
1519     {     0.00000022800,  1.54501542908,     2274.11694950980},
1520     {     0.00000020474,  2.36236861670,     1589.07289528380},
1521     {     0.00000020179,  3.36390759347,     5088.62883976680},
1522     {     0.00000020013,  2.57546546037,    12303.06777661000},
1523     {     0.00000019920,  0.44761063096,     6677.70173505060},
1524     {     0.00000026550,  5.11303525089,     2700.71514038580},
1525     {     0.00000021104,  3.52541056271,       15.25247118500},
1526     {     0.00000021424,  4.97083417225,     3340.67973700260},
1527     {     0.00000018502,  5.57854926842,     1990.74501704100},
1528     {     0.00000017805,  6.12513609945,     4292.33083295040},
1529     {     0.00000016463,  2.60307709195,     3341.59274776800},
1530     {     0.00000016592,  1.25515357212,     3894.18182954220},
1531     {     0.00000019864,  2.52765519587,     4399.99435688900},
1532     {     0.00000015002,  1.03518790208,     2288.34404351140},
1533     {     0.00000020011,  4.73112374598,     4690.47983635860},
1534     {     0.00000015431,  2.46932776517,     4535.05943692440},
1535     {     0.00000020193,  5.78561467842,     7079.37385680780},
1536     {     0.00000015298,  2.26504738206,     3723.50895892300},
1537     {     0.00000015019,  3.36690751539,     6681.24210705180},
1538     {     0.00000013219,  5.61412860968,    10025.36039844840},
1539     {     0.00000013517,  2.12392880454,     5486.77784317500},
1540     {     0.00000015019,  1.33613594479,     6681.20759974740},
1541     {     0.00000012676,  2.95036175206,     3496.03282613400},
1542     {     0.00000013644,  1.97710249337,     5614.72937620960},
1543     {     0.00000013011,  1.51458564766,     5628.95647021120},
1544     {     0.00000011353,  6.23411904718,      135.06508003540},
1545     {     0.00000013508,  3.42721826602,     5621.84292321040},
1546     {     0.00000010866,  5.28165480979,     2818.03500860600},
1547     {     0.00000011880,  3.12847055823,      426.59819087600},
1548     {     0.00000010467,  2.73598607050,     2787.04302385740},
1549     {     0.00000011131,  5.84122566289,     2803.80791460440},
1550     {     0.00000011770,  2.58277425311,     8432.76438481560},
1551     {     0.00000011861,  5.47552055459,     3553.91152213780},
1552     {     0.00000008540,  1.91739325491,    11773.37681151540},
1553     {     0.00000009819,  4.52958330672,     6489.77658728800},
1554     {     0.00000008552,  3.16147568714,      162.46663613220},
1555     {     0.00000010957,  4.15775327007,     2388.89402044920},
1556     {     0.00000008948,  4.23164385777,     7477.52286021600},
1557     {     0.00000008131,  1.61308074119,     2957.71589447660},
1558     {     0.00000008352,  2.18475645206,       23.87843774780},
1559     {     0.00000008030,  5.69889507906,     6041.32756708560},
1560     {     0.00000007878,  5.71359767892,     9623.68827669120},
1561     {     0.00000008713,  4.43300582398,     5092.15195811580},
1562     {     0.00000008421,  3.16355067250,     3347.72597370060},
1563     {     0.00000006670,  5.07423317095,     8031.09226305840},
1564     {     0.00000008656,  4.33239148117,     3339.63210563160},
1565     {     0.00000007354,  6.17934256606,     3583.34103067380},
1566     {     0.00000005749,  3.67719823582,     8429.24126646660},
1567     {     0.00000006235,  3.54003325209,      692.15760122680},
1568     {     0.00000005458,  1.05139431657,     4933.20844033260},
1569     {     0.00000006132,  1.66182646558,     6525.80445396540},
1570     {     0.00000005197,  1.14841109166,       28.44918746780},
1571     {     0.00000004950,  5.28919125231,     6681.29216370240},
1572     {     0.00000005516,  6.12492946392,     2487.41604494780},
1573     {     0.00000004890,  3.10255139433,        5.52292430740},
1574     {     0.00000005354,  0.37154896863,    12832.75874170460},
1575     {     0.00000004751,  0.23374681550,       36.02786667740},
1576     {     0.00000006362,  2.11339432269,     5884.92684658320},
1577     {     0.00000004996,  2.44835744792,     5099.26550511660},
1578     {     0.00000004952,  5.69770765577,     6681.15754309680},
1579     {     0.00000004678,  0.27799012787,    10018.31416175040},
1580     {     0.00000004746,  0.00950199989,     7210.91581849420},
1581     {     0.00000004862,  5.60331599025,     6467.92575796160},
1582     {     0.00000005544,  2.00929051393,      522.57741809380},
1583     {     0.00000004998,  1.51094959078,     1744.42598441520},
1584     {     0.00000005397,  0.18842154970,     2942.46342329160},
1585     {     0.00000004098,  3.95776844736,        3.88133535800},
1586     {     0.00000005414,  5.66147396313,    23384.28698689860},
1587     {     0.00000005467,  0.19258681316,     7632.94325965020},
1588     {     0.00000004305,  2.89452294830,     2810.92146160520},
1589     {     0.00000004118,  1.59475420886,     7234.79425624200},
1590     {     0.00000004489,  4.16951490492,     2906.90068882300},
1591     {     0.00000005277,  2.22681020305,     3127.31333126180},
1592     {     0.00000003882,  2.26433789475,     2699.73481931760},
1593     {     0.00000003544,  1.76658498504,     1758.65307841680},
1594     {     0.00000003408,  2.65743533541,     4929.68532198360},
1595     {     0.00000004336,  4.43081904792,      640.87760738220},
1596     {     0.00000003804,  2.91373968131,    15643.68020330980},
1597     {     0.00000003176,  1.75893480952,     9595.23908922340},
1598     {     0.00000003309,  6.13831291678,    10419.98628350760},
1599     {     0.00000003077,  2.56194751001,     7064.12138562280},
1600     {     0.00000003236,  2.32387839882,     5085.03841111500},
1601     {     0.00000003284,  2.86216479710,     7740.60678358880},
1602     {     0.00000002958,  1.27767445188,      574.34479833480},
1603     {     0.00000002805,  0.43144651568,     5828.02847164760},
1604     {     0.00000002851,  0.98625869565,     3191.04922956520},
1605     {     0.00000003324,  2.59010987850,     2118.76386037840},
1606     {     0.00000003039,  1.86739127757,        7.04623669800},
1607     {     0.00000002738,  1.76460911547,      639.89728631400},
1608     {     0.00000002757,  3.70511041849,    10021.85453375160},
1609     {     0.00000003376,  1.53123149565,     6674.11130639880},
1610     {     0.00000002757,  1.67433972403,    10021.82002644720},
1611     {     0.00000002670,  3.11556212899,     6836.64525283380},
1612     {     0.00000002583,  3.77302627584,     2921.12778282460},
1613     {     0.00000002510,  0.30461555756,     3475.67750673520},
1614     {     0.00000002288,  2.81266012379,     7875.67186362420},
1615     {     0.00000002411,  0.97123911611,     3319.83703120740},
1616     {     0.00000002410,  2.95969382172,     6682.20517446780},
1617     {     0.00000002211,  0.61268074323,    10973.55568635000},
1618     {     0.00000002246,  4.12573972297,       59.37386191360},
1619     {     0.00000002183,  2.17530786579,    15113.98923821520},
1620     {     0.00000002445,  5.91435376684,     5331.35744374080},
1621     {     0.00000001944,  5.47623245699,    11371.70468975820},
1622     {     0.00000002390,  3.87952069289,     3355.86489788480},
1623     {     0.00000001904,  5.11178589044,     1066.49547719000},
1624     {     0.00000002302,  1.15940039520,     3320.25710730100},
1625     {     0.00000001955,  5.88703346758,     6894.52394883760},
1626     {     0.00000001837,  3.07635198966,     3325.35995551480},
1627     {     0.00000002131,  2.99610007510,     6254.62666252360},
1628     {     0.00000001807,  4.98332871905,     1648.44675719740},
1629     {     0.00000002133,  1.91321292871,     8969.56889691100},
1630     {     0.00000001936,  3.55090266368,     3767.21061757580},
1631     {     0.00000001989,  5.37314833955,      206.18554843720},
1632     {     0.00000001674,  5.49537183178,      266.60704172180},
1633     {     0.00000001732,  1.81246269542,      536.80451209540},
1634     {     0.00000001645,  1.32190162152,     3264.34635542420},
1635     {     0.00000001715,  3.25682611470,     7903.07341972100},
1636     {     0.00000001560,  5.75414697537,     3360.96774609859},
1637     {     0.00000001581,  1.72981711161,     3134.42687826260},
1638     {     0.00000001498,  4.89621878281,     9830.38901398780},
1639     {     0.00000001549,  5.85472144829,       20.77539549240},
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1979     {     0.00000000088,  2.39227137305,     1062.90504853820},
1980     {     0.00000000104,  4.99513842450,     1581.95934828300},
1981     {     0.00000000081,  5.89798943131,    16858.41522263039},
1982     {     0.00000000082,  0.44163602941,     4782.87363546000},
1983     {     0.00000000106,  2.50029020488,     5401.43028077160},
1984     {     0.00000000086,  3.61631911304,     8965.97846825920},
1985     {     0.00000000087,  5.68212398189,     1883.08149310240},
1986     {     0.00000000095,  5.35237938692,     4996.17273089800},
1987     {     0.00000000079,  2.01092788145,     1329.51209026000},
1988     {     0.00000000078,  0.88224980818,     2171.02417529120},
1989     {     0.00000000105,  2.37775757409,     9638.94074787620},
1990     {     0.00000000089,  5.33260517891,     2125.87740737920},
1991     {     0.00000000076,  5.20798256417,     9872.27408296480},
1992     {     0.00000000083,  0.03796627991,    16703.12944380180},
1993     {     0.00000000075,  6.26330392154,    27682.14074415640},
1994     {     0.00000000090,  4.84737761448,    14071.43950907579},
1995     {     0.00000000094,  4.89545753204,     9389.05354078620},
1996     {     0.00000000077,  0.03584521510,    20206.14119633100},
1997     {     0.00000000095,  5.93429183368,    13362.51701710200},
1998     {     0.00000000081,  1.00694559686,    16865.52876963120},
1999     {     0.00000000077,  4.12929175062,     4005.36847182980},
2000     {     0.00000000082,  1.47379060963,       16.83220104979},
2001     {     0.00000000073,  4.59130182630,      362.12113673080},
2002     {     0.00000000074,  3.60955612323,    25685.87280280800},
2003     {     0.00000000084,  2.71424539413,    19617.07636932279},
2004     {     0.00000000072,  0.01101776823,     3568.08855948880},
2005     {     0.00000000071,  1.71603072644,     2060.81785407180},
2006     {     0.00000000072,  1.89061725205,    18451.07854656599},
2007     {     0.00000000071,  3.22816907346,     3472.15438838620},
2008     {     0.00000000076,  0.30413402871,       72.05573335480},
2009     {     0.00000000070,  3.17652165983,     3448.27595063840},
2010     {     0.00000000077,  3.14666622167,    39601.89191244960},
2011     {     0.00000000071,  0.33254450188,    23141.55838292460},
2012     {     0.00000000074,  0.10153043438,    17402.33328172660},
2013     {     0.00000000090,  0.67485041721,      949.17560896980},
2014     {     0.00000000096,  1.02302727880,     4106.40549114620},
2015     {     0.00000000095,  5.15356240747,        1.48447270830},
2016     {     0.00000000067,  1.00856695957,    17232.75309859360},
2017     {     0.00000000068,  1.78474324075,      224.34479570190},
2018     {     0.00000000077,  0.15786375115,    16066.06586147480},
2019     {     0.00000000066,  1.10881345668,     4459.36821880260},
2020     {     0.00000000067,  2.14790314493,     6357.71943674220},
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2168     {     0.00000000055,  4.41207846373,    14712.31711645800},
2169     {     0.00000000043,  1.28825253886,     6643.09181776180},
2170     {     0.00000000047,  4.72697589436,     6666.99775939800},
2171     {     0.00000000041,  1.62359144351,    24491.42579258340},
2172     {     0.00000000041,  0.08345338645,    12839.87228870540},
2173     {     0.00000000043,  3.96439822837,     7696.88787128380},
2174     {     0.00000000044,  0.86899972844,    17388.10618772499},
2175     {     0.00000000040,  3.10894579374,    34554.81386366760},
2176     {     0.00000000056,  5.61583520495,    16511.61386738740},
2177     {     0.00000000052,  3.11577112744,     1162.47470440780},
2178     {     0.00000000055,  5.48941084697,    18208.34994259200},
2179     {     0.00000000050,  1.65058020951,    11614.43329373220},
2180     {     0.00000000039,  4.21787836291,     4186.69526145100},
2181     {     0.00000000039,  2.66514604756,     7218.02936549500},
2182     {     0.00000000046,  0.66730374401,     3113.13629391080},
2183     {     0.00000000039,  0.15854793246,    48300.16010269000},
2184     {     0.00000000041,  5.70248947899,     6106.88005506480},
2185     {     0.00000000040,  4.05255896019,    19406.67828817460},
2186     {     0.00000000040,  4.77396367544,    42544.35533574120},
2187     {     0.00000000053,  3.15301214737,      183.86958690200},
2188     {     0.00000000039,  0.51075209632,    17810.20093918380},
2189     {     0.00000000039,  1.62656815590,     9947.05568153210},
2190     {     0.00000000040,  5.62692686678,    26880.31981303260},
2191     {     0.00000000038,  4.59191939331,    10037.08975128440},
2192     {     0.00000000038,  3.66575761860,     6997.61672305620},
2193     {     0.00000000045,  6.15994065455,     3289.33208883739},
2194     {     0.00000000041,  2.77511547733,    16328.72425753579},
2195     {     0.00000000038,  1.43009196037,    10787.63034454580},
2196     {     0.00000000044,  3.57766817797,    14556.89671702380},
2197     {     0.00000000042,  2.92470448863,     4025.72379122860},
2198     {     0.00000000036,  5.66533524812,     3511.28529731900},
2199     {     0.00000000046,  5.30655793995,    17499.36014031540},
2200     {     0.00000000045,  4.15997441733,       36.99559061100},
2201     {     0.00000000037,  3.97235274323,        7.76267071600},
2202     {     0.00000000042,  2.12026198801,    14128.24277124560},
2203     {     0.00000000036,  2.75306774319,     3450.81874791920},
2204     {     0.00000000039,  1.63389094852,     1545.35398297880},
2205     {     0.00000000042,  5.03809379637,    31968.94865279940},
2206     {     0.00000000037,  1.41975087808,     7447.01791784600},
2207     {     0.00000000039,  5.00412653703,     2540.79130153440},
2208     {     0.00000000043,  4.22348706116,    13369.56325380000},
2209     {     0.00000000036,  0.53048140495,      176.69373013380},
2210     {     0.00000000035,  2.25519417749,    19669.33668423559},
2211     {     0.00000000041,  0.69504492745,     3495.96551583120},
2212     {     0.00000000036,  5.24607321878,     2679.37949991880},
2213     {     0.00000000038,  3.14212980126,    30220.93223973240},
2214     {     0.00000000037,  5.40231426955,     3152.68727893721},
2215     {     0.00000000036,  1.04457226935,    20426.57109242200},
2216     {     0.00000000035,  0.32478189872,     3499.55594448300},
2217     {     0.00000000048,  2.09368659974,    32920.66705904999},
2218     {     0.00000000036,  2.63906375223,     8948.22825590860},
2219     {     0.00000000036,  5.56218018463,     7788.36365908440},
2220     {     0.00000000041,  0.34392346712,    13575.74880223720},
2221     {     0.00000000035,  5.11595749110,     7322.10246078180},
2222     {     0.00000000035,  5.54490491000,     9945.57120882380},
2223     {     0.00000000041,  2.83917412143,     3347.29609057390},
2224     {     0.00000000041,  4.06132121378,     3929.67725370800},
2225     {     0.00000000043,  4.03006170081,    38086.87455647900},
2226     {     0.00000000035,  3.14536502087,    24150.08005134500},
2227     {     0.00000000036,  3.31106643723,     9329.67967887260},
2228     {     0.00000000035,  4.64515512748,     9886.77220006400},
2229     {     0.00000000044,  1.03765557298,    20040.15144184979},
2230     {     0.00000000046,  0.52431064900,    28230.18722269139},
2231     {     0.00000000044,  4.61169478741,     3341.03250279340},
2232     {     0.00000000034,  2.95014695560,     6652.77566593180},
2233     {     0.00000000033,  2.51023857323,     2675.85638156980},
2234     {     0.00000000033,  3.62122540203,     6674.17861670160},
2235     {     0.00000000033,  3.87873599689,    25665.51748340920},
2236     {     0.00000000035,  0.31892534784,     6645.19698672220},
2237     {     0.00000000039,  0.38844155951,    18849.22754997420},
2238     {     0.00000000031,  3.42450440874,     4403.51747523800},
2239     {     0.00000000032,  1.28727861900,     9495.66943335380},
2240     {     0.00000000037,  2.68901627056,     7321.12213971360},
2241     {     0.00000000030,  3.11091269619,     9993.38809263160},
2242     {     0.00000000032,  3.56378902470,     6148.01076995600},
2243     {     0.00000000032,  4.23069713034,    10448.43547097540},
2244     {     0.00000000038,  4.21359344480,     3312.16323923200},
2245     {     0.00000000036,  0.26736453929,    36659.42848915800},
2246     {     0.00000000031,  1.91001170906,    31172.65064598300},
2247     {     0.00000000030,  1.79692038909,    10001.48196070061},
2248     {     0.00000000037,  5.48379757539,     3311.18291816379},
2249     {     0.00000000038,  2.88322299393,    10025.42770875120},
2250     {     0.00000000035,  5.38142679524,     3185.25933756840},
2251     {     0.00000000031,  0.35494900654,    10177.19036923080},
2252     {     0.00000000029,  1.34098342476,    29822.78323632420},
2253     {     0.00000000030,  1.39448996174,     4825.54491639400},
2254     {     0.00000000031,  2.46180759992,    10018.24685144760},
2255     {     0.00000000032,  0.41003961929,     3451.79906898740},
2256     {     0.00000000028,  4.68714611901,     2111.65031337760},
2257     {     0.00000000029,  3.94252949224,    23958.63178523340},
2258     {     0.00000000028,  3.38078853114,    32124.36905223359},
2259     {     0.00000000031,  3.18465833136,     3341.04230982650},
2260     {     0.00000000029,  2.25225231358,    26084.02180621620},
2261     {     0.00000000033,  3.49105794187,     3774.32416457660},
2262     {     0.00000000033,  1.71768192600,    34911.41207609100},
2263     {     0.00000000037,  5.42512626922,    31022.75317085620},
2264     {     0.00000000027,  0.98751632143,    16335.83780453660},
2265     {     0.00000000027,  5.29268187817,    29698.28751133580},
2266     {     0.00000000030,  5.45398309970,     8646.06348025360},
2267     {     0.00000000029,  0.21596596499,    20213.25474333179},
2268     {     0.00000000027,  2.67440637509,    16547.64173406480},
2269     {     0.00000000027,  2.31773999101,     6688.27109009760},
2270     {     0.00000000026,  2.05025380662,     5562.46906129680},
2271     {     0.00000000026,  3.28284041047,     2075.04494807340},
2272     {     0.00000000026,  5.00342153930,    48429.28218232440},
2273     {     0.00000000026,  3.79854522408,    12306.59089495900},
2274     {     0.00000000026,  1.89599447067,    13341.67431130680},
2275     {     0.00000000035,  1.72244330701,    24606.13555322000},
2276     {     0.00000000026,  4.44769438876,    10016.31435579200},
2277     {     0.00000000027,  0.93597359176,    13605.17831077320},
2278     {     0.00000000026,  5.00365698783,    13355.33615979840},
2279     {     0.00000000031,  6.27193804892,     1485.98012106520},
2280     {     0.00000000035,  0.76911517486,     6155.05700665400},
2281     {     0.00000000027,  1.27122182637,     6364.83298374300},
2282     {     0.00000000026,  5.55897683200,    20597.24396304120},
2283     {     0.00000000025,  6.22235600230,     5223.69391980220},
2284     {     0.00000000034,  3.38467726966,     2284.75361485960},
2285     {     0.00000000031,  0.88233421548,     3340.18254357310},
2286     {     0.00000000025,  0.83746118261,    12725.45343477500},
2287     {     0.00000000027,  5.67024059955,     1478.86657406440},
2288     {     0.00000000027,  0.42473501075,    33406.12426699800},
2289     {     0.00000000026,  2.15914082099,     3987.62326001460},
2290     {     0.00000000025,  2.91073064727,     3212.59358336240},
2291     {     0.00000000027,  4.12996350734,    13383.22510229160},
2292     {     0.00000000027,  6.05316799952,    13286.18363552360},
2293     {     0.00000000027,  5.81931319013,    24341.52831745660},
2294     {     0.00000000029,  4.41519700273,    16894.51039961060},
2295     {     0.00000000024,  0.20360604382,     3229.42578441220},
2296     {     0.00000000024,  2.10152754634,    14955.04572043200},
2297     {     0.00000000031,  5.90226054729,    11128.97608578420},
2298     {     0.00000000023,  3.37817298437,     6850.80503653260},
2299     {     0.00000000031,  0.35678160238,    31570.79964939120},
2300     {     0.00000000023,  2.38961518808,    23024.17620493700},
2301     {     0.00000000029,  3.03470840975,    22747.29071487440},
2302     {     0.00000000026,  0.51379054479,    29978.20363575840},
2303     {     0.00000000023,  4.26635202793,     3296.89351439480},
2304     {     0.00000000027,  2.64320191197,    24093.27678917520},
2305     {     0.00000000023,  4.96777735461,      799.82112516540},
2306     {     0.00000000024,  3.32945091041,    12140.60114047780},
2307     {     0.00000000025,  3.30212831704,     6740.59871531320},
2308     {     0.00000000023,  5.51381740402,    33561.54466643220},
2309     {     0.00000000023,  0.28172423109,     6593.91664885980},
2310     {     0.00000000022,  5.48861732897,    30376.35263916660},
2311     {     0.00000000023,  2.40580065766,     3344.11829139661},
2312     {     0.00000000028,  5.87506884260,     7747.72033058960},
2313     {     0.00000000021,  2.40354177453,     3304.00706139560},
2314     {     0.00000000024,  1.63482389429,     7483.58877584580},
2315     {     0.00000000028,  1.56312692708,    43340.65334255760},
2316     {     0.00000000022,  5.32476938106,    12928.73796892240},
2317     {     0.00000000026,  3.86983068409,    11353.89216764020},
2318     {     0.00000000023,  4.43657224846,     3344.15279870100},
2319     {     0.00000000021,  3.66824260126,    14951.52260208300},
2320     {     0.00000000022,  0.10813974117,    15423.26756087100},
2321     {     0.00000000025,  5.63091190933,     3416.87849797540},
2322     {     0.00000000025,  1.57746144847,    11567.19126307820},
2323     {     0.00000000026,  2.50180659493,    21791.69097326579},
2324     {     0.00000000022,  4.94823700773,     6681.64492949320},
2325     {     0.00000000026,  0.84448534014,     3397.51080163540},
2326     {     0.00000000021,  4.33866377991,    12729.66596748600},
2327     {     0.00000000021,  0.37058306281,     3391.89276456221},
2328     {     0.00000000022,  1.64362371744,     8852.24902869080},
2329     {     0.00000000027,  0.10733929729,     5195.24473233440},
2330     {     0.00000000021,  1.13140972844,    19403.77727388480},
2331     {     0.00000000026,  2.01526337234,     5032.77809620220},
2332     {     0.00000000021,  5.55525732543,    41748.05732892480},
2333     {     0.00000000021,  2.07959936360,    15106.87569121440},
2334     {     0.00000000024,  3.60866487742,    10006.58480891440},
2335     {     0.00000000028,  5.64135432549,    12516.36687204800},
2336     {     0.00000000027,  5.93032400892,     3074.00538497800},
2337     {     0.00000000025,  3.74768371499,     3232.94890276120},
2338     {     0.00000000022,  3.15578357220,    13366.04013545100},
2339     {     0.00000000021,  3.34013182507,    20752.66436247540},
2340     {     0.00000000026,  1.21869004343,     3377.21779200400},
2341     {     0.00000000024,  2.12604737559,     3171.03224356680},
2342     {     0.00000000022,  4.02124729955,    30774.50164257480},
2343     {     0.00000000024,  3.74309736843,     6747.71226231400},
2344     {     0.00000000023,  2.20705996255,    23553.86717003160},
2345     {     0.00000000021,  3.57070941130,    37895.42629036740},
2346     {     0.00000000023,  2.56549590800,    21192.36415686840},
2347     {     0.00000000021,  3.34401260695,    15010.89646399660},
2348     {     0.00000000019,  2.58752283276,    36261.27948574980},
2349     {     0.00000000021,  5.93180632509,    42146.20633233299},
2350     {     0.00000000018,  1.24405924793,     6768.53305793940},
2351     {     0.00000000019,  2.79026853354,    39203.74290904139},
2352     {     0.00000000024,  2.19710154155,    34513.26307268280},
2353     {     0.00000000020,  1.69850924464,    49225.58018914080},
2354     {     0.00000000018,  1.32432984119,    13497.51478683460},
2355     {     0.00000000018,  2.46520012266,     6944.30877677240},
2356     {     0.00000000018,  5.07942001013,     3337.07205469860},
2357     {     0.00000000018,  5.00983720257,     1655.56030419820},
2358     {     0.00000000018,  0.78739197008,    19676.45023123640},
2359     {     0.00000000018,  0.05420901908,     2142.64229812620},
2360 ];
2361 
2362 
2363 static const ln_vsop[LONG_L2] mars_longitude_l2 = [
2364     {     0.00058152577,  2.04961712429,     3340.61242669980},
2365     {     0.00013459579,  2.45738706163,     6681.22485339960},
2366     {     0.00002432575,  2.79737979284,    10021.83728009940},
2367     {     0.00000401065,  3.13581149963,    13362.44970679920},
2368     {     0.00000451384,  0.00000000000,        0.00000000000},
2369     {     0.00000222025,  3.19437046607,        3.52311834900},
2370     {     0.00000120954,  0.54327128607,      155.42039943420},
2371     {     0.00000062971,  3.47765178989,    16703.06213349900},
2372     {     0.00000053644,  3.54171478781,     3344.13554504880},
2373     {     0.00000034273,  6.00208464365,     2281.23049651060},
2374     {     0.00000031659,  4.14001980084,      191.44826611160},
2375     {     0.00000029839,  1.99838739380,      796.29800681640},
2376     {     0.00000023172,  4.33401932281,      242.72860397400},
2377     {     0.00000021663,  3.44500841809,      398.14900340820},
2378     {     0.00000016050,  6.11000263211,     2146.16541647520},
2379     {     0.00000020369,  5.42202383442,      553.56940284240},
2380     {     0.00000014924,  6.09549588012,     3185.19202726560},
2381     {     0.00000016229,  0.65685105422,        0.98032106820},
2382     {     0.00000014317,  2.61898820749,     1349.86740965880},
2383     {     0.00000014411,  4.01941740099,      951.71840625060},
2384     {     0.00000011944,  3.86196758615,     6684.74797174860},
2385     {     0.00000015655,  1.22093822826,     1748.01641306700},
2386     {     0.00000011261,  4.71857181601,     2544.31441988340},
2387     {     0.00000013360,  0.60151621438,     1194.44701022460},
2388     {     0.00000010395,  0.25075540193,      382.89653222320},
2389     {     0.00000009415,  0.68050215057,     1059.38193018920},
2390     {     0.00000009580,  3.82256319681,    20043.67456019880},
2391     {     0.00000008996,  3.88272784458,     3738.76143010800},
2392     {     0.00000007498,  5.46428174266,     1751.53953141600},
2393     {     0.00000006499,  5.47802397833,     1592.59601363280},
2394     {     0.00000006307,  2.34134269478,     3097.88382272579},
2395     {     0.00000006864,  2.57523762859,     3149.16416058820},
2396     {     0.00000005871,  1.14862855780,        7.11354700080},
2397     {     0.00000006675,  2.37862627319,     4136.91043351620},
2398     {     0.00000004655,  4.43102251490,     6151.53388830500},
2399     {     0.00000004201,  3.68638044545,     5614.72937620960},
2400     {     0.00000004796,  2.89378142432,     3333.49887969900},
2401     {     0.00000004074,  6.12610105396,     5628.95647021120},
2402     {     0.00000003660,  4.06581319964,     1990.74501704100},
2403     {     0.00000003284,  2.79214099721,     3894.18182954220},
2404     {     0.00000003615,  2.46526861067,      529.69096509460},
2405     {     0.00000003214,  0.68469193035,     8962.45534991020},
2406     {     0.00000003087,  4.56932030502,     3496.03282613400},
2407     {     0.00000002918,  5.41494777349,     2914.01423582380},
2408     {     0.00000002925,  1.23098223044,     2787.04302385740},
2409     {     0.00000002808,  1.38431632694,     4292.33083295040},
2410     {     0.00000002652,  1.05282528913,     3341.59274776800},
2411     {     0.00000002920,  3.41297158184,     3337.08930835080},
2412     {     0.00000002423,  0.96484330240,     4535.05943692440},
2413     {     0.00000002311,  4.84742235872,     9492.14631500480},
2414     {     0.00000002597,  5.74792546254,     3340.59517304760},
2415     {     0.00000002190,  3.26596280325,      213.29909543800},
2416     {     0.00000002598,  1.49506860128,     3340.62968035200},
2417     {     0.00000002365,  4.18303842420,    10025.36039844840},
2418     {     0.00000002630,  4.67732434694,     3583.34103067380},
2419     {     0.00000002606,  2.64976204169,     2388.89402044920},
2420     {     0.00000001822,  0.97105743952,     1589.07289528380},
2421     {     0.00000002397,  1.04493547179,     4399.99435688900},
2422     {     0.00000002203,  0.16281603659,     6525.80445396540},
2423     {     0.00000002373,  4.26885534124,     7079.37385680780},
2424     {     0.00000002366,  0.00564620006,     4690.47983635860},
2425     {     0.00000001623,  4.95374152644,     5088.62883976680},
2426     {     0.00000002143,  0.47993241836,     2700.71514038580},
2427     {     0.00000001646,  4.94105214632,     1221.84856632140},
2428     {     0.00000001588,  1.11405721408,    12303.06777661000},
2429     {     0.00000001518,  0.11076145171,     2957.71589447660},
2430     {     0.00000001774,  3.80344931471,     3723.50895892300},
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2691     {     0.00000000023,  3.00396120711,    12566.15169998280},
2692     {     0.00000000022,  4.95564076891,    13362.38239649640},
2693     {     0.00000000026,  5.35396491473,    17101.21113690720},
2694     {     0.00000000025,  0.78394576420,     3863.18984479360},
2695     {     0.00000000029,  0.72436044897,     9638.94074787620},
2696     {     0.00000000023,  4.78936229419,    11925.27409260060},
2697     {     0.00000000028,  0.45519439131,     6709.67404086740},
2698     {     0.00000000026,  4.87772426583,    13149.15061136120},
2699     {     0.00000000023,  5.40586773017,    13892.14067189380},
2700     {     0.00000000023,  2.35248036676,    30774.50164257480},
2701     {     0.00000000028,  1.10862278422,     8425.65083781480},
2702     {     0.00000000023,  3.61712960620,     1581.95934828300},
2703     {     0.00000000026,  0.31100585552,     3603.69635007260},
2704     {     0.00000000020,  2.43389989577,    19406.67828817460},
2705     {     0.00000000025,  5.91413646106,     6680.24453233140},
2706     {     0.00000000020,  5.43460902247,    17395.21973472580},
2707     {     0.00000000025,  1.00211327228,     7321.12213971360},
2708     {     0.00000000020,  5.58281555175,    18606.49894600020},
2709     {     0.00000000025,  3.57752663624,     3873.82651014340},
2710     {     0.00000000021,  2.14222861506,    14421.83163698840},
2711     {     0.00000000020,  5.47581404162,    20735.83216142559},
2712     {     0.00000000021,  5.53809813850,    15265.88651930040},
2713     {     0.00000000019,  5.69034956533,    17013.90293236740},
2714     {     0.00000000019,  5.76144586324,    17085.95866572220},
2715     {     0.00000000022,  2.98924680598,     9602.35263622420},
2716     {     0.00000000019,  5.73996220529,     3651.45322556820},
2717     {     0.00000000018,  0.52367856726,    14054.60730802600},
2718     {     0.00000000022,  5.16650472247,     3376.64029337720},
2719     {     0.00000000020,  2.67348019896,    10448.43547097540},
2720     {     0.00000000018,  3.70248341637,    37057.57749256620},
2721     {     0.00000000018,  2.14231646843,    13363.43002786740},
2722     {     0.00000000020,  6.25669293739,     1744.42598441520},
2723     {     0.00000000020,  1.60190678685,    23296.97878235879},
2724     {     0.00000000023,  4.54770256231,    13362.51701710200},
2725     {     0.00000000024,  0.54356017220,     6475.03930496240},
2726     {     0.00000000023,  2.73656801737,     6261.74020952440},
2727     {     0.00000000018,  5.45243764566,    40000.04091585779},
2728     {     0.00000000018,  1.77799263643,     8799.98871377800},
2729     {     0.00000000018,  1.18266196226,    31172.65064598300},
2730     {     0.00000000019,  3.66181465270,     1596.18644228460},
2731     {     0.00000000018,  3.46673198156,     3546.79797513700},
2732     {     0.00000000022,  2.15272313802,     3335.08950239240},
2733     {     0.00000000018,  0.13829920233,     3877.41693879520},
2734     {     0.00000000020,  4.57210028361,     6701.58017279840},
2735     {     0.00000000019,  5.09290088720,     3205.54734666440},
2736     {     0.00000000016,  3.67355426368,    20995.39296644940},
2737     {     0.00000000016,  6.13550943291,     3134.42687826260},
2738     {     0.00000000016,  6.22620467137,    22854.59602180400},
2739     {     0.00000000016,  1.44137713060,     6460.81221096080},
2740     {     0.00000000015,  1.18753446282,     7203.80227149340},
2741     {     0.00000000016,  3.90125903944,     7322.10246078180},
2742     {     0.00000000015,  4.93156258719,     3304.58456002240},
2743     {     0.00000000017,  0.49763390696,    18208.34994259200},
2744     {     0.00000000017,  3.32863823640,     3333.56619000180},
2745     {     0.00000000014,  5.31587329158,    19645.52555679060},
2746     {     0.00000000017,  3.01193328720,     3344.49376205780},
2747     {     0.00000000016,  4.54660273048,     4392.88080988820},
2748     {     0.00000000013,  5.26350209812,    16702.99482319620},
2749     {     0.00000000016,  6.12947849429,    26087.90314157420},
2750     {     0.00000000013,  5.84447235851,      536.80451209540},
2751     {     0.00000000017,  4.09065954177,    16511.61386738740},
2752     {     0.00000000015,  5.73438221173,    14867.73751589219},
2753     {     0.00000000013,  2.54721959021,     6675.70192909220},
2754     {     0.00000000014,  1.31577259278,    21150.81336588360},
2755     {     0.00000000013,  2.12815796147,     3346.13535100720},
2756     {     0.00000000013,  3.59360902373,    12410.73130054860},
2757     {     0.00000000016,  5.67307416663,    11527.12508919240},
2758     {     0.00000000016,  0.84938642384,    10184.30391623160},
2759     {     0.00000000013,  6.16919624193,     3077.52850332700},
2760     {     0.00000000014,  3.93053280186,     3312.16323923200},
2761     {     0.00000000014,  2.55072089788,      206.18554843720},
2762     {     0.00000000013,  4.69830610865,    16703.12944380180},
2763     {     0.00000000012,  0.92968593112,    10713.99488132620},
2764     {     0.00000000011,  6.09331837551,     8827.39026987480},
2765     {     0.00000000014,  3.77650372404,    17499.36014031540},
2766     {     0.00000000011,  1.09619387864,    16547.64173406480},
2767     {     0.00000000011,  5.05016560122,    24076.44458812540},
2768     {     0.00000000015,  6.16612008928,     3347.65866339780},
2769     {     0.00000000011,  1.92845507292,    11769.85369316640},
2770     {     0.00000000013,  1.01843193479,    10018.24685144760},
2771     {     0.00000000015,  0.92188099847,     3281.23856478620},
2772     {     0.00000000013,  5.19040439871,    16489.76303806100},
2773     {     0.00000000011,  0.29063320387,     2906.90068882300},
2774     {     0.00000000011,  5.65061614555,    13605.17831077320},
2775     {     0.00000000013,  5.06832582026,    13575.74880223720},
2776     {     0.00000000011,  5.42648525700,    17232.75309859360},
2777     {     0.00000000014,  2.18442424174,    12808.88030395680},
2778     {     0.00000000010,  3.12070301287,     2803.80791460440},
2779     {     0.00000000011,  1.35555533168,     2277.70737816160},
2780     {     0.00000000010,  5.89715293869,     6768.53305793940},
2781     {     0.00000000010,  5.93295499002,    23937.85638974100},
2782     {     0.00000000012,  1.20813089438,     3336.73109134180},
2783     {     0.00000000011,  2.56209057142,    13369.56325380000},
2784     {     0.00000000012,  0.50116227157,    34513.26307268280},
2785     {     0.00000000010,  4.37163145009,     3607.21946842160},
2786     {     0.00000000011,  4.03902225289,     4407.10790388980},
2787     {     0.00000000010,  4.18585556139,        0.01725365220},
2788     {     0.00000000011,  0.06058557016,    26880.31981303260},
2789     {     0.00000000011,  5.12397606143,    33406.12426699800},
2790     {     0.00000000011,  1.00077091959,    12979.55317457600},
2791     {     0.00000000010,  0.39595065439,    14955.04572043200},
2792     {     0.00000000011,  3.36133910370,    16894.51039961060},
2793     {     0.00000000010,  1.63992012008,      220.41264243880},
2794     {     0.00000000010,  5.76293648428,    31968.94865279940},
2795     {     0.00000000013,  1.44898528338,    10025.42770875120},
2796     {     0.00000000011,  4.36692917575,    34115.11406927460},
2797     {     0.00000000010,  4.84826192777,    12839.87228870540},
2798     {     0.00000000010,  1.85828895892,     6593.91664885980},
2799     {     0.00000000010,  5.75866529304,     6717.25272007700},
2800     {     0.00000000012,  4.33022696919,     7747.72033058960},
2801     {     0.00000000011,  5.96309733546,    20040.15144184979},
2802     {     0.00000000010,  3.58563293895,    20354.51535906720},
2803     {     0.00000000010,  4.88835260040,    10042.19259949820},
2804     {     0.00000000010,  2.48515633128,    25665.51748340920},
2805     {     0.00000000009,  1.77145376267,    32367.09765620760},
2806 ];
2807 
2808 
2809 static const ln_vsop[LONG_L3] mars_longitude_l3 = [
2810     {     0.00001467867,  0.44429839460,     3340.61242669980},
2811     {     0.00000692668,  0.88679887123,     6681.22485339960},
2812     {     0.00000189478,  1.28336839921,    10021.83728009940},
2813     {     0.00000041615,  1.64210455567,    13362.44970679920},
2814     {     0.00000022660,  2.05278956965,      155.42039943420},
2815     {     0.00000008126,  1.99049724299,    16703.06213349900},
2816     {     0.00000010455,  1.57992093693,        3.52311834900},
2817     {     0.00000004902,  2.82516875010,      242.72860397400},
2818     {     0.00000005379,  3.14159265359,        0.00000000000},
2819     {     0.00000003782,  2.01848153986,     3344.13554504880},
2820     {     0.00000003181,  4.59108786647,     3185.19202726560},
2821     {     0.00000003133,  0.65141319517,      553.56940284240},
2822     {     0.00000001698,  5.53803382831,      951.71840625060},
2823     {     0.00000001525,  5.71698515888,      191.44826611160},
2824     {     0.00000001451,  0.46068490220,      796.29800681640},
2825     {     0.00000001473,  2.33727441522,    20043.67456019880},
2826     {     0.00000001314,  5.36403056955,        0.98032106820},
2827     {     0.00000001178,  4.14644990348,     1349.86740965880},
2828     {     0.00000001138,  2.37914351932,     6684.74797174860},
2829     {     0.00000001046,  1.76915268602,      382.89653222320},
2830     {     0.00000000902,  5.35475854699,     1194.44701022460},
2831     {     0.00000000813,  2.74852234414,     1748.01641306700},
2832     {     0.00000000629,  6.08292992203,     3496.03282613400},
2833     {     0.00000000564,  1.87914711325,      398.14900340820},
2834     {     0.00000000566,  5.85439216540,        7.11354700080},
2835     {     0.00000000646,  3.17980126471,     3583.34103067380},
2836     {     0.00000000461,  5.99300094958,     2787.04302385740},
2837     {     0.00000000515,  1.00397565149,     3149.16416058820},
2838     {     0.00000000524,  4.94366714135,     6525.80445396540},
2839     {     0.00000000405,  1.25868884474,     2281.23049651060},
2840     {     0.00000000396,  2.33533869272,     3738.76143010800},
2841     {     0.00000000473,  0.85569341494,     4136.91043351620},
2842     {     0.00000000337,  5.42720231008,     1059.38193018920},
2843     {     0.00000000312,  3.71767667252,     3097.88382272579},
2844     {     0.00000000280,  5.77799085447,     3341.59274776800},
2845     {     0.00000000282,  2.71397487800,    10025.36039844840},
2846     {     0.00000000215,  5.72936855193,     4535.05943692440},
2847     {     0.00000000213,  2.52113312108,     1990.74501704100},
2848     {     0.00000000253,  2.68513749891,    23384.28698689860},
2849     {     0.00000000271,  1.11020953644,     2388.89402044920},
2850     {     0.00000000186,  4.87399580961,     2957.71589447660},
2851     {     0.00000000178,  3.91361250070,     1592.59601363280},
2852     {     0.00000000175,  0.87350226081,     3894.18182954220},
2853     {     0.00000000191,  4.57651964364,     3337.08930835080},
2854     {     0.00000000166,  2.74261580519,     7079.37385680780},
2855     {     0.00000000132,  1.21969793594,     7477.52286021600},
2856     {     0.00000000176,  5.82269855073,     4399.99435688900},
2857     {     0.00000000144,  1.41866825837,     6489.77658728800},
2858     {     0.00000000116,  3.26440506489,     9492.14631500480},
2859     {     0.00000000110,  5.25036780309,     8962.45534991020},
2860     {     0.00000000109,  2.69848602723,     6151.53388830500},
2861     {     0.00000000099,  3.53126616352,     6923.95345737360},
2862     {     0.00000000094,  5.83398846011,    12303.06777661000},
2863     {     0.00000000082,  5.71976568172,     4292.33083295040},
2864     {     0.00000000082,  0.07031928087,     6127.65545055720},
2865     {     0.00000000079,  5.82605787124,     1589.07289528380},
2866     {     0.00000000086,  5.29348370173,     9866.41688066520},
2867     {     0.00000000101,  0.00033367659,     3347.72597370060},
2868     {     0.00000000076,  4.33662644570,     4933.20844033260},
2869     {     0.00000000066,  4.98095301409,     5486.77784317500},
2870     {     0.00000000066,  1.74326529570,     3870.30339179440},
2871     {     0.00000000059,  1.47406427963,     7234.79425624200},
2872     {     0.00000000065,  4.13790023458,     3340.59517304760},
2873     {     0.00000000066,  6.17474740457,     6682.20517446780},
2874     {     0.00000000065,  6.16873733389,     3340.62968035200},
2875     {     0.00000000061,  3.04498621253,    13365.97282514820},
2876     {     0.00000000057,  0.34435287503,     6681.24210705180},
2877     {     0.00000000052,  3.10877560472,    10419.98628350760},
2878     {     0.00000000053,  1.49212635155,     5729.50644714900},
2879     {     0.00000000052,  6.16231097097,     7740.60678358880},
2880     {     0.00000000057,  4.59725498148,     6681.20759974740},
2881     {     0.00000000047,  6.08280843167,     7875.67186362420},
2882     {     0.00000000046,  2.22700618360,     6283.07584999140},
2883     {     0.00000000042,  4.17552906301,     4690.47983635860},
2884     {     0.00000000053,  4.86310998799,     5621.84292321040},
2885     {     0.00000000039,  3.01231289993,    26724.89941359840},
2886     {     0.00000000044,  1.83807443880,     3723.50895892300},
2887     {     0.00000000045,  3.66313190536,    12832.75874170460},
2888     {     0.00000000049,  2.90677449550,     5331.35744374080},
2889     {     0.00000000041,  5.09013551341,     8969.56889691100},
2890     {     0.00000000035,  1.80197655191,     9830.38901398780},
2891     {     0.00000000036,  6.20064893632,     6836.64525283380},
2892     {     0.00000000041,  4.73855176222,     6677.70173505060},
2893     {     0.00000000043,  0.12056288166,     7632.94325965020},
2894     {     0.00000000036,  3.95211035317,     5092.15195811580},
2895     {     0.00000000041,  1.02183708699,     3339.63210563160},
2896     {     0.00000000032,  6.08260895536,     4929.68532198360},
2897     {     0.00000000029,  1.62918363864,    10818.13528691580},
2898     {     0.00000000033,  5.28926114198,     6298.32832117640},
2899     {     0.00000000035,  2.19127331195,     3553.91152213780},
2900     {     0.00000000031,  1.71403126017,     6674.11130639880},
2901     {     0.00000000027,  2.59859773299,     9623.68827669120},
2902     {     0.00000000037,  6.26363818135,    15643.68020330980},
2903     {     0.00000000026,  0.41795219764,     6688.33840040040},
2904     {     0.00000000025,  2.61050876047,     8955.34180290940},
2905     {     0.00000000024,  2.72770670140,     7210.91581849420},
2906     {     0.00000000022,  0.56923205824,     3333.49887969900},
2907     {     0.00000000024,  1.08927112722,    13362.46696045140},
2908     {     0.00000000024,  1.27631664508,     2146.16541647520},
2909     {     0.00000000021,  2.25460322522,     6681.29216370240},
2910     {     0.00000000021,  1.21340354488,      529.69096509460},
2911     {     0.00000000019,  2.21770037001,     3340.54511639700},
2912     {     0.00000000019,  0.66923624814,    10021.85453375160},
2913     {     0.00000000019,  4.96725594495,    10021.82002644720},
2914     {     0.00000000021,  2.66383165337,     6681.15754309680},
2915     {     0.00000000019,  5.34528034089,    13362.43245314700},
2916     {     0.00000000020,  4.05200075148,    16173.37116840440},
2917     {     0.00000000018,  6.12827330419,     2118.76386037840},
2918     {     0.00000000019,  1.81106961128,     3340.67973700260},
2919     {     0.00000000023,  3.65530501555,     5884.92684658320},
2920     {     0.00000000017,  3.49526304116,    13760.59871020740},
2921     {     0.00000000017,  2.19106157796,    13171.00144068760},
2922     {     0.00000000018,  2.57298367742,     6894.52394883760},
2923     {     0.00000000015,  3.38406160245,    16706.58525184800},
2924     {     0.00000000020,  5.66097673948,    11773.37681151540},
2925     {     0.00000000016,  5.03015729119,     8031.09226305840},
2926     {     0.00000000018,  5.85813180984,    15113.98923821520},
2927     {     0.00000000015,  0.77504052248,    10028.95082710020},
2928     {     0.00000000015,  0.57957141835,    10973.55568635000},
2929     {     0.00000000014,  0.24974244701,     5088.62883976680},
2930     {     0.00000000018,  3.07924421940,    12964.30070339100},
2931     {     0.00000000015,  2.68623334057,    10021.90459040220},
2932     {     0.00000000015,  3.09469457587,    10021.76996979660},
2933     {     0.00000000013,  3.93023649028,    10264.56588407340},
2934     {     0.00000000013,  5.65831284328,    13207.02930736500},
2935     {     0.00000000013,  1.84300811278,     9070.11887384880},
2936     {     0.00000000014,  0.29740739896,    18984.29263000960},
2937     {     0.00000000013,  2.52001940946,     7064.12138562280},
2938     {     0.00000000013,  3.67191025834,     3320.25710730100},
2939     {     0.00000000013,  0.38182731490,    11081.21921028860},
2940     {     0.00000000015,  5.65316717493,     9638.94074787620},
2941     {     0.00000000015,  1.98431328230,    14158.74771361560},
2942     {     0.00000000012,  5.41217638500,    12310.18132361080},
2943     {     0.00000000013,  2.16005341496,     3503.07906283200},
2944     {     0.00000000013,  2.04039005845,     3360.96774609859},
2945     {     0.00000000012,  3.10587105006,    10551.52824519400},
2946     {     0.00000000012,  0.10001647761,     3355.86489788480},
2947     {     0.00000000011,  2.14032736093,    10014.72373309860},
2948     {     0.00000000011,  1.79726060971,     6438.49624942560},
2949     {     0.00000000014,  0.17608466993,    11216.28429032400},
2950     {     0.00000000011,  3.38101843423,    30065.51184029820},
2951     {     0.00000000010,  0.14034808917,     5459.37628707820},
2952     {     0.00000000012,  1.39972628733,     7322.10246078180},
2953     {     0.00000000010,  5.01174496801,     8432.76438481560},
2954     {     0.00000000010,  4.85370121323,     8827.39026987480},
2955     {     0.00000000012,  1.85790840539,    10575.40668294180},
2956     {     0.00000000011,  5.68929132609,     2544.31441988340},
2957     {     0.00000000013,  0.11973675130,     8270.29774868340},
2958     {     0.00000000010,  3.45366828680,     8671.96987044060},
2959     {     0.00000000010,  1.63456773166,     6467.92575796160},
2960     {     0.00000000012,  0.48472196247,     9468.26787725700},
2961     {     0.00000000010,  1.79285582925,     3981.49003408200},
2962     {     0.00000000012,  4.35157153740,    13358.92658845020},
2963     {     0.00000000012,  4.70754717702,     8273.82086703240},
2964     {     0.00000000009,  5.67195388102,     6041.32756708560},
2965     {     0.00000000011,  0.28291831064,    10022.81760116760},
2966     {     0.00000000012,  0.19598354169,     3767.21061757580},
2967     {     0.00000000009,  0.79888103600,     7107.82304427560},
2968     {     0.00000000009,  2.63887133820,     6040.34724601740},
2969     {     0.00000000010,  4.24040970796,    10018.31416175040},
2970     {     0.00000000008,  4.41344390506,     3532.06069281140},
2971     {     0.00000000009,  4.61082143531,     6254.62666252360},
2972     {     0.00000000010,  3.14867092101,    12295.95422960920},
2973     {     0.00000000008,  4.30808895338,    13517.87010623340},
2974     {     0.00000000007,  3.72930971887,    20047.19767854780},
2975     {     0.00000000007,  5.31461308603,     3980.50971301380},
2976     {     0.00000000007,  4.41228197932,    19513.98359510420},
2977     {     0.00000000006,  0.70081238478,    22324.90505670940},
2978     {     0.00000000007,  3.46042125643,    16304.91313009080},
2979     {     0.00000000006,  4.18130136613,     9225.53927328300},
2980     {     0.00000000007,  2.07260074047,     2274.11694950980},
2981     {     0.00000000008,  4.84690285943,     5614.72937620960},
2982     {     0.00000000007,  5.81948406996,    18454.60166491500},
2983     {     0.00000000006,  4.58700022729,    12935.85151592320},
2984     {     0.00000000006,  3.09847010281,    10235.13637553740},
2985     {     0.00000000007,  5.65100333611,     3325.35995551480},
2986     {     0.00000000006,  3.88836191013,     8429.24126646660},
2987     {     0.00000000006,  6.08444137601,      426.59819087600},
2988     {     0.00000000007,  4.39290235530,    16699.53901514999},
2989     {     0.00000000006,  4.96952219943,    11614.43329373220},
2990     {     0.00000000007,  3.86534915027,    17101.21113690720},
2991     {     0.00000000005,  3.27691563611,      213.29909543800},
2992     {     0.00000000006,  2.22078885531,    13916.01910964160},
2993     {     0.00000000005,  5.40200843260,    11371.70468975820},
2994     {     0.00000000006,  3.73369549160,    33406.12426699800},
2995     {     0.00000000005,  1.76068977855,     1066.49547719000},
2996     {     0.00000000005,  3.34460420545,     4562.46099302120},
2997     {     0.00000000005,  5.87001587166,    16547.64173406480},
2998     {     0.00000000005,  2.58164780968,    10404.73381232260},
2999     {     0.00000000005,  0.95143416553,     6872.67311951120},
3000     {     0.00000000005,  3.29623418943,    13362.38239649640},
3001     {     0.00000000005,  4.15921606694,        0.01725365220},
3002     {     0.00000000005,  1.88015249528,    15508.61512327440},
3003     {     0.00000000005,  4.69029931558,     2700.71514038580},
3004 ];
3005 
3006 
3007 static const ln_vsop[LONG_L4] mars_longitude_l4 = [
3008     {     0.00000027242,  5.63997742320,     6681.22485339960},
3009     {     0.00000025511,  5.13956279086,     3340.61242669980},
3010     {     0.00000011147,  6.03556608878,    10021.83728009940},
3011     {     0.00000003190,  3.56206901204,      155.42039943420},
3012     {     0.00000003251,  0.12915616460,    13362.44970679920},
3013     {     0.00000000790,  0.48979114861,    16703.06213349900},
3014     {     0.00000000783,  1.31770747646,      242.72860397400},
3015     {     0.00000000500,  3.08200921500,     3185.19202726560},
3016     {     0.00000000374,  2.15499052115,      553.56940284240},
3017     {     0.00000000338,  6.23352693699,        3.52311834900},
3018     {     0.00000000199,  0.45348344109,     3344.13554504880},
3019     {     0.00000000168,  3.76870889622,     3496.03282613400},
3020     {     0.00000000171,  0.84135133604,    20043.67456019880},
3021     {     0.00000000115,  1.67425271260,     3583.34103067380},
3022     {     0.00000000080,  0.85706484335,     6684.74797174860},
3023     {     0.00000000091,  3.43800003890,     6525.80445396540},
3024     {     0.00000000062,  4.48712111677,     2787.04302385740},
3025     {     0.00000000043,  5.18700577258,     3097.88382272579},
3026     {     0.00000000047,  0.00000000000,        0.00000000000},
3027     {     0.00000000037,  1.18296722277,    23384.28698689860},
3028     {     0.00000000024,  4.29204464862,     6836.64525283380},
3029     {     0.00000000026,  1.20348583477,    10025.36039844840},
3030     {     0.00000000024,  5.60827511165,     4136.91043351620},
3031     {     0.00000000022,  5.74642710221,     3149.16416058820},
3032     {     0.00000000018,  2.03318579635,     6923.95345737360},
3033     {     0.00000000015,  4.26014468247,     3341.59274776800},
3034     {     0.00000000018,  2.33884195894,     3894.18182954220},
3035     {     0.00000000015,  0.76745028682,     3738.76143010800},
3036     {     0.00000000013,  3.78255342218,     9866.41688066520},
3037     {     0.00000000013,  4.84669665560,     6127.65545055720},
3038     {     0.00000000015,  5.90904577370,     2388.89402044920},
3039     {     0.00000000012,  4.04057703674,     4535.05943692440},
3040     {     0.00000000011,  3.87847882201,     1059.38193018920},
3041     {     0.00000000011,  6.15709897926,     6489.77658728800},
3042     {     0.00000000010,  1.72288144187,     9492.14631500480},
3043     {     0.00000000010,  1.57846217224,    13365.97282514820},
3044     {     0.00000000008,  2.41269301261,     1592.59601363280},
3045     {     0.00000000008,  3.38799237939,     2957.71589447660},
3046     {     0.00000000008,  6.09858519460,     7477.52286021600},
3047     {     0.00000000010,  1.26692397596,     1990.74501704100},
3048     {     0.00000000010,  1.19094173671,     7079.37385680780},
3049     {     0.00000000011,  4.27677188971,     4399.99435688900},
3050     {     0.00000000008,  4.14850970681,    13207.02930736500},
3051     {     0.00000000008,  1.54297406750,    26724.89941359840},
3052     {     0.00000000007,  0.26868468775,     9830.38901398780},
3053     {     0.00000000007,  0.08101546764,    10818.13528691580},
3054     {     0.00000000007,  2.42508289520,    10264.56588407340},
3055     {     0.00000000007,  5.57348066316,     6438.49624942560},
3056     {     0.00000000007,  4.62218969676,    10177.25767953360},
3057     {     0.00000000008,  0.34286691468,     3723.50895892300},
3058     {     0.00000000006,  1.60196605908,    10419.98628350760},
3059     {     0.00000000006,  4.33371839115,     4292.33083295040},
3060     {     0.00000000007,  4.61281837777,     7875.67186362420},
3061     {     0.00000000006,  4.67857531326,     2544.31441988340},
3062     {     0.00000000007,  1.51290306715,     5331.35744374080},
3063     {     0.00000000006,  4.16295898909,    12303.06777661000},
3064     {     0.00000000006,  4.52108494056,     3532.06069281140},
3065     {     0.00000000006,  4.66651817095,     7740.60678358880},
3066     {     0.00000000005,  6.26581073985,     5729.50644714900},
3067     {     0.00000000005,  2.75621336253,     4690.47983635860},
3068     {     0.00000000005,  2.78107610422,     4933.20844033260},
3069     {     0.00000000005,  4.63812650627,     6682.20517446780},
3070     {     0.00000000005,  5.81870543856,     2146.16541647520},
3071     {     0.00000000004,  4.97648147254,     3347.72597370060},
3072     {     0.00000000004,  1.92818801589,    16706.58525184800},
3073     {     0.00000000004,  3.51723776816,     5486.77784317500},
3074     {     0.00000000004,  4.37622919020,     3337.08930835080},
3075     {     0.00000000003,  3.74520053012,     6298.32832117640},
3076     {     0.00000000003,  4.94059407345,    11081.21921028860},
3077     {     0.00000000003,  5.20767397767,     9468.26787725700},
3078     {     0.00000000002,  5.60261719076,     3333.49887969900},
3079     {     0.00000000003,  6.08152672681,     3339.63210563160},
3080     {     0.00000000002,  1.90275008409,    30065.51184029820},
3081     {     0.00000000003,  3.36064341832,     5621.84292321040},
3082     {     0.00000000002,  0.01141937510,    10551.52824519400},
3083 ];
3084 
3085 
3086 static const ln_vsop[LONG_L5] mars_longitude_l5 = [
3087     {     0.00000000762,  4.03556368806,     6681.22485339960},
3088     {     0.00000000511,  4.48770393640,    10021.83728009940},
3089     {     0.00000000360,  5.07296615717,      155.42039943420},
3090     {     0.00000000202,  4.88361321440,    13362.44970679920},
3091     {     0.00000000165,  3.48592135141,     3340.61242669980},
3092     {     0.00000000100,  6.09065293613,      242.72860397400},
3093     {     0.00000000062,  5.25625355993,    16703.06213349900},
3094     {     0.00000000064,  1.57192173495,     3185.19202726560},
3095     {     0.00000000035,  3.68331841812,      553.56940284240},
3096     {     0.00000000016,  5.23951751422,     3496.03282613400},
3097     {     0.00000000017,  5.60862454832,    20043.67456019880},
3098     {     0.00000000016,  0.16723854805,     3583.34103067380},
3099     {     0.00000000011,  1.93419597527,     6525.80445396540},
3100     {     0.00000000007,  5.17525588419,     3344.13554504880},
3101     {     0.00000000007,  2.97300501488,     2787.04302385740},
3102     {     0.00000000005,  0.39000584564,     3097.88382272579},
3103     {     0.00000000005,  5.60123387975,     6684.74797174860},
3104     {     0.00000000004,  5.97749583912,    23384.28698689860},
3105     {     0.00000000003,  2.29064254081,     9866.41688066520},
3106     {     0.00000000003,  0.52716684104,     6923.95345737360},
3107     {     0.00000000003,  6.06139189331,    10025.36039844840},
3108     {     0.00000000002,  0.00000000000,        0.00000000000},
3109     {     0.00000000002,  0.06588431932,    26724.89941359840},
3110     {     0.00000000001,  3.33966357719,     6127.65545055720},
3111 ];
3112 
3113 
3114 static const ln_vsop[LAT_B0] mars_latitude_b0 = [
3115     {     0.03197134986,  3.76832042431,     3340.61242669980},
3116     {     0.00298033234,  4.10616996305,     6681.22485339960},
3117     {     0.00289104742,  0.00000000000,        0.00000000000},
3118     {     0.00031365539,  4.44651053090,    10021.83728009940},
3119     {     0.00003484100,  4.78812549260,    13362.44970679920},
3120     {     0.00000442999,  5.65233014206,     3337.08930835080},
3121     {     0.00000443401,  5.02642622964,     3344.13554504880},
3122     {     0.00000399109,  5.13056816928,    16703.06213349900},
3123     {     0.00000292506,  3.79290674178,     2281.23049651060},
3124     {     0.00000181982,  6.13648041445,     6151.53388830500},
3125     {     0.00000163159,  4.26399640691,      529.69096509460},
3126     {     0.00000159678,  2.23194572851,     1059.38193018920},
3127     {     0.00000139323,  2.41796458896,     8962.45534991020},
3128     {     0.00000149297,  2.16501221175,     5621.84292321040},
3129     {     0.00000142686,  1.18215016908,     3340.59517304760},
3130     {     0.00000142685,  3.21292181638,     3340.62968035200},
3131     {     0.00000082544,  5.36667920373,     6684.74797174860},
3132     {     0.00000073639,  5.09187695770,      398.14900340820},
3133     {     0.00000072660,  5.53775735826,     6283.07584999140},
3134     {     0.00000086377,  5.74429749104,     3738.76143010800},
3135     {     0.00000083276,  5.98866355811,     6677.70173505060},
3136     {     0.00000060116,  3.67960801961,      796.29800681640},
3137     {     0.00000063111,  0.73049101791,     5884.92684658320},
3138     {     0.00000062338,  4.85072128690,     2942.46342329160},
3139     {     0.00000046951,  5.54339769619,     3340.54511639700},
3140     {     0.00000046953,  5.13486674212,     3340.67973700260},
3141     {     0.00000046630,  5.47361589877,    20043.67456019880},
3142     {     0.00000045588,  2.13262340840,     2810.92146160520},
3143     {     0.00000041269,  0.20003146001,     9492.14631500480},
3144     {     0.00000047199,  4.52184637077,     3149.16416058820},
3145     {     0.00000038540,  4.08008471951,     4136.91043351620},
3146     {     0.00000033069,  4.06582536024,     1751.53953141600},
3147     {     0.00000029694,  5.92218475216,     3532.06069281140},
3148     {     0.00000032736,  2.62070842911,     2914.01423582380},
3149     {     0.00000029521,  2.75342613814,    12303.06777661000},
3150     {     0.00000028169,  2.06282641876,     5486.77784317500},
3151     {     0.00000028618,  4.94710659219,     3870.30339179440},
3152     {     0.00000026603,  3.55085867185,     6681.24210705180},
3153     {     0.00000026603,  1.52008697887,     6681.20759974740},
3154     {     0.00000023336,  2.27624326713,     1589.07289528380},
3155     {     0.00000026052,  2.60064406111,     4399.99435688900},
3156     {     0.00000022637,  2.27507286962,     1194.44701022460},
3157     {     0.00000018887,  6.04416592185,     7079.37385680780},
3158     {     0.00000014846,  3.41358397277,     5088.62883976680},
3159     {     0.00000019947,  2.67364901180,     8432.76438481560},
3160     {     0.00000014682,  5.89211770913,     9623.68827669120},
3161     {     0.00000014152,  2.42511982523,     3333.49887969900},
3162     {     0.00000013310,  2.62839885122,      426.59819087600},
3163     {     0.00000014008,  1.67425471692,     6254.62666252360},
3164     {     0.00000015104,  2.81013512447,     3496.03282613400},
3165     {     0.00000013011,  5.70759990125,    10025.36039844840},
3166     {     0.00000012080,  1.51805176385,     3185.19202726560},
3167     {     0.00000013183,  0.04521300408,    10018.31416175040},
3168     {     0.00000011553,  5.57419195540,      191.44826611160},
3169     {     0.00000011196,  0.55829476182,     5092.15195811580},
3170     {     0.00000011530,  2.13314729185,    11773.37681151540},
3171     {     0.00000010435,  5.72413969529,     6467.92575796160},
3172     {     0.00000009846,  0.86942034707,     1592.59601363280},
3173     {     0.00000009761,  1.09343319930,     2544.31441988340},
3174     {     0.00000008754,  5.47281526854,     6681.29216370240},
3175     {     0.00000008937,  4.83790383087,     6489.77658728800},
3176     {     0.00000008652,  4.72119070324,      213.29909543800},
3177     {     0.00000008797,  2.86598300684,     3341.59274776800},
3178     {     0.00000008384,  2.65895188994,     4535.05943692440},
3179     {     0.00000008213,  4.82608471380,     3553.91152213780},
3180     {     0.00000008799,  1.52911067895,     3339.63210563160},
3181     {     0.00000008103,  1.00994223680,     9225.53927328300},
3182     {     0.00000008754,  5.88131156904,     6681.15754309680},
3183     {     0.00000007209,  4.41679451115,     7477.52286021600},
3184     {     0.00000008559,  4.79005521282,     4690.47983635860},
3185     {     0.00000006087,  1.89070780881,     9595.23908922340},
3186     {     0.00000006974,  0.53247180771,    12832.75874170460},
3187     {     0.00000005584,  6.18908858151,     4292.33083295040},
3188     {     0.00000005038,  6.06394187474,     7210.91581849420},
3189     {     0.00000005127,  0.11856223993,     4562.46099302120},
3190     {     0.00000004863,  1.33050477323,     3894.18182954220},
3191     {     0.00000005592,  3.97792233579,     3127.31333126180},
3192     {     0.00000004965,  5.74590187611,     1990.74501704100},
3193     {     0.00000005531,  5.81704574177,    23384.28698689860},
3194     {     0.00000004184,  3.88899448118,    10021.85453375160},
3195     {     0.00000004184,  1.85821886750,    10021.82002644720},
3196     {     0.00000004685,  1.11750605341,     3319.83703120740},
3197     {     0.00000003954,  2.65571428448,     4929.68532198360},
3198     {     0.00000005174,  3.62345890346,     2700.71514038580},
3199     {     0.00000004639,  6.14089828121,        7.11354700080},
3200     {     0.00000004686,  3.27732030640,     3361.38782219220},
3201     {     0.00000004999,  3.09122275925,    15643.68020330980},
3202     {     0.00000003919,  2.96551660306,     7740.60678358880},
3203     {     0.00000003361,  1.85015691730,     2957.71589447660},
3204     {     0.00000004247,  4.19639326313,     2146.16541647520},
3205     {     0.00000004101,  6.22534362774,    10213.28554621100},
3206     {     0.00000003124,  0.08537434136,    10419.98628350760},
3207     {     0.00000003079,  2.41163576579,     3344.20285535160},
3208     {     0.00000003093,  1.98041916263,     3337.02199804800},
3209     {     0.00000003044,  4.38894724131,     1221.84856632140},
3210     {     0.00000002879,  2.93292958734,     2787.04302385740},
3211     {     0.00000003372,  4.45558231622,     6674.11130639880},
3212     {     0.00000002510,  4.06246201858,     6872.67311951120},
3213     {     0.00000002616,  1.23659105217,     4933.20844033260},
3214     {     0.00000003011,  4.33966319613,     2388.89402044920},
3215     {     0.00000003094,  2.40386312988,     2118.76386037840},
3216     {     0.00000002516,  2.30275461207,     3723.50895892300},
3217     {     0.00000002192,  1.68875393217,      639.89728631400},
3218     {     0.00000002157,  6.07606060132,     9808.53818466140},
3219     {     0.00000002686,  2.38168997181,    15113.98923821520},
3220     {     0.00000002156,  2.87768495226,     6041.32756708560},
3221     {     0.00000002495,  3.87397844397,     7903.07341972100},
3222     {     0.00000002253,  0.47470647524,     3475.67750673520},
3223     {     0.00000002443,  3.02632472426,     3767.21061757580},
3224     {     0.00000001937,  0.38000939550,    13358.92658845020},
3225     {     0.00000002213,  3.91980714687,     3205.54734666440},
3226     {     0.00000002386,  6.23866730110,    12964.30070339100},
3227     {     0.00000001806,  2.38402930496,    11243.68584642080},
3228     {     0.00000002265,  1.85773978984,     6525.80445396540},
3229     {     0.00000001642,  1.86812819920,     6680.24453233140},
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3493     {     0.00000000063,  0.18907107644,    30065.51184029820},
3494     {     0.00000000064,  4.61910278723,     9886.77220006400},
3495     {     0.00000000073,  0.93704276887,    20735.83216142559},
3496     {     0.00000000060,  5.83782810193,     8646.06348025360},
3497     {     0.00000000062,  4.81385996015,    20199.09495963300},
3498     {     0.00000000059,  5.00167022948,     6414.61781167780},
3499     {     0.00000000068,  3.84295373259,     6571.01853218020},
3500     {     0.00000000061,  2.81706693695,     6944.30877677240},
3501     {     0.00000000065,  4.49019257083,      632.78373931320},
3502     {     0.00000000058,  5.65218977997,     9945.57120882380},
3503     {     0.00000000071,  2.51550158926,     9638.94074787620},
3504     {     0.00000000057,  3.27978831470,      206.18554843720},
3505     {     0.00000000058,  2.97636193658,    21795.21409161479},
3506     {     0.00000000056,  2.23539566426,    20995.39296644940},
3507     {     0.00000000057,  1.88470380043,    18451.07854656599},
3508     {     0.00000000071,  4.82445654330,     8542.97070603500},
3509     {     0.00000000061,  3.65964735564,    14421.83163698840},
3510     {     0.00000000056,  3.13785930666,     8799.98871377800},
3511     {     0.00000000057,  4.89910616374,     9602.35263622420},
3512     {     0.00000000065,  3.37158994673,    11610.91017538320},
3513     {     0.00000000067,  1.92961865108,    21265.52312652020},
3514     {     0.00000000055,  1.95164531766,     9588.12554222260},
3515     {     0.00000000057,  2.82246123078,    10124.93005431800},
3516     {     0.00000000057,  6.10387785338,    19800.94595622480},
3517     {     0.00000000055,  5.20958408712,     3237.51965248120},
3518     {     0.00000000057,  4.12311973381,    10028.95082710020},
3519     {     0.00000000054,  1.41693548950,    15906.76412668260},
3520     {     0.00000000053,  2.16367301961,     6418.14093002680},
3521     {     0.00000000060,  2.64664637730,    10018.24685144760},
3522     {     0.00000000068,  5.36545296940,     1228.96211332220},
3523     {     0.00000000051,  5.73844646896,     6048.44111408640},
3524     {     0.00000000053,  0.32024828883,    12721.57209941700},
3525     {     0.00000000051,  0.06318823307,    20206.14119633100},
3526     {     0.00000000049,  4.53400634462,     6675.70192909220},
3527     {     0.00000000051,  1.15453549218,    10156.90236013480},
3528     {     0.00000000064,  4.56324217308,    16703.07938715119},
3529     {     0.00000000060,  3.61007876606,     9468.26787725700},
3530     {     0.00000000059,  3.08394474122,    10025.42770875120},
3531     {     0.00000000064,  2.53221459501,    16703.04487984680},
3532     {     0.00000000056,  3.31981662811,     6518.75821726740},
3533     {     0.00000000047,  1.44559124267,     6643.09181776180},
3534     {     0.00000000050,  1.92346411481,    11614.43329373220},
3535     {     0.00000000047,  4.03823773711,    23958.63178523340},
3536     {     0.00000000046,  3.70969689047,     8859.36257569160},
3537     {     0.00000000060,  2.55451756882,    11780.49035851620},
3538     {     0.00000000047,  1.69255946598,     6660.86953400080},
3539     {     0.00000000044,  6.09481156053,     6460.81221096080},
3540     {     0.00000000044,  2.63075457414,    13936.79450513400},
3541     {     0.00000000053,  0.77837832855,    16865.52876963120},
3542     {     0.00000000049,  1.83317426993,    17654.78053974960},
3543     {     0.00000000042,  4.30403794400,     9065.54812412880},
3544     {     0.00000000047,  0.52827244925,     6686.74777770700},
3545     {     0.00000000042,  5.72053684220,     7203.80227149340},
3546     {     0.00000000041,  0.98430028881,    20426.57109242200},
3547     {     0.00000000051,  3.54371303345,    20597.24396304120},
3548     {     0.00000000041,  0.21190431801,     7314.00859271280},
3549     {     0.00000000038,  2.53053802253,    13207.02930736500},
3550     {     0.00000000039,  5.15577529354,     6670.58818804980},
3551     {     0.00000000045,  0.52366150729,    16489.76303806100},
3552     {     0.00000000051,  3.25181148972,     7799.98064550240},
3553     {     0.00000000049,  0.77149145450,    17101.21113690720},
3554     {     0.00000000038,  6.06656444914,     9389.05354078620},
3555     {     0.00000000036,  0.84094545235,    23937.85638974100},
3556 ];
3557 
3558 
3559 static const ln_vsop[LAT_B1] mars_latitude_b1 = [
3560     {     0.00217310991,  6.04472194776,     3340.61242669980},
3561     {     0.00020976948,  3.14159265359,        0.00000000000},
3562     {     0.00012834709,  1.60810667915,     6681.22485339960},
3563     {     0.00003320981,  2.62947004077,    10021.83728009940},
3564     {     0.00000627200,  3.11898601248,    13362.44970679920},
3565     {     0.00000101990,  3.52113557592,    16703.06213349900},
3566     {     0.00000075107,  0.95983758515,     3337.08930835080},
3567     {     0.00000029264,  3.40307682710,     3344.13554504880},
3568     {     0.00000023251,  3.69342549027,     5621.84292321040},
3569     {     0.00000022190,  2.21703408598,     2281.23049651060},
3570     {     0.00000015454,  3.89610159362,    20043.67456019880},
3571     {     0.00000011867,  3.83861019788,     6684.74797174860},
3572     {     0.00000012038,  2.13866775328,     6151.53388830500},
3573     {     0.00000009697,  5.48941186798,     3340.62968035200},
3574     {     0.00000009697,  3.45863925102,     3340.59517304760},
3575     {     0.00000011537,  1.90395033905,     3532.06069281140},
3576     {     0.00000009276,  0.71941312462,     2942.46342329160},
3577     {     0.00000009240,  2.51747952408,     5884.92684658320},
3578     {     0.00000009876,  6.13507416822,     1059.38193018920},
3579     {     0.00000009265,  4.55759125226,     8962.45534991020},
3580     {     0.00000007822,  6.10932267009,     2810.92146160520},
3581     {     0.00000010369,  0.60195347181,      529.69096509460},
3582     {     0.00000008522,  4.40106741096,     3496.03282613400},
3583     {     0.00000007683,  1.21169696624,     6677.70173505060},
3584     {     0.00000007134,  1.93610705535,     2544.31441988340},
3585     {     0.00000006512,  3.11636422105,     3738.76143010800},
3586     {     0.00000006278,  6.23176923902,     3185.19202726560},
3587     {     0.00000005833,  0.74324094343,      398.14900340820},
3588     {     0.00000005033,  2.28727456802,     3149.16416058820},
3589     {     0.00000004958,  1.54200127913,     6283.07584999140},
3590     {     0.00000004325,  3.90636722132,     5092.15195811580},
3591     {     0.00000004813,  3.88560399245,     5486.77784317500},
3592     {     0.00000004474,  2.18937641288,     4136.91043351620},
3593     {     0.00000003023,  5.19879000530,     5088.62883976680},
3594     {     0.00000003194,  1.12695072198,     3340.67973700260},
3595     {     0.00000003167,  0.76774265684,     4399.99435688900},
3596     {     0.00000003066,  0.93923788410,     2914.01423582380},
3597     {     0.00000002840,  2.51888046278,     3870.30339179440},
3598     {     0.00000002622,  3.25368667606,     3339.63210563160},
3599     {     0.00000003192,  1.53317813619,     3340.54511639700},
3600     {     0.00000002879,  4.20588113950,    10025.36039844840},
3601     {     0.00000002435,  2.49243229030,     1751.53953141600},
3602     {     0.00000002066,  2.96021692416,     3894.18182954220},
3603     {     0.00000002366,  1.08506560814,      796.29800681640},
3604     {     0.00000002192,  0.22905210418,     4690.47983635860},
3605     {     0.00000002398,  0.43514026515,     1194.44701022460},
3606     {     0.00000002238,  4.06454135883,     7079.37385680780},
3607     {     0.00000001825,  5.46319390380,     1592.59601363280},
3608     {     0.00000001808,  4.83342714362,     8432.76438481560},
3609     {     0.00000002251,  4.25857270742,    23384.28698689860},
3610     {     0.00000001728,  1.06103820676,     3341.59274776800},
3611     {     0.00000001833,  1.57091276737,     4292.33083295040},
3612     {     0.00000001581,  0.93404031162,     4535.05943692440},
3613     {     0.00000001722,  2.98790749378,     6254.62666252360},
3614     {     0.00000001395,  3.43004445438,     2146.16541647520},
3615     {     0.00000001739,  4.00666290186,     9492.14631500480},
3616     {     0.00000001535,  2.94481028624,     6489.77658728800},
3617     {     0.00000001394,  2.71952784799,     7477.52286021600},
3618     {     0.00000001257,  1.34371702718,     2787.04302385740},
3619     {     0.00000001600,  5.41971849753,     3127.31333126180},
3620     {     0.00000001274,  4.11492658217,     1990.74501704100},
3621     {     0.00000001190,  4.24621398204,     3723.50895892300},
3622     {     0.00000001144,  5.30298760566,     6681.20759974740},
3623     {     0.00000001376,  0.38090537503,     1589.07289528380},
3624     {     0.00000001144,  1.05059380873,     6681.24210705180},
3625     {     0.00000001062,  0.51072898484,     6674.11130639880},
3626     {     0.00000001355,  0.30172057784,     6525.80445396540},
3627     {     0.00000001119,  0.28227067739,    12303.06777661000},
3628     {     0.00000000855,  0.15965897606,     2957.71589447660},
3629     {     0.00000001066,  2.74229978174,     2388.89402044920},
3630     {     0.00000001056,  4.82485604808,     3583.34103067380},
3631     {     0.00000000770,  3.92387598679,        7.11354700080},
3632     {     0.00000000922,  5.97832717399,     3097.88382272579},
3633     {     0.00000000713,  2.61601602080,     9225.53927328300},
3634     {     0.00000000693,  5.86945792010,     4933.20844033260},
3635     {     0.00000000738,  5.02837731897,    12832.75874170460},
3636     {     0.00000000763,  1.29638960572,     7740.60678358880},
3637     {     0.00000000656,  1.57943668761,     6467.92575796160},
3638     {     0.00000000663,  0.56970117211,      426.59819087600},
3639     {     0.00000000616,  2.90595542135,     3553.91152213780},
3640     {     0.00000000609,  4.27586920886,     4562.46099302120},
3641     {     0.00000000608,  4.61163488420,    10419.98628350760},
3642     {     0.00000000599,  4.51624214272,     6836.64525283380},
3643     {     0.00000000565,  3.63229110969,      155.42039943420},
3644     {     0.00000000562,  0.31418284081,      213.29909543800},
3645     {     0.00000000519,  1.00557611591,     4929.68532198360},
3646     {     0.00000000504,  4.17532879019,     6041.32756708560},
3647     {     0.00000000660,  3.62669217851,     7210.91581849420},
3648     {     0.00000000576,  4.54911948486,    13365.97282514820},
3649     {     0.00000000625,  1.44798343162,     3333.49887969900},
3650     {     0.00000000520,  1.30331504622,    15643.68020330980},
3651     {     0.00000000444,  2.08076069460,    10021.85453375160},
3652     {     0.00000000542,  2.02587783935,     2288.34404351140},
3653     {     0.00000000509,  1.65323927554,      191.44826611160},
3654     {     0.00000000444,  0.04999320087,    10021.82002644720},
3655     {     0.00000000557,  3.31349841992,     9623.68827669120},
3656     {     0.00000000472,  6.26731124720,     6438.49624942560},
3657     {     0.00000000559,  4.16781257217,    11773.37681151540},
3658     {     0.00000000399,  1.32358791559,     7875.67186362420},
3659     {     0.00000000445,  1.49656750781,     6682.20517446780},
3660     {     0.00000000385,  0.75203057166,     5614.72937620960},
3661     {     0.00000000386,  1.92088879703,     3325.35995551480},
3662     {     0.00000000377,  3.38213849272,     6681.15754309680},
3663     {     0.00000000360,  3.62049849377,     6680.24453233140},
3664     {     0.00000000352,  3.40685833182,     9830.38901398780},
3665     {     0.00000000346,  2.54878403272,     2274.11694950980},
3666     {     0.00000000336,  5.51924409428,     3361.38782219220},
3667     {     0.00000000329,  3.58450091417,     1066.49547719000},
3668     {     0.00000000343,  3.80876454378,     9595.23908922340},
3669     {     0.00000000383,  4.58860426691,     3360.96774609859},
3670     {     0.00000000367,  4.94614944232,     7903.07341972100},
3671     {     0.00000000318,  3.12211289329,    10818.13528691580},
3672     {     0.00000000298,  5.16474580641,     1748.01641306700},
3673     {     0.00000000310,  5.77231072116,     3205.54734666440},
3674     {     0.00000000378,  2.97214989967,     6681.29216370240},
3675     {     0.00000000303,  3.44801982034,     3319.83703120740},
3676     {     0.00000000292,  1.69888047283,     6127.65545055720},
3677     {     0.00000000288,  1.13506530643,     8955.34180290940},
3678     {     0.00000000281,  0.80027819229,    10018.31416175040},
3679     {     0.00000000326,  5.96924076920,      639.89728631400},
3680     {     0.00000000309,  1.38061994912,     3767.21061757580},
3681     {     0.00000000375,  4.48892934736,     5331.35744374080},
3682     {     0.00000000271,  4.61196466416,    26724.89941359840},
3683     {     0.00000000266,  3.08927427780,     5729.50644714900},
3684     {     0.00000000290,  2.44792712887,     3355.86489788480},
3685     {     0.00000000335,  6.08508450491,     3320.25710730100},
3686     {     0.00000000300,  0.25476556615,     2700.71514038580},
3687     {     0.00000000289,  3.45335160291,      382.89653222320},
3688     {     0.00000000260,  3.56570589402,     8827.39026987480},
3689     {     0.00000000246,  0.64772929845,     9866.41688066520},
3690     {     0.00000000298,  4.38515379625,     1052.26838318840},
3691     {     0.00000000251,  4.40903417777,    12964.30070339100},
3692     {     0.00000000260,  1.27300653213,     3347.72597370060},
3693     {     0.00000000280,  1.49182583330,    10213.28554621100},
3694     {     0.00000000225,  2.73440886519,     6872.67311951120},
3695     {     0.00000000225,  5.16642343920,     6923.95345737360},
3696     {     0.00000000226,  2.68107364511,     1221.84856632140},
3697     {     0.00000000222,  4.38874821491,      242.72860397400},
3698     {     0.00000000209,  5.01591708290,     6144.42034130420},
3699     {     0.00000000268,  2.27786943096,      553.56940284240},
3700     {     0.00000000218,  0.53299582810,     6298.32832117640},
3701     {     0.00000000261,  3.89759063291,     6894.52394883760},
3702     {     0.00000000213,  1.06038488787,     2118.76386037840},
3703     {     0.00000000210,  4.74220753176,     9381.93999378540},
3704     {     0.00000000192,  0.18364684632,      522.57741809380},
3705     {     0.00000000186,  1.48154759746,     7064.12138562280},
3706     {     0.00000000176,  3.93023367762,     2921.12778282460},
3707     {     0.00000000208,  4.86366921136,     3344.20285535160},
3708     {     0.00000000201,  0.36731227894,     8969.56889691100},
3709     {     0.00000000209,  4.43309730358,     3337.02199804800},
3710     {     0.00000000163,  4.54501296893,    11243.68584642080},
3711     {     0.00000000161,  1.62341728854,    11081.21921028860},
3712     {     0.00000000152,  3.98251813705,    10021.90459040220},
3713     {     0.00000000145,  1.06283180181,      951.71840625060},
3714     {     0.00000000149,  4.55824612447,    10551.52824519400},
3715     {     0.00000000184,  5.37374692745,    16173.37116840440},
3716     {     0.00000000143,  2.00077774476,     6688.33840040040},
3717     {     0.00000000145,  4.53139041634,     3312.16323923200},
3718     {     0.00000000156,  6.26070301430,     5628.95647021120},
3719     {     0.00000000157,  5.56167088817,      536.80451209540},
3720     {     0.00000000133,  5.43195789258,    13358.92658845020},
3721     {     0.00000000144,  1.31943624453,     3364.49086444760},
3722     {     0.00000000156,  4.10544868136,     6158.64743530580},
3723     {     0.00000000157,  6.23025291402,     8273.82086703240},
3724     {     0.00000000134,  4.31700501659,     8031.09226305840},
3725     {     0.00000000124,  1.26816196203,     8270.29774868340},
3726     {     0.00000000156,  4.39354558071,    10021.76996979660},
3727     {     0.00000000144,  2.48806691402,     3503.07906283200},
3728     {     0.00000000118,  1.78550823737,    18984.29263000960},
3729     {     0.00000000110,  6.12714281903,     7632.94325965020},
3730     {     0.00000000127,  3.05541911618,     3316.73398895200},
3731     {     0.00000000109,  0.91919644775,    10014.72373309860},
3732     {     0.00000000102,  1.54908471746,     7234.79425624200},
3733     {     0.00000000100,  5.04817125533,    13760.59871020740},
3734     {     0.00000000132,  2.66590263580,     8429.24126646660},
3735     {     0.00000000126,  0.13960736597,     1349.86740965880},
3736     {     0.00000000100,  0.74385347353,     2487.41604494780},
3737     {     0.00000000091,  0.24627212892,     3980.50971301380},
3738     {     0.00000000112,  2.30475590800,     3346.13535100720},
3739     {     0.00000000103,  4.23425277305,     3475.67750673520},
3740     {     0.00000000109,  3.21402242606,    17654.78053974960},
3741     {     0.00000000082,  0.28323060532,    15113.98923821520},
3742     {     0.00000000083,  0.53618493739,    13362.43245314700},
3743     {     0.00000000096,  3.66896983898,    12168.00269657460},
3744     {     0.00000000083,  2.56708795058,    13362.46696045140},
3745     {     0.00000000077,  4.92321070753,    16706.58525184800},
3746     {     0.00000000097,  2.11149094902,     3178.14579056760},
3747     {     0.00000000074,  0.95663828948,     2699.73481931760},
3748     {     0.00000000083,  1.82502676147,        3.52311834900},
3749     {     0.00000000085,  5.22946780555,     3304.58456002240},
3750     {     0.00000000083,  3.10647417000,     1758.65307841680},
3751     {     0.00000000070,  5.11510436801,     5828.02847164760},
3752     {     0.00000000077,  1.77323016185,     3335.08950239240},
3753     {     0.00000000082,  5.25824044848,      853.19638175200},
3754     {     0.00000000067,  0.98915661779,      433.71173787680},
3755     {     0.00000000078,  3.62913840245,     1596.18644228460},
3756     {     0.00000000078,  1.56367501585,     3336.73109134180},
3757     {     0.00000000084,  4.62334317796,    11371.70468975820},
3758     {     0.00000000072,  3.62008128206,     1581.95934828300},
3759     {     0.00000000072,  4.05769658716,     4407.10790388980},
3760     {     0.00000000085,  0.75421401009,     5459.37628707820},
3761     {     0.00000000074,  1.03163916867,     5085.03841111500},
3762     {     0.00000000058,  3.24082931383,    13517.87010623340},
3763     {     0.00000000056,  3.73441989631,    10713.99488132620},
3764     {     0.00000000061,  1.52242466354,    18052.92954315780},
3765     {     0.00000000053,  0.69821482369,     6702.00024889200},
3766     {     0.00000000057,  2.76439103910,     3344.49376205780},
3767     {     0.00000000069,  1.99074407937,    10575.40668294180},
3768     {     0.00000000059,  1.90513947603,    10022.81760116760},
3769     {     0.00000000051,  0.93662679832,    14314.16811304980},
3770     {     0.00000000069,  5.42699929964,     3376.64029337720},
3771     {     0.00000000053,  4.87818342068,     8671.96987044060},
3772     {     0.00000000065,  3.39290651505,    14584.29827312060},
3773     {     0.00000000057,  1.70570965163,     2648.45482547300},
3774     {     0.00000000054,  5.49765437527,     3369.06161416760},
3775     {     0.00000000054,  2.28971906454,    12566.15169998280},
3776     {     0.00000000068,  4.60849144076,     7373.38245462640},
3777     {     0.00000000049,  2.89959771413,    13916.01910964160},
3778     {     0.00000000058,  4.18351190862,    10177.25767953360},
3779     {     0.00000000058,  4.51310742397,     4032.77002792660},
3780     {     0.00000000048,  3.42793333559,     1744.42598441520},
3781     {     0.00000000064,  0.45002982477,     3863.18984479360},
3782     {     0.00000000047,  5.88584556234,    10973.55568635000},
3783     {     0.00000000057,  1.76184909465,    11216.28429032400},
3784     {     0.00000000053,  1.35755250698,    21393.54196985760},
3785     {     0.00000000059,  2.91197893810,     3981.49003408200},
3786     {     0.00000000053,  4.03461050047,    11769.85369316640},
3787     {     0.00000000052,  2.05672710904,    10404.73381232260},
3788     {     0.00000000060,  4.31863902545,     3077.52850332700},
3789     {     0.00000000060,  4.94577585891,     3603.69635007260},
3790     {     0.00000000052,  3.45056061273,     9808.53818466140},
3791     {     0.00000000048,  3.83792333621,    13171.00144068760},
3792     {     0.00000000050,  1.55014152662,      419.48464387520},
3793     {     0.00000000042,  1.56007012481,     8425.65083781480},
3794     {     0.00000000040,  4.52149159432,    10235.13637553740},
3795     {     0.00000000045,  4.94000875201,    16304.91313009080},
3796     {     0.00000000042,  2.03301048111,     7107.82304427560},
3797     {     0.00000000055,  2.94325348897,      640.87760738220},
3798     {     0.00000000039,  0.82091082076,    12310.18132361080},
3799     {     0.00000000040,  3.29013672690,     6247.51311552280},
3800     {     0.00000000040,  0.33830589904,     6531.66165626500},
3801     {     0.00000000044,  4.73395183232,    20597.24396304120},
3802     {     0.00000000037,  0.01359265708,     3914.95722503460},
3803     {     0.00000000037,  3.04848190227,     2766.26762836500},
3804     {     0.00000000037,  4.13243009725,    17256.63153634140},
3805     {     0.00000000043,  3.27442666790,    20995.39296644940},
3806     {     0.00000000035,  0.29856523330,     9779.10867612540},
3807     {     0.00000000045,  0.96453304167,    18454.60166491500},
3808     {     0.00000000036,  0.18334758502,     6660.86953400080},
3809     {     0.00000000043,  1.23912278835,     8439.87793181640},
3810     {     0.00000000034,  2.83078633705,     6696.47732458460},
3811     {     0.00000000043,  5.80649509131,     9168.64089834740},
3812     {     0.00000000034,  3.46884113350,     9070.11887384880},
3813     {     0.00000000037,  5.04438408684,     1692.16566950240},
3814     {     0.00000000040,  1.15262282119,    14712.31711645800},
3815     {     0.00000000035,  2.33581709312,       76.26607127560},
3816     {     0.00000000040,  3.54052855946,    14158.74771361560},
3817     {     0.00000000032,  4.96078703650,    24734.15439655740},
3818     {     0.00000000029,  2.34589185801,    13745.34623902240},
3819     {     0.00000000030,  6.17825920695,    12935.85151592320},
3820     {     0.00000000036,  4.78354946118,     3191.04922956520},
3821     {     0.00000000028,  4.98887480054,    30065.51184029820},
3822     {     0.00000000028,  2.51507274088,      692.15760122680},
3823     {     0.00000000027,  1.02364014288,    13207.02930736500},
3824     {     0.00000000035,  2.06348913435,     9468.26787725700},
3825     {     0.00000000027,  6.07463404086,    20199.09495963300},
3826     {     0.00000000027,  4.97808057680,    13362.38239649640},
3827     {     0.00000000033,  1.46173724832,    12295.95422960920},
3828     {     0.00000000025,  4.54782445360,     9499.25986200560},
3829     {     0.00000000025,  5.21847833578,     5099.26550511660},
3830     {     0.00000000025,  5.90368432966,    19513.98359510420},
3831     {     0.00000000025,  5.54544644558,    10264.56588407340},
3832     {     0.00000000029,  5.69085985167,    16699.53901514999},
3833     {     0.00000000030,  1.43603228163,     6040.34724601740},
3834     {     0.00000000028,  5.41811683281,    15110.46611986620},
3835     {     0.00000000032,  2.25828272513,     6665.97238221460},
3836     {     0.00000000023,  5.38626329146,     6660.44945790720},
3837     {     0.00000000023,  3.75194149686,    14054.60730802600},
3838     {     0.00000000028,  4.86716760481,     6701.58017279840},
3839     {     0.00000000027,  5.26172837256,     6816.28993343500},
3840     {     0.00000000023,  4.66125245752,    13149.15061136120},
3841     {     0.00000000027,  0.91821785260,     9638.94074787620},
3842     {     0.00000000023,  0.60587177409,     6604.95878212400},
3843     {     0.00000000025,  0.78041098485,    11766.26326451460},
3844     {     0.00000000025,  3.94777048397,    10020.85695903120},
3845     {     0.00000000026,  5.36280311705,     9485.03276800400},
3846     {     0.00000000020,  2.45752476953,    10028.95082710020},
3847     {     0.00000000020,  0.38029885589,    11614.43329373220},
3848     {     0.00000000026,  4.53241539149,    13362.51701710200},
3849     {     0.00000000019,  3.71366407424,     9588.12554222260},
3850     {     0.00000000022,  5.20856925736,    13892.14067189380},
3851 ];
3852 
3853 
3854 static const ln_vsop[LAT_B2] mars_latitude_b2 = [
3855     {     0.00008888446,  1.06196052751,     3340.61242669980},
3856     {     0.00002595393,  3.14159265359,        0.00000000000},
3857     {     0.00000918914,  0.11538431190,     6681.22485339960},
3858     {     0.00000267883,  0.78837893063,    10021.83728009940},
3859     {     0.00000066911,  1.39435595847,    13362.44970679920},
3860     {     0.00000014267,  1.87268116087,    16703.06213349900},
3861     {     0.00000007948,  2.58819177832,     3337.08930835080},
3862     {     0.00000002709,  2.29241371893,    20043.67456019880},
3863     {     0.00000002911,  1.36634316448,     3344.13554504880},
3864     {     0.00000002528,  6.00423798411,     3496.03282613400},
3865     {     0.00000001617,  5.72212771018,     5621.84292321040},
3866     {     0.00000001625,  4.63140305669,     3185.19202726560},
3867     {     0.00000001173,  2.04871812080,     6684.74797174860},
3868     {     0.00000001066,  1.15825195582,     2281.23049651060},
3869     {     0.00000001043,  3.54796199484,     3532.06069281140},
3870     {     0.00000000724,  4.20458660775,     5884.92684658320},
3871     {     0.00000000610,  5.22430575829,     2810.92146160520},
3872     {     0.00000000557,  2.75698163218,     2942.46342329160},
3873     {     0.00000000655,  2.84033212598,     6677.70173505060},
3874     {     0.00000000641,  5.44557723446,     5486.77784317500},
3875     {     0.00000000498,  4.59850630546,     3894.18182954220},
3876     {     0.00000000501,  0.52535712881,     5088.62883976680},
3877     {     0.00000000521,  4.66308888977,     1059.38193018920},
3878     {     0.00000000490,  3.99314993252,     2544.31441988340},
3879     {     0.00000000408,  4.93937427401,     3339.63210563160},
3880     {     0.00000000396,  0.51430149629,     3340.62968035200},
3881     {     0.00000000470,  2.68379670864,    23384.28698689860},
3882     {     0.00000000389,  6.00426372731,     8962.45534991020},
3883     {     0.00000000446,  3.81307040390,     6151.53388830500},
3884     {     0.00000000396,  4.76665218791,     3340.59517304760},
3885     {     0.00000000360,  0.30420986478,     4136.91043351620},
3886     {     0.00000000368,  2.55488502496,    10025.36039844840},
3887     {     0.00000000417,  2.05816647037,      529.69096509460},
3888     {     0.00000000393,  1.18623350431,     3097.88382272579},
3889     {     0.00000000318,  4.89083986180,     5092.15195811580},
3890     {     0.00000000311,  0.52479429819,     3149.16416058820},
3891     {     0.00000000339,  1.91330658550,     4690.47983635860},
3892     {     0.00000000351,  3.22939666067,     4292.33083295040},
3893     {     0.00000000400,  4.99682542425,     6525.80445396540},
3894     {     0.00000000269,  5.24048656863,     4399.99435688900},
3895     {     0.00000000269,  6.01045237753,     2787.04302385740},
3896     {     0.00000000242,  5.84228858137,     3723.50895892300},
3897     {     0.00000000300,  3.33780918870,     3583.34103067380},
3898     {     0.00000000230,  1.39226657786,     3738.76143010800},
3899     {     0.00000000192,  5.54090794612,     3341.59274776800},
3900     {     0.00000000185,  2.67271130688,     6283.07584999140},
3901     {     0.00000000184,  2.21130914624,     7079.37385680780},
3902     {     0.00000000170,  5.17306622171,     6254.62666252360},
3903     {     0.00000000186,  3.68212348930,     1592.59601363280},
3904     {     0.00000000168,  2.39044142684,     1990.74501704100},
3905     {     0.00000000201,  0.91789291159,     2388.89402044920},
3906     {     0.00000000171,  4.81773821378,     1194.44701022460},
3907     {     0.00000000181,  2.50145688400,      398.14900340820},
3908     {     0.00000000177,  5.42788143021,     4535.05943692440},
3909     {     0.00000000153,  5.20921140136,     2146.16541647520},
3910     {     0.00000000131,  2.41348963069,     3340.67973700260},
3911     {     0.00000000150,  1.54231915192,     6438.49624942560},
3912     {     0.00000000149,  0.96225780576,     7477.52286021600},
3913     {     0.00000000129,  5.26033357561,      155.42039943420},
3914     {     0.00000000158,  4.47988793489,     3333.49887969900},
3915     {     0.00000000133,  6.05902381899,     6836.64525283380},
3916     {     0.00000000120,  4.73910738283,     2957.71589447660},
3917     {     0.00000000117,  2.22260771124,     6674.11130639880},
3918     {     0.00000000136,  5.83288551607,      796.29800681640},
3919     {     0.00000000157,  1.15241959296,     6489.77658728800},
3920     {     0.00000000110,  4.19180987487,     4933.20844033260},
3921     {     0.00000000130,  2.84683198305,     3340.54511639700},
3922     {     0.00000000121,  2.52786285342,     9492.14631500480},
3923     {     0.00000000108,  0.08979902661,     1748.01641306700},
3924     {     0.00000000117,  5.82410316896,     2914.01423582380},
3925     {     0.00000000086,  2.01927297840,        7.11354700080},
3926     {     0.00000000082,  3.80856644509,     6681.20759974740},
3927     {     0.00000000082,  5.83941329915,     6681.24210705180},
3928     {     0.00000000076,  0.08262821070,     6127.65545055720},
3929     {     0.00000000091,  2.96288127149,    13365.97282514820},
3930     {     0.00000000080,  2.85318684748,     8955.34180290940},
3931     {     0.00000000083,  5.02941237478,    12303.06777661000},
3932     {     0.00000000074,  3.62624366705,     6923.95345737360},
3933     {     0.00000000072,  1.17271788888,     3127.31333126180},
3934     {     0.00000000095,  4.98093994365,     1589.07289528380},
3935     {     0.00000000087,  5.81716080338,     7740.60678358880},
3936     {     0.00000000089,  0.48604673074,     3870.30339179440},
3937     {     0.00000000066,  3.06598137329,    26724.89941359840},
3938     {     0.00000000067,  6.01736846209,     6682.20517446780},
3939     {     0.00000000070,  0.64135636261,     2288.34404351140},
3940     {     0.00000000063,  3.19176567675,    12832.75874170460},
3941     {     0.00000000063,  2.70869032431,      242.72860397400},
3942     {     0.00000000062,  5.92753482553,     7875.67186362420},
3943     {     0.00000000074,  5.12213534011,     9866.41688066520},
3944     {     0.00000000076,  2.80770234482,     5331.35744374080},
3945     {     0.00000000063,  1.40446619803,     5729.50644714900},
3946     {     0.00000000065,  1.35907629616,     1349.86740965880},
3947     {     0.00000000056,  2.65764515134,      951.71840625060},
3948     {     0.00000000067,  4.84212554978,     2274.11694950980},
3949     {     0.00000000069,  2.48893325965,    10419.98628350760},
3950     {     0.00000000051,  5.98407977888,     6041.32756708560},
3951     {     0.00000000049,  4.85570926461,     4562.46099302120},
3952     {     0.00000000058,  4.99207597345,     8969.56889691100},
3953     {     0.00000000043,  5.63823020899,     4929.68532198360},
3954     {     0.00000000058,  6.20594898525,     3347.72597370060},
3955     {     0.00000000057,  2.89730834453,    10018.31416175040},
3956     {     0.00000000058,  3.89480774042,      553.56940284240},
3957     {     0.00000000047,  5.12333023108,      426.59819087600},
3958     {     0.00000000042,  1.03283454214,     6681.29216370240},
3959     {     0.00000000051,  1.17739312127,     1751.53953141600},
3960     {     0.00000000036,  4.71576514590,     6298.32832117640},
3961     {     0.00000000041,  4.11801359055,    10021.82002644720},
3962     {     0.00000000036,  2.79629985388,      213.29909543800},
3963     {     0.00000000033,  5.67092277262,    15643.68020330980},
3964     {     0.00000000033,  1.68550281175,     9830.38901398780},
3965     {     0.00000000032,  2.78277698783,     7210.91581849420},
3966     {     0.00000000041,  6.14975635778,    10021.85453375160},
3967     {     0.00000000031,  1.46914313245,    10818.13528691580},
3968     {     0.00000000030,  5.11654548214,    11773.37681151540},
3969     {     0.00000000030,  5.94013525093,     3767.21061757580},
3970     {     0.00000000028,  1.35093398031,     3553.91152213780},
3971     {     0.00000000027,  0.84036429724,     7632.94325965020},
3972     {     0.00000000029,  5.76529104850,     8031.09226305840},
3973     {     0.00000000026,  0.25856730853,     1066.49547719000},
3974     {     0.00000000024,  0.67405360149,     3360.96774609859},
3975     {     0.00000000024,  2.34265028137,     3320.25710730100},
3976     {     0.00000000028,  1.81680368660,     9623.68827669120},
3977     {     0.00000000022,  6.24243881749,     8432.76438481560},
3978     {     0.00000000021,  5.25722436514,     6680.24453233140},
3979     {     0.00000000023,  4.24982817116,     3325.35995551480},
3980     {     0.00000000022,  5.05378057964,     3355.86489788480},
3981     {     0.00000000026,  5.21495958693,      382.89653222320},
3982     {     0.00000000023,  2.27453854146,     7234.79425624200},
3983     {     0.00000000025,  1.69816682992,     6872.67311951120},
3984     {     0.00000000023,  4.13297133971,      639.89728631400},
3985     {     0.00000000019,  4.63736307953,     8429.24126646660},
3986     {     0.00000000018,  0.29318941103,      640.87760738220},
3987     {     0.00000000017,  3.12909635955,     6467.92575796160},
3988     {     0.00000000016,  1.92178558286,     6681.15754309680},
3989     {     0.00000000016,  0.47472874553,     1052.26838318840},
3990     {     0.00000000016,  0.09800770199,    11081.21921028860},
3991     {     0.00000000018,  3.26217306584,     7064.12138562280},
3992     {     0.00000000016,  5.48746970528,     9595.23908922340},
3993     {     0.00000000019,  4.63958564261,     8273.82086703240},
3994     {     0.00000000015,  2.52623641715,      191.44826611160},
3995     {     0.00000000016,  1.95271387752,     2699.73481931760},
3996     {     0.00000000015,  4.31015619343,     8827.39026987480},
3997     {     0.00000000014,  1.08241159656,    10973.55568635000},
3998     {     0.00000000015,  6.00000660183,    11371.70468975820},
3999     {     0.00000000013,  0.22518942674,     6688.33840040040},
4000     {     0.00000000013,  2.42192861366,    10575.40668294180},
4001     {     0.00000000011,  2.53752217003,    12964.30070339100},
4002     {     0.00000000011,  4.80028625279,    11769.85369316640},
4003     {     0.00000000014,  3.84407896636,    16173.37116840440},
4004     {     0.00000000011,  1.79883656022,     9779.10867612540},
4005     {     0.00000000010,  3.38769942924,    16706.58525184800},
4006     {     0.00000000013,  2.15740232885,     6894.52394883760},
4007     {     0.00000000010,  5.38827104551,    12310.18132361080},
4008     {     0.00000000012,  3.76810144879,     9225.53927328300},
4009     {     0.00000000011,  3.25290731199,     8671.96987044060},
4010     {     0.00000000011,  2.90564118820,     6040.34724601740},
4011     {     0.00000000010,  5.69430086859,    13207.02930736500},
4012     {     0.00000000009,  3.26007781906,    13760.59871020740},
4013     {     0.00000000009,  2.65306894671,    10551.52824519400},
4014     {     0.00000000009,  1.95264065659,     9070.11887384880},
4015     {     0.00000000011,  0.42402934223,     9381.93999378540},
4016 ];
4017 
4018 
4019 static const ln_vsop[LAT_B3] mars_latitude_b3 = [
4020     {     0.00000330418,  2.04215300484,     3340.61242669980},
4021     {     0.00000093057,  0.00000000000,        0.00000000000},
4022     {     0.00000014546,  5.38525967237,    10021.83728009940},
4023     {     0.00000008731,  4.90252313032,     6681.22485339960},
4024     {     0.00000005215,  5.97441462813,    13362.44970679920},
4025     {     0.00000001422,  0.21283650226,    16703.06213349900},
4026     {     0.00000000585,  4.14327356645,     3337.08930835080},
4027     {     0.00000000489,  1.32053432093,     3496.03282613400},
4028     {     0.00000000332,  0.67062028539,    20043.67456019880},
4029     {     0.00000000281,  3.02888736938,     3185.19202726560},
4030     {     0.00000000095,  0.68129190368,     5621.84292321040},
4031     {     0.00000000117,  6.20178829761,     3344.13554504880},
4032     {     0.00000000100,  2.70816972496,     3097.88382272579},
4033     {     0.00000000086,  0.38064581922,     6684.74797174860},
4034     {     0.00000000071,  6.24412260280,     3894.18182954220},
4035     {     0.00000000079,  5.14539339999,     3532.06069281140},
4036     {     0.00000000080,  3.42045199039,     6525.80445396540},
4037     {     0.00000000061,  3.81929342821,     2942.46342329160},
4038     {     0.00000000066,  0.95264988100,    23384.28698689860},
4039     {     0.00000000062,  1.65751945223,     3583.34103067380},
4040     {     0.00000000062,  5.30607853843,     2544.31441988340},
4041     {     0.00000000042,  0.30552815689,     3339.63210563160},
4042     {     0.00000000037,  4.37754880706,     2787.04302385740},
4043     {     0.00000000043,  4.90457279180,     4292.33083295040},
4044     {     0.00000000036,  3.58183533863,     4690.47983635860},
4045     {     0.00000000034,  0.89018356943,    10025.36039844840},
4046     {     0.00000000032,  2.34732348899,     5088.62883976680},
4047     {     0.00000000028,  1.23206084526,     3723.50895892300},
4048     {     0.00000000026,  0.56214389305,      155.42039943420},
4049     {     0.00000000026,  4.11359839477,     6677.70173505060},
4050     {     0.00000000026,  0.37391494322,     2146.16541647520},
4051     {     0.00000000024,  5.78802013510,     5884.92684658320},
4052     {     0.00000000021,  2.91916849909,      529.69096509460},
4053     {     0.00000000019,  4.86965145048,     4136.91043351620},
4054     {     0.00000000023,  1.04314198221,     5486.77784317500},
4055     {     0.00000000018,  4.95637454569,     3149.16416058820},
4056     {     0.00000000017,  6.23546258970,     7079.37385680780},
4057     {     0.00000000017,  3.82096761296,     3341.59274776800},
4058     {     0.00000000019,  5.66874348929,     2388.89402044920},
4059     {     0.00000000015,  5.13426153783,     6489.77658728800},
4060     {     0.00000000014,  0.53723500958,     1990.74501704100},
4061     {     0.00000000014,  3.07166661567,     2957.71589447660},
4062     {     0.00000000012,  1.00141464760,     3340.62968035200},
4063     {     0.00000000012,  5.24418015401,     3340.59517304760},
4064     {     0.00000000013,  0.41162836180,     8962.45534991020},
4065     {     0.00000000012,  3.81140154428,     9866.41688066520},
4066     {     0.00000000012,  4.25382428399,     6151.53388830500},
4067     {     0.00000000015,  3.63297907536,     4535.05943692440},
4068     {     0.00000000012,  1.61461268629,     1592.59601363280},
4069     {     0.00000000010,  5.80958145013,     3333.49887969900},
4070     {     0.00000000010,  1.23772110632,     6836.64525283380},
4071     {     0.00000000009,  1.44366353557,    26724.89941359840},
4072     {     0.00000000008,  2.02732749775,     6923.95345737360},
4073     {     0.00000000009,  3.19116537565,     6438.49624942560},
4074     {     0.00000000008,  1.85197515729,     1194.44701022460},
4075     {     0.00000000008,  2.56762648035,      398.14900340820},
4076     {     0.00000000007,  3.69377532737,     4399.99435688900},
4077     {     0.00000000005,  4.73479766634,     6127.65545055720},
4078     {     0.00000000005,  0.39109547220,     5092.15195811580},
4079     {     0.00000000006,  1.41716854423,    13365.97282514820},
4080     {     0.00000000005,  3.98879770109,     6283.07584999140},
4081     {     0.00000000005,  1.86523815587,     1059.38193018920},
4082     {     0.00000000006,  5.52177150128,     7477.52286021600},
4083     {     0.00000000005,  1.92244747457,     2810.92146160520},
4084 ];
4085 
4086 
4087 static const ln_vsop[LAT_B4] mars_latitude_b4 = [
4088     {     0.00000006007,  3.37637101191,     3340.61242669980},
4089     {     0.00000006625,  0.00000000000,        0.00000000000},
4090     {     0.00000000464,  3.77202757150,    10021.83728009940},
4091     {     0.00000000405,  0.63107416776,     6681.22485339960},
4092     {     0.00000000299,  4.32966790803,    13362.44970679920},
4093     {     0.00000000109,  4.85358280107,    16703.06213349900},
4094     {     0.00000000077,  2.88080440451,     3496.03282613400},
4095     {     0.00000000039,  1.43197590360,     3185.19202726560},
4096     {     0.00000000031,  5.67989354532,     3337.08930835080},
4097     {     0.00000000031,  5.33373014736,    20043.67456019880},
4098     {     0.00000000017,  4.32019018052,     3097.88382272579},
4099     {     0.00000000013,  1.77444975035,     6525.80445396540},
4100     {     0.00000000010,  0.04059602724,     3583.34103067380},
4101     {     0.00000000007,  4.46709463778,     6684.74797174860},
4102     {     0.00000000006,  1.85656049405,     2787.04302385740},
4103     {     0.00000000006,  1.15875671922,     3894.18182954220},
4104     {     0.00000000006,  5.76437007548,    23384.28698689860},
4105     {     0.00000000003,  2.91488661915,     6836.64525283380},
4106 ];
4107 
4108 
4109 static const ln_vsop[LAT_B5] mars_latitude_b5 = [
4110     {     0.00000000368,  4.63460005338,     3340.61242669980},
4111     {     0.00000000045,  5.14206308865,     6681.22485339960},
4112     {     0.00000000035,  3.14159265359,        0.00000000000},
4113     {     0.00000000012,  2.68434578055,    13362.44970679920},
4114     {     0.00000000010,  4.43919916342,     3496.03282613400},
4115     {     0.00000000006,  1.70177189273,    10021.83728009940},
4116     {     0.00000000005,  3.20415104620,    16703.06213349900},
4117     {     0.00000000004,  6.15670065734,     3185.19202726560},
4118     {     0.00000000001,  3.71915090755,    20043.67456019880},
4119 ];
4120 
4121 
4122 static const ln_vsop[RADIUS_R0] mars_radius_r0 = [
4123     {     1.53033488271,  0.00000000000,        0.00000000000},
4124     {     0.14184953160,  3.47971283528,     3340.61242669980},
4125     {     0.00660776362,  3.81783443019,     6681.22485339960},
4126     {     0.00046179117,  4.15595316782,    10021.83728009940},
4127     {     0.00008109733,  5.55958416318,     2810.92146160520},
4128     {     0.00007485318,  1.77239078402,     5621.84292321040},
4129     {     0.00005523191,  1.36436303770,     2281.23049651060},
4130     {     0.00003825160,  4.49407183687,    13362.44970679920},
4131     {     0.00002306537,  0.09081579001,     2544.31441988340},
4132     {     0.00001999396,  5.36059617709,     3337.08930835080},
4133     {     0.00002484394,  4.92545639920,     2942.46342329160},
4134     {     0.00001960195,  4.74249437639,     3344.13554504880},
4135     {     0.00001167119,  2.11260868341,     5092.15195811580},
4136     {     0.00001102816,  5.00908403998,      398.14900340820},
4137     {     0.00000899066,  4.40791133207,      529.69096509460},
4138     {     0.00000992252,  5.83861961952,     6151.53388830500},
4139     {     0.00000807354,  2.10217065501,     1059.38193018920},
4140     {     0.00000797915,  3.44839203899,      796.29800681640},
4141     {     0.00000740975,  1.49906336885,     2146.16541647520},
4142     {     0.00000692339,  2.13378874689,     8962.45534991020},
4143     {     0.00000633144,  0.89353283242,     3340.59517304760},
4144     {     0.00000725583,  1.24516810723,     8432.76438481560},
4145     {     0.00000633140,  2.92430446399,     3340.62968035200},
4146     {     0.00000574355,  0.82896244455,     2914.01423582380},
4147     {     0.00000526166,  5.38292991236,     3738.76143010800},
4148     {     0.00000629978,  1.28737486495,     1751.53953141600},
4149     {     0.00000472775,  5.19850522346,     3127.31333126180},
4150     {     0.00000348095,  4.83219199976,    16703.06213349900},
4151     {     0.00000283713,  2.90692064724,     3532.06069281140},
4152     {     0.00000279543,  5.25749685380,     6283.07584999140},
4153     {     0.00000233857,  5.10545987572,     5486.77784317500},
4154     {     0.00000219427,  5.58340231744,      191.44826611160},
4155     {     0.00000269896,  3.76393625127,     5884.92684658320},
4156     {     0.00000208335,  5.25476078693,     3340.54511639700},
4157     {     0.00000275217,  2.90817482492,     1748.01641306700},
4158     {     0.00000275506,  1.21767950614,     6254.62666252360},
4159     {     0.00000239119,  2.03669934656,     1194.44701022460},
4160     {     0.00000223189,  4.19861535147,     3149.16416058820},
4161     {     0.00000182689,  5.08062725665,     6684.74797174860},
4162     {     0.00000186207,  5.69871572410,     6677.70173505060},
4163     {     0.00000176000,  5.95341919657,     3870.30339179440},
4164     {     0.00000178617,  4.18423004741,     3333.49887969900},
4165     {     0.00000208330,  4.84626439637,     3340.67973700260},
4166     {     0.00000228126,  3.25526555588,     6872.67311951120},
4167     {     0.00000144312,  0.21306219460,     5088.62883976680},
4168     {     0.00000163527,  3.79888811958,     4136.91043351620},
4169     {     0.00000133126,  1.53906679361,     7903.07341972100},
4170     {     0.00000141755,  2.47792380112,     4562.46099302120},
4171     {     0.00000114927,  4.31748869065,     1349.86740965880},
4172     {     0.00000118789,  2.12168482244,     1589.07289528380},
4173     {     0.00000102094,  6.18145185708,     9492.14631500480},
4174     {     0.00000128570,  5.49884728795,     8827.39026987480},
4175     {     0.00000111546,  0.55346108403,    11243.68584642080},
4176     {     0.00000082498,  1.62220096558,    11773.37681151540},
4177     {     0.00000083204,  0.61551135046,     8429.24126646660},
4178     {     0.00000084463,  0.62274409931,     1592.59601363280},
4179     {     0.00000086666,  1.74984525176,     2700.71514038580},
4180     {     0.00000071813,  2.47494065480,    12303.06777661000},
4181     {     0.00000085321,  1.61634750496,     4690.47983635860},
4182     {     0.00000063641,  2.67334163937,      426.59819087600},
4183     {     0.00000068601,  2.40188234283,     4399.99435688900},
4184     {     0.00000058559,  4.72052839990,      213.29909543800},
4185     {     0.00000062009,  1.10068565926,     1221.84856632140},
4186     {     0.00000066499,  2.21296335919,     6041.32756708560},
4187     {     0.00000055810,  1.23288066320,     3185.19202726560},
4188     {     0.00000054969,  5.72695354791,      951.71840625060},
4189     {     0.00000052430,  3.02368095530,     4292.33083295040},
4190     {     0.00000055688,  5.44688671707,     3723.50895892300},
4191     {     0.00000058959,  3.26242460622,     6681.24210705180},
4192     {     0.00000044638,  2.01459444131,     8031.09226305840},
4193     {     0.00000058959,  1.23165296790,     6681.20759974740},
4194     {     0.00000042439,  2.26554261514,      155.42039943420},
4195     {     0.00000038955,  2.57760417339,     3341.59274776800},
4196     {     0.00000051550,  5.72324451485,     7079.37385680780},
4197     {     0.00000048940,  5.61613493545,     3553.91152213780},
4198     {     0.00000045406,  5.43303278149,     6467.92575796160},
4199     {     0.00000036438,  4.43922435395,     3894.18182954220},
4200     {     0.00000035980,  1.15972378713,     2288.34404351140},
4201     {     0.00000035268,  5.49032233898,     1990.74501704100},
4202     {     0.00000042192,  1.63254827838,     5628.95647021120},
4203     {     0.00000044292,  5.00344221303,     5614.72937620960},
4204     {     0.00000033616,  5.17029030468,    20043.67456019880},
4205     {     0.00000043256,  1.03722397198,    11769.85369316640},
4206     {     0.00000039237,  1.24237030858,     3339.63210563160},
4207     {     0.00000031949,  4.59259676953,     2274.11694950980},
4208     {     0.00000030352,  2.44163963455,    11371.70468975820},
4209     {     0.00000032269,  2.38222363233,     4535.05943692440},
4210     {     0.00000031855,  4.37536980289,        3.52311834900},
4211     {     0.00000029342,  4.06035002188,     3097.88382272579},
4212     {     0.00000031967,  1.93969979134,      382.89653222320},
4213     {     0.00000026164,  5.58463559826,     9623.68827669120},
4214     {     0.00000027903,  4.25809486053,     3191.04922956520},
4215     {     0.00000033044,  0.85475620169,      553.56940284240},
4216     {     0.00000027544,  1.57668645170,     9595.23908922340},
4217     {     0.00000025163,  0.81337734264,    10713.99488132620},
4218     {     0.00000022045,  0.85711201558,     3319.83703120740},
4219     {     0.00000024759,  5.38993953923,     2818.03500860600},
4220     {     0.00000023352,  6.01458974590,     3496.03282613400},
4221     {     0.00000024723,  2.58025225634,     2803.80791460440},
4222     {     0.00000019361,  5.18528881954,     6681.29216370240},
4223     {     0.00000019118,  5.41969355400,    10025.36039844840},
4224     {     0.00000019361,  5.59378511334,     6681.15754309680},
4225     {     0.00000018331,  5.79565723310,     7064.12138562280},
4226     {     0.00000018188,  5.61299105522,        7.11354700080},
4227     {     0.00000020393,  4.53615443964,     6489.77658728800},
4228     {     0.00000021258,  6.19174428363,    14054.60730802600},
4229     {     0.00000017094,  1.54988538094,     2957.71589447660},
4230     {     0.00000022794,  3.41719468533,     7632.94325965020},
4231     {     0.00000020561,  2.98654120324,     3361.38782219220},
4232     {     0.00000017050,  6.15529583629,    10404.73381232260},
4233     {     0.00000018007,  2.81505100996,     4032.77002792660},
4234     {     0.00000016487,  3.84534133372,    10973.55568635000},
4235     {     0.00000016056,  0.92819026247,    14584.29827312060},
4236     {     0.00000021008,  2.38506850221,     4989.05918389720},
4237     {     0.00000016291,  1.92190075688,     7373.38245462640},
4238     {     0.00000016286,  6.28252184173,     7210.91581849420},
4239     {     0.00000018575,  4.07319565284,     2388.89402044920},
4240     {     0.00000015976,  4.58379703739,     3264.34635542420},
4241     {     0.00000019909,  2.73523951203,     5099.26550511660},
4242     {     0.00000019667,  1.86294734899,     3443.70520091840},
4243     {     0.00000016500,  4.14061657170,     7477.52286021600},
4244     {     0.00000019492,  6.03778625701,    10018.31416175040},
4245     {     0.00000015097,  2.65433832872,     2787.04302385740},
4246     {     0.00000019099,  0.22623513076,    13745.34623902240},
4247     {     0.00000017164,  3.18826299350,     3347.72597370060},
4248     {     0.00000013407,  2.12775612449,     3344.20285535160},
4249     {     0.00000015407,  2.20766468871,     2118.76386037840},
4250     {     0.00000017246,  3.67064642858,     3205.54734666440},
4251     {     0.00000013091,  4.27475419816,    14314.16811304980},
4252     {     0.00000016437,  2.86612474805,    14712.31711645800},
4253     {     0.00000016648,  4.52135149200,     6674.11130639880},
4254     {     0.00000013718,  1.68586111426,     3337.02199804800},
4255     {     0.00000011824,  0.19675650045,     3475.67750673520},
4256     {     0.00000011757,  3.23020638064,     5828.02847164760},
4257     {     0.00000011884,  4.82075035433,     7234.79425624200},
4258     {     0.00000010608,  1.73995972784,      639.89728631400},
4259     {     0.00000011143,  0.23833349966,    12832.75874170460},
4260     {     0.00000011028,  0.44555687290,    10213.28554621100},
4261     {     0.00000010238,  5.74731032428,      242.72860397400},
4262     {     0.00000010052,  2.45096419672,     4929.68532198360},
4263     {     0.00000010061,  0.78904152333,     9381.93999378540},
4264     {     0.00000010065,  5.37509927353,     5085.03841111500},
4265     {     0.00000011897,  0.79890074455,     3265.83082813250},
4266     {     0.00000008983,  0.96474320941,     4933.20844033260},
4267     {     0.00000008976,  4.18310051894,     9225.53927328300},
4268     {     0.00000008982,  1.98499607259,    15113.98923821520},
4269     {     0.00000008325,  1.93706224943,     1648.44675719740},
4270     {     0.00000007832,  2.04997038646,     1758.65307841680},
4271     {     0.00000007964,  3.92258783522,     2921.12778282460},
4272     {     0.00000010223,  2.66509814753,     2487.41604494780},
4273     {     0.00000008277,  0.94860765545,     2906.90068882300},
4274     {     0.00000007371,  0.84436508721,      692.15760122680},
4275     {     0.00000007529,  5.68043313811,    13916.01910964160},
4276     {     0.00000007907,  2.81314645975,    15643.68020330980},
4277     {     0.00000006956,  3.32212696002,     3230.40610548040},
4278     {     0.00000007426,  6.09654676653,     3583.34103067380},
4279     {     0.00000006402,  4.19806999276,     5202.35827933520},
4280     {     0.00000006523,  6.11927838278,      135.06508003540},
4281     {     0.00000006127,  0.00122595969,     6836.64525283380},
4282     {     0.00000006223,  6.10653136990,    17256.63153634140},
4283     {     0.00000008161,  5.24822786208,    10575.40668294180},
4284     {     0.00000006163,  3.60026818309,    10021.85453375160},
4285     {     0.00000006163,  1.56949585888,    10021.82002644720},
4286     {     0.00000005673,  0.13638905291,    13524.91634293140},
4287     {     0.00000006257,  4.50450316951,     8425.65083781480},
4288     {     0.00000005249,  2.70116504868,     4459.36821880260},
4289     {     0.00000006470,  2.74232480124,     7740.60678358880},
4290     {     0.00000005523,  6.06378363783,    10419.98628350760},
4291     {     0.00000005548,  5.75002125481,    12168.00269657460},
4292     {     0.00000006827,  4.69340338938,    17654.78053974960},
4293     {     0.00000004993,  4.68464837021,      522.57741809380},
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5087     {     0.00000000084,  4.33209852801,    51449.32426327820},
5088     {     0.00000000079,  4.42171441227,      151.04766984290},
5089     {     0.00000000082,  2.85230384631,    14164.81362924540},
5090     {     0.00000000106,  4.19479352477,     9090.47419324760},
5091     {     0.00000000078,  4.29426802519,      187.92514776260},
5092     {     0.00000000078,  5.38566529072,     2655.56837247380},
5093     {     0.00000000084,  2.15121245434,     3311.12060839640},
5094     {     0.00000000083,  4.28280129037,    74923.09699802278},
5095     {     0.00000000077,  1.45903147715,     2544.38173018620},
5096     {     0.00000000078,  3.92028514294,    16762.43599541260},
5097     {     0.00000000098,  3.78877505378,     3198.43379966360},
5098     {     0.00000000092,  2.80228448795,     3707.83675566220},
5099     {     0.00000000082,  2.45812896343,     9815.65173166220},
5100     {     0.00000000076,  3.92674885488,     2910.08208256070},
5101     {     0.00000000103,  2.90157610001,    12032.93761653920},
5102     {     0.00000000076,  3.20012751409,     7733.49323658800},
5103     {     0.00000000098,  3.28574616663,     3289.33208883739},
5104     {     0.00000000086,  0.44954589670,     2942.39611298880},
5105     {     0.00000000077,  2.05948930109,    12928.73796892240},
5106     {     0.00000000075,  0.85784191736,    28638.90558114660},
5107     {     0.00000000101,  0.72388999452,    48827.43118573260},
5108     {     0.00000000093,  0.96205455167,      151.89728108520},
5109     {     0.00000000083,  4.42677043697,     2060.81785407180},
5110     {     0.00000000085,  5.19438010130,     2146.14816282300},
5111     {     0.00000000078,  0.05738144523,    10507.80933288900},
5112     {     0.00000000096,  6.24132708355,       11.04570026390},
5113     {     0.00000000088,  2.27514694850,    13361.46938573100},
5114     {     0.00000000074,  5.19118661748,     1055.44977692610},
5115     {     0.00000000095,  1.32630130009,     9278.84721956680},
5116     {     0.00000000091,  5.56686260659,    27873.58901026800},
5117     {     0.00000000084,  0.41519041956,     4296.90158267040},
5118     {     0.00000000074,  5.09773610570,     9755.23023837760},
5119     {     0.00000000102,  0.99471814765,     8186.51266249260},
5120     {     0.00000000073,  4.78565969143,    10787.63034454580},
5121     {     0.00000000090,  1.23322132624,     9093.99731159660},
5122     {     0.00000000089,  1.52171318808,     5088.21980485270},
5123     {     0.00000000075,  3.17716258197,     4403.51747523800},
5124     {     0.00000000076,  2.66623960187,    12725.45343477500},
5125     {     0.00000000072,  2.57646391241,    10817.08765554480},
5126     {     0.00000000078,  0.17721609024,     3391.89276456221},
5127     {     0.00000000073,  1.65072523242,     5452.26274007740},
5128     {     0.00000000072,  2.24247662338,      272.67295735160},
5129     {     0.00000000084,  5.31880055844,     4716.38622654560},
5130     {     0.00000000081,  5.46340742050,     3856.07629779280},
5131     {     0.00000000091,  2.82213463878,      367.22432896240},
5132     {     0.00000000076,  5.54629636453,     4349.16189758320},
5133     {     0.00000000073,  4.61913155968,     3288.35211178700},
5134     {     0.00000000097,  0.68615321372,    10006.58480891440},
5135     {     0.00000000071,  0.29424294238,     1324.94134054000},
5136     {     0.00000000074,  1.74142938655,    78263.70942472259},
5137     {     0.00000000076,  0.00928867044,     6534.41316687600},
5138     {     0.00000000084,  2.33518173212,     3738.74417645580},
5139     {     0.00000000075,  3.61437779765,    12306.59089495900},
5140     {     0.00000000085,  0.94196641948,     2146.18267012740},
5141     {     0.00000000071,  2.07200856102,     9124.92198604240},
5142     {     0.00000000071,  4.48060598672,     9153.90361602180},
5143     {     0.00000000073,  0.28701671181,    10654.62101941260},
5144     {     0.00000000072,  0.84342376295,     3334.54651107000},
5145     {     0.00000000094,  5.72469267962,      206.70073729660},
5146     {     0.00000000091,  5.12701600437,     3392.87274161260},
5147     {     0.00000000076,  5.96038992872,     3482.79105373600},
5148     {     0.00000000071,  1.16745785331,     1574.84580128220},
5149     {     0.00000000071,  1.08624489534,     3866.78027344540},
5150     {     0.00000000071,  3.83802267632,    25298.29315444680},
5151     {     0.00000000075,  4.30016984862,    10177.19036923080},
5152     {     0.00000000081,  5.71063897801,    14687.39104733920},
5153     {     0.00000000070,  0.07475004834,    12839.87228870540},
5154     {     0.00000000080,  5.87829926376,     3495.96551583120},
5155     {     0.00000000069,  0.30282686836,    12012.58229714040},
5156     {     0.00000000071,  2.07966257785,     1063.31408345230},
5157     {     0.00000000071,  0.12080952310,    27433.88921587499},
5158     {     0.00000000072,  1.77506111582,     3564.95722240170},
5159     {     0.00000000069,  0.33478558217,        5.52292430740},
5160     {     0.00000000068,  1.56404561711,     2398.55036473080},
5161     {     0.00000000090,  2.61953849393,     3346.67834232960},
5162     {     0.00000000068,  1.06108185791,      191.38095580880},
5163     {     0.00000000093,  3.72700623766,     2472.67876262220},
5164     {     0.00000000077,  0.87794040199,     2917.94638908690},
5165     {     0.00000000067,  3.29797798194,     8006.16619393960},
5166     {     0.00000000082,  4.33799969295,     9360.60435331840},
5167     {     0.00000000068,  4.84097033274,    12942.96506292400},
5168     {     0.00000000083,  5.35554906977,     2125.81009707640},
5169     {     0.00000000083,  1.82578570378,     3511.28529731900},
5170     {     0.00000000068,  2.68247854175,    20213.25474333179},
5171     {     0.00000000086,  0.81171860574,      209.77597708900},
5172     {     0.00000000084,  4.36595418339,     3738.77868376020},
5173     {     0.00000000071,  2.76447756531,    15650.79375031060},
5174     {     0.00000000066,  3.31414998734,     8830.91338822380},
5175     {     0.00000000090,  0.71593793107,     3451.79906898740},
5176     {     0.00000000067,  4.04202356962,     3930.20969621960},
5177     {     0.00000000068,  4.35822797929,    12299.54465826100},
5178     {     0.00000000073,  3.66802441649,      194.97138446060},
5179     {     0.00000000077,  5.89874180574,     4307.58330413540},
5180     {     0.00000000089,  2.09613892664,     5312.56460055460},
5181     {     0.00000000068,  1.05513114246,     1987.22189869200},
5182     {     0.00000000082,  5.86597589657,     7747.72033058960},
5183     {     0.00000000071,  0.65820952553,      860.30992875280},
5184     {     0.00000000064,  0.98960038205,     3376.17516116840},
5185     {     0.00000000067,  5.22683619088,    24606.13555322000},
5186     {     0.00000000070,  0.96227192685,     8428.83223155250},
5187     {     0.00000000064,  5.15148312244,     8966.38750317330},
5188     {     0.00000000062,  6.18276166360,     3966.28261901220},
5189     {     0.00000000061,  1.47350010728,     1685.05212250160},
5190     {     0.00000000069,  4.32901678608,     8436.69653807870},
5191     {     0.00000000064,  2.11869877898,     3305.04969223120},
5192     {     0.00000000079,  5.29501968122,     8322.55806359620},
5193     {     0.00000000060,  1.17940250396,    97670.38771289718},
5194     {     0.00000000060,  5.15547946009,     4665.55376723980},
5195     {     0.00000000061,  4.04008021030,     2942.48067694380},
5196     {     0.00000000061,  0.44282820959,     4686.95671800959},
5197     {     0.00000000079,  2.10625649179,     7917.30051372260},
5198     {     0.00000000075,  4.81216780547,    27299.24421193320},
5199     {     0.00000000058,  1.69747168940,    12082.65513417120},
5200     {     0.00000000075,  1.85618011420,    52566.19261584059},
5201     {     0.00000000057,  5.11652903646,     1898.33396428740},
5202     {     0.00000000075,  5.15830659680,    45884.96776244100},
5203     {     0.00000000060,  2.68566185208,     6283.05859633920},
5204     {     0.00000000056,  3.77198339507,      299.12639426920},
5205     {     0.00000000072,  0.05525158510,     6286.59896834040},
5206     {     0.00000000075,  5.79419108898,     1059.36467653700},
5207     {     0.00000000056,  0.47178586543,     1727.66109366820},
5208     {     0.00000000061,  2.00931045169,     2942.44616963940},
5209     {     0.00000000060,  2.60462801513,    30376.35263916660},
5210     {     0.00000000057,  4.18603648623,     4531.53631857540},
5211     {     0.00000000059,  1.95998946118,     7593.79509706520},
5212     {     0.00000000059,  0.11151543852,     5960.08562219340},
5213     {     0.00000000068,  3.50707258885,     7064.10413197060},
5214     {     0.00000000056,  2.43554289279,    11567.19126307820},
5215     {     0.00000000060,  0.23404709116,     2619.47319549360},
5216     {     0.00000000066,  2.94716590333,     8446.99147881720},
5217     {     0.00000000059,  5.49704665474,     7322.10246078180},
5218     {     0.00000000064,  3.95992112220,     3050.12694723020},
5219     {     0.00000000055,  2.19506741266,        7.04623669800},
5220     {     0.00000000058,  0.32431074295,    19645.52555679060},
5221     {     0.00000000075,  4.12415692769,    21150.81336588360},
5222     {     0.00000000075,  3.99896297048,     5483.25472482600},
5223     {     0.00000000057,  0.21772333641,    17402.33328172660},
5224     {     0.00000000069,  3.20209555520,    16066.06586147480},
5225     {     0.00000000056,  2.00267092675,    17660.30346405700},
5226     {     0.00000000060,  4.71643347424,     6283.09310364360},
5227     {     0.00000000054,  0.38782719267,      360.11078196160},
5228     {     0.00000000073,  3.41087754271,    14556.89671702380},
5229     {     0.00000000068,  5.74655335863,      987.74627292800},
5230 ];
5231 
5232 
5233 static const ln_vsop[RADIUS_R1] mars_radius_r1 = [
5234     {     0.01107433345,  2.03250524857,     3340.61242669980},
5235     {     0.00103175887,  2.37071847807,     6681.22485339960},
5236     {     0.00012877200,  0.00000000000,        0.00000000000},
5237     {     0.00010815880,  2.70888095665,    10021.83728009940},
5238     {     0.00001194550,  3.04702256206,    13362.44970679920},
5239     {     0.00000438582,  2.88835054603,     2281.23049651060},
5240     {     0.00000395700,  3.42323670971,     3344.13554504880},
5241     {     0.00000182576,  1.58427562964,     2544.31441988340},
5242     {     0.00000135851,  3.38507063082,    16703.06213349900},
5243     {     0.00000128199,  0.62991771813,     1059.38193018920},
5244     {     0.00000127059,  1.95391155885,      796.29800681640},
5245     {     0.00000118443,  2.99762091382,     2146.16541647520},
5246     {     0.00000128362,  6.04343227063,     3337.08930835080},
5247     {     0.00000087534,  3.42053385867,      398.14900340820},
5248     {     0.00000083021,  3.85575072018,     3738.76143010800},
5249     {     0.00000075604,  4.45097659377,     6151.53388830500},
5250     {     0.00000072002,  2.76443992447,      529.69096509460},
5251     {     0.00000066545,  2.54878381470,     1751.53953141600},
5252     {     0.00000054305,  0.67754203387,     8962.45534991020},
5253     {     0.00000051043,  3.72584855417,     6684.74797174860},
5254     {     0.00000066413,  4.40596377334,     1748.01641306700},
5255     {     0.00000047860,  2.28524521788,     2914.01423582380},
5256     {     0.00000049420,  5.72961379219,     3340.59517304760},
5257     {     0.00000049420,  1.47720011103,     3340.62968035200},
5258     {     0.00000057519,  0.54356133120,     1194.44701022460},
5259     {     0.00000048320,  2.58061402348,     3149.16416058820},
5260     {     0.00000036383,  6.02729341698,     3185.19202726560},
5261     {     0.00000037161,  5.81436290851,     1349.86740965880},
5262     {     0.00000036035,  5.89515829011,     3333.49887969900},
5263     {     0.00000031111,  0.97820401887,      191.44826611160},
5264     {     0.00000038957,  2.31902442004,     4136.91043351620},
5265     {     0.00000027256,  5.41369838171,     1592.59601363280},
5266     {     0.00000024302,  3.75838444077,      155.42039943420},
5267     {     0.00000022808,  1.74818178182,     5088.62883976680},
5268     {     0.00000022322,  0.93941901193,      951.71840625060},
5269     {     0.00000021712,  3.83569490817,     6283.07584999140},
5270     {     0.00000021302,  0.78030571909,     1589.07289528380},
5271     {     0.00000021631,  4.56903942095,     3532.06069281140},
5272     {     0.00000017957,  4.21923537063,     3870.30339179440},
5273     {     0.00000018241,  0.41334220202,     5486.77784317500},
5274     {     0.00000016250,  3.80772429678,     3340.54511639700},
5275     {     0.00000016803,  5.54855432911,     3097.88382272579},
5276     {     0.00000016852,  4.53696884484,     4292.33083295040},
5277     {     0.00000015749,  4.75766175289,     9492.14631500480},
5278     {     0.00000015747,  3.72356261757,    20043.67456019880},
5279     {     0.00000020429,  3.13541604634,     4690.47983635860},
5280     {     0.00000014699,  5.95340513928,     3894.18182954220},
5281     {     0.00000016251,  3.39910570757,     3340.67973700260},
5282     {     0.00000014256,  3.99914527335,     1990.74501704100},
5283     {     0.00000016529,  0.96740368703,     4399.99435688900},
5284     {     0.00000013011,  5.14215010082,     6677.70173505060},
5285     {     0.00000012482,  1.03238555854,     3341.59274776800},
5286     {     0.00000016454,  3.53827765951,     2700.71514038580},
5287     {     0.00000016167,  2.34891110870,      553.56940284240},
5288     {     0.00000013169,  0.41462220221,     5614.72937620960},
5289     {     0.00000011270,  1.02387117266,    12303.06777661000},
5290     {     0.00000012410,  6.23139144626,     5628.95647021120},
5291     {     0.00000012747,  0.69046237163,     3723.50895892300},
5292     {     0.00000011828,  6.25270937134,     2274.11694950980},
5293     {     0.00000010382,  1.23229650709,      426.59819087600},
5294     {     0.00000011207,  1.31732435116,     3496.03282613400},
5295     {     0.00000010345,  0.90062869301,     4535.05943692440},
5296     {     0.00000012214,  4.22347837212,     7079.37385680780},
5297     {     0.00000009764,  3.45310129694,      382.89653222320},
5298     {     0.00000008583,  1.16478890510,     2787.04302385740},
5299     {     0.00000007879,  5.73808303461,     2288.34404351140},
5300     {     0.00000009192,  1.81719352796,     6681.24210705180},
5301     {     0.00000007752,  4.15038634174,     6041.32756708560},
5302     {     0.00000009192,  6.06960723129,     6681.20759974740},
5303     {     0.00000009008,  2.58179552398,     2388.89402044920},
5304     {     0.00000006770,  0.24011880700,    11773.37681151540},
5305     {     0.00000007088,  3.51428380287,     8031.09226305840},
5306     {     0.00000009159,  3.90203365989,     3553.91152213780},
5307     {     0.00000007233,  3.70260535699,     2818.03500860600},
5308     {     0.00000006701,  4.25537421062,      242.72860397400},
5309     {     0.00000006534,  0.04317593308,     2957.71589447660},
5310     {     0.00000008783,  2.19764346848,     1221.84856632140},
5311     {     0.00000006540,  2.11811131682,     8429.24126646660},
5312     {     0.00000006835,  4.04527289029,    10025.36039844840},
5313     {     0.00000007279,  4.26969778292,     2803.80791460440},
5314     {     0.00000007679,  1.00816125095,     8432.76438481560},
5315     {     0.00000005736,  3.13988802339,      213.29909543800},
5316     {     0.00000005343,  3.78184164680,     5092.15195811580},
5317     {     0.00000005985,  2.96429619989,     6489.77658728800},
5318     {     0.00000005132,  3.98288020531,        7.11354700080},
5319     {     0.00000006264,  1.90345600186,     5621.84292321040},
5320     {     0.00000005238,  2.67050910776,     7477.52286021600},
5321     {     0.00000006264,  1.60046198142,     3347.72597370060},
5322     {     0.00000006527,  2.76220386403,     3339.63210563160},
5323     {     0.00000004594,  1.82031785094,     2810.92146160520},
5324     {     0.00000005460,  4.60869963415,     3583.34103067380},
5325     {     0.00000004730,  0.90611934427,     5099.26550511660},
5326     {     0.00000005484,  4.91405753832,     7632.94325965020},
5327     {     0.00000004002,  4.14100005210,     9623.68827669120},
5328     {     0.00000003836,  0.03411499404,     7234.79425624200},
5329     {     0.00000003618,  5.76553319747,     4933.20844033260},
5330     {     0.00000003747,  0.08776717073,     6525.80445396540},
5331     {     0.00000003016,  3.73804058695,     6681.29216370240},
5332     {     0.00000003975,  4.91286826343,     2942.46342329160},
5333     {     0.00000003911,  0.67457174687,     3127.31333126180},
5334     {     0.00000003923,  3.07698893109,        3.52311834900},
5335     {     0.00000003943,  0.53936955267,     5884.92684658320},
5336     {     0.00000002902,  4.66228680082,     7210.91581849420},
5337     {     0.00000002803,  1.00505054832,     7064.12138562280},
5338     {     0.00000003152,  4.54611126545,     2487.41604494780},
5339     {     0.00000002797,  0.05226680768,      639.89728631400},
5340     {     0.00000002758,  5.17057629399,     5828.02847164760},
5341     {     0.00000003020,  4.14658810846,     6681.15754309680},
5342     {     0.00000003000,  0.82762095066,     5085.03841111500},
5343     {     0.00000003022,  2.59437829291,     2906.90068882300},
5344     {     0.00000002673,  0.69433657973,     2699.73481931760},
5345     {     0.00000002593,  1.08691889359,     4929.68532198360},
5346     {     0.00000003127,  0.99947199034,     2118.76386037840},
5347     {     0.00000002597,  5.01157388627,    10018.31416175040},
5348     {     0.00000002606,  5.34395258978,    10973.55568635000},
5349     {     0.00000002779,  3.98360727591,     6467.92575796160},
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5873     {     0.00000000029,  0.38968519354,    35707.71008290740},
5874     {     0.00000000035,  1.98847450868,    14556.89671702380},
5875     {     0.00000000032,  0.36447448811,     5466.42252377620},
5876     {     0.00000000029,  2.84335822989,     3651.45322556820},
5877     {     0.00000000029,  1.70561861073,    42146.20633233299},
5878     {     0.00000000029,  6.27427740112,    31022.75317085620},
5879     {     0.00000000029,  4.85775467825,       36.02786667740},
5880     {     0.00000000029,  0.65663514164,     3344.11829139661},
5881     {     0.00000000039,  2.60584004585,     6679.74038069130},
5882     {     0.00000000031,  4.96068967529,    15423.26756087100},
5883     {     0.00000000032,  4.30747041560,    30376.35263916660},
5884     {     0.00000000031,  4.97488131714,    48031.13317891620},
5885     {     0.00000000036,  5.21102353378,      860.30992875280},
5886     {     0.00000000029,  2.68740712720,     3344.15279870100},
5887     {     0.00000000029,  4.89226176414,    14469.58851248400},
5888     {     0.00000000035,  0.63682098833,    23553.86717003160},
5889     {     0.00000000028,  3.93317215375,     2655.56837247380},
5890     {     0.00000000028,  4.95417710116,      792.77488846740},
5891     {     0.00000000031,  1.20412048035,    16328.72425753579},
5892     {     0.00000000033,  2.23175098152,    44768.09940987860},
5893     {     0.00000000033,  5.53387746412,    38086.87455647900},
5894     {     0.00000000028,  5.39448318150,     1250.83019630080},
5895     {     0.00000000034,  0.46215642912,     2751.54759969160},
5896     {     0.00000000031,  6.25053987025,    17388.10618772499},
5897     {     0.00000000028,  1.84806130514,     2075.04494807340},
5898     {     0.00000000029,  4.75344799610,    28230.18722269139},
5899     {     0.00000000028,  4.36162258057,    39203.74290904139},
5900     {     0.00000000032,  5.19762814944,     1214.80232962340},
5901     {     0.00000000027,  1.83675735374,    45494.58142974879},
5902     {     0.00000000028,  4.99070749177,     6593.91664885980},
5903     {     0.00000000027,  3.31433250805,    12942.96506292400},
5904     {     0.00000000029,  4.94569969969,       87.30820453981},
5905     {     0.00000000027,  1.32843166459,     7203.80227149340},
5906 ];
5907 
5908 
5909 static const ln_vsop[RADIUS_R2] mars_radius_r2 = [
5910     {     0.00044242249,  0.47930604954,     3340.61242669980},
5911     {     0.00008138042,  0.86998389204,     6681.22485339960},
5912     {     0.00001274915,  1.22593985222,    10021.83728009940},
5913     {     0.00000187388,  1.57298976045,    13362.44970679920},
5914     {     0.00000040745,  1.97082077028,     3344.13554504880},
5915     {     0.00000052395,  3.14159265359,        0.00000000000},
5916     {     0.00000026617,  1.91665337822,    16703.06213349900},
5917     {     0.00000017828,  4.43491476419,     2281.23049651060},
5918     {     0.00000011713,  4.52509926559,     3185.19202726560},
5919     {     0.00000010210,  5.39147322060,     1059.38193018920},
5920     {     0.00000009950,  0.41865678448,      796.29800681640},
5921     {     0.00000009236,  4.53559625376,     2146.16541647520},
5922     {     0.00000007299,  3.14214513120,     2544.31441988340},
5923     {     0.00000007214,  2.29302335628,     6684.74797174860},
5924     {     0.00000006810,  5.26707245601,      155.42039943420},
5925     {     0.00000006526,  2.30772456100,     3738.76143010800},
5926     {     0.00000007783,  5.93373461009,     1748.01641306700},
5927     {     0.00000005840,  1.05191820290,     1349.86740965880},
5928     {     0.00000006750,  5.30191763402,     1194.44701022460},
5929     {     0.00000004695,  0.76881032874,     3097.88382272579},
5930     {     0.00000005390,  1.00200068360,     3149.16416058820},
5931     {     0.00000004406,  2.45557331437,      951.71840625060},
5932     {     0.00000004286,  3.89642578846,     1592.59601363280},
5933     {     0.00000003516,  1.84991934524,      398.14900340820},
5934     {     0.00000003699,  2.26016989021,    20043.67456019880},
5935     {     0.00000003378,  3.81703201748,     1751.53953141600},
5936     {     0.00000004585,  0.80785643853,     4136.91043351620},
5937     {     0.00000003201,  2.11661594157,     5614.72937620960},
5938     {     0.00000003620,  1.32428600053,     3333.49887969900},
5939     {     0.00000002915,  1.19342490174,      529.69096509460},
5940     {     0.00000002979,  2.86468474914,     6151.53388830500},
5941     {     0.00000003057,  4.55288594507,     5628.95647021120},
5942     {     0.00000002906,  1.20300479533,     3894.18182954220},
5943     {     0.00000003848,  3.86071515455,      553.56940284240},
5944     {     0.00000002819,  2.48714583532,     1990.74501704100},
5945     {     0.00000002657,  6.07409846258,     4292.33083295040},
5946     {     0.00000002698,  2.92100135189,     3496.03282613400},
5947     {     0.00000002396,  5.94193484091,     2787.04302385740},
5948     {     0.00000002263,  2.56188049651,      191.44826611160},
5949     {     0.00000002169,  5.36834559071,     8962.45534991020},
5950     {     0.00000002149,  2.74919289456,      242.72860397400},
5951     {     0.00000002218,  1.85260509629,     3337.08930835080},
5952     {     0.00000001998,  5.76396921426,     3341.59274776800},
5953     {     0.00000001999,  3.82347205028,     2914.01423582380},
5954     {     0.00000001835,  5.68648448195,     1589.07289528380},
5955     {     0.00000001810,  3.32122811143,     5088.62883976680},
5956     {     0.00000001968,  4.17404480033,     3340.59517304760},
5957     {     0.00000002411,  4.68376177281,     4690.47983635860},
5958     {     0.00000001967,  6.20570363430,     3340.62968035200},
5959     {     0.00000001626,  5.67648778513,     4535.05943692440},
5960     {     0.00000002161,  1.07446445419,     2388.89402044920},
5961     {     0.00000001965,  3.10811453974,     3583.34103067380},
5962     {     0.00000001985,  5.75867975763,     4399.99435688900},
5963     {     0.00000001504,  4.95929390466,      382.89653222320},
5964     {     0.00000001276,  4.82147500391,     2957.71589447660},
5965     {     0.00000001475,  2.22614544794,     3723.50895892300},
5966     {     0.00000001196,  3.26743061042,     9492.14631500480},
5967     {     0.00000001349,  4.87558985925,     6525.80445396540},
5968     {     0.00000001436,  2.69754023270,     7079.37385680780},
5969     {     0.00000001223,  2.61880227353,    10025.36039844840},
5970     {     0.00000001402,  5.19177439326,     2700.71514038580},
5971     {     0.00000001202,  0.93436294282,     2810.92146160520},
5972     {     0.00000000870,  5.81258009514,    12303.06777661000},
5973     {     0.00000000867,  2.20048756217,     2699.73481931760},
5974     {     0.00000000831,  2.01782919511,     5092.15195811580},
5975     {     0.00000000856,  5.96129932558,      426.59819087600},
5976     {     0.00000000847,  2.26415579047,     6283.07584999140},
5977     {     0.00000000917,  1.40259081260,     6489.77658728800},
5978     {     0.00000000833,  1.17376008822,     7477.52286021600},
5979     {     0.00000001041,  6.27097603149,     3347.72597370060},
5980     {     0.00000000965,  3.40293030184,     5621.84292321040},
5981     {     0.00000000723,  4.26276570887,     4933.20844033260},
5982     {     0.00000000770,  2.06490049164,     5486.77784317500},
5983     {     0.00000000706,  2.34080074294,        7.11354700080},
5984     {     0.00000000954,  2.11093711712,     3870.30339179440},
5985     {     0.00000000844,  2.23791576390,     3553.91152213780},
5986     {     0.00000000647,  2.24565892529,     3340.54511639700},
5987     {     0.00000000653,  3.98464883505,     6677.70173505060},
5988     {     0.00000000717,  0.29523050971,     6681.24210705180},
5989     {     0.00000000828,  0.22887694811,     3532.06069281140},
5990     {     0.00000000612,  1.56040446304,     7234.79425624200},
5991     {     0.00000000717,  4.54583138124,     6681.20759974740},
5992     {     0.00000000585,  3.29614213819,     1221.84856632140},
5993     {     0.00000000646,  1.83615168340,     3340.67973700260},
5994     {     0.00000000560,  5.05995427063,     8031.09226305840},
5995     {     0.00000000651,  0.16211451692,     7632.94325965020},
5996     {     0.00000000488,  3.07833516040,     6836.64525283380},
5997     {     0.00000000534,  4.25727954634,     3339.63210563160},
5998     {     0.00000000507,  2.59915154873,    23384.28698689860},
5999     {     0.00000000376,  6.27013206389,     2487.41604494780},
6000     {     0.00000000342,  4.71066540976,      639.89728631400},
6001     {     0.00000000449,  1.34119375784,      640.87760738220},
6002     {     0.00000000332,  2.66137676648,     9623.68827669120},
6003     {     0.00000000341,  5.96083550282,     4929.68532198360},
6004     {     0.00000000347,  6.09473597335,     7740.60678358880},
6005     {     0.00000000324,  6.05446352414,     2118.76386037840},
6006     {     0.00000000406,  4.95790035333,     8969.56889691100},
6007     {     0.00000000310,  0.02051325960,     6127.65545055720},
6008     {     0.00000000402,  2.84641476266,     5331.35744374080},
6009     {     0.00000000319,  1.44556053767,     5729.50644714900},
6010     {     0.00000000298,  5.73923165875,     6041.32756708560},
6011     {     0.00000000294,  3.06922916435,    10419.98628350760},
6012     {     0.00000000282,  6.04219786503,     7875.67186362420},
6013     {     0.00000000276,  5.11697230915,    11773.37681151540},
6014     {     0.00000000261,  2.89861311314,     7210.91581849420},
6015     {     0.00000000257,  1.08764384198,     2288.34404351140},
6016     {     0.00000000273,  3.83429606896,     8429.24126646660},
6017     {     0.00000000288,  6.13587869160,     6682.20517446780},
6018     {     0.00000000302,  3.61511244935,    12832.75874170460},
6019     {     0.00000000235,  2.21419308330,     6681.29216370240},
6020     {     0.00000000317,  3.60614958531,     2301.58581590939},
6021     {     0.00000000288,  5.08466449059,     2274.11694950980},
6022     {     0.00000000254,  0.36594869690,     3767.21061757580},
6023     {     0.00000000235,  2.62463894760,     6681.15754309680},
6024     {     0.00000000223,  3.46012483249,     6923.95345737360},
6025     {     0.00000000207,  3.44496733465,    10177.25767953360},
6026     {     0.00000000215,  0.57778871417,    10973.55568635000},
6027     {     0.00000000203,  3.89606611321,    10018.31416175040},
6028     {     0.00000000191,  2.41041363946,     8955.34180290940},
6029     {     0.00000000191,  1.58000924939,    10818.13528691580},
6030     {     0.00000000194,  2.45866911623,     7064.12138562280},
6031     {     0.00000000183,  1.67726083027,      213.29909543800},
6032     {     0.00000000191,  0.58807580019,     5828.02847164760},
6033     {     0.00000000238,  1.99795553508,    10575.40668294180},
6034     {     0.00000000246,  2.17522479887,     4562.46099302120},
6035     {     0.00000000177,  0.66443060538,    10021.85453375160},
6036     {     0.00000000176,  4.91646923030,    10021.82002644720},
6037     {     0.00000000217,  2.93960990684,    13365.97282514820},
6038     {     0.00000000213,  0.15664432335,     2942.46342329160},
6039     {     0.00000000166,  4.75384735897,     3914.95722503460},
6040     {     0.00000000155,  1.78567177351,     9830.38901398780},
6041     {     0.00000000164,  5.17682847411,     6298.32832117640},
6042     {     0.00000000176,  5.21146444811,     9866.41688066520},
6043     {     0.00000000157,  2.69801327811,     6894.52394883760},
6044     {     0.00000000148,  6.26338410775,     1039.02661079040},
6045     {     0.00000000148,  0.36640929573,     6688.33840040040},
6046     {     0.00000000150,  1.22257750814,      574.34479833480},
6047     {     0.00000000138,  2.09458777391,     1066.49547719000},
6048     {     0.00000000165,  6.15932460183,    15643.68020330980},
6049     {     0.00000000161,  4.66659171956,     8273.82086703240},
6050     {     0.00000000126,  0.68196579031,     6438.49624942560},
6051     {     0.00000000127,  1.69257165301,     3981.49003408200},
6052     {     0.00000000118,  2.78189840631,     3360.96774609859},
6053     {     0.00000000130,  0.84499223832,     3355.86489788480},
6054     {     0.00000000120,  0.30079432657,     3127.31333126180},
6055     {     0.00000000123,  1.63529824790,     6674.11130639880},
6056     {     0.00000000129,  2.26711428102,     6467.92575796160},
6057     {     0.00000000104,  0.07355376701,     3325.35995551480},
6058     {     0.00000000130,  4.41777190830,     3320.25710730100},
6059     {     0.00000000095,  1.32397695499,     7903.07341972100},
6060     {     0.00000000113,  0.65843018903,     3178.14579056760},
6061     {     0.00000000092,  4.98212090453,     9779.10867612540},
6062     {     0.00000000100,  4.11210877353,      536.80451209540},
6063     {     0.00000000096,  3.52474152096,     3475.67750673520},
6064     {     0.00000000106,  5.41425307049,    15113.98923821520},
6065     {     0.00000000100,  2.91165340473,      692.15760122680},
6066     {     0.00000000107,  3.76142120324,    13517.87010623340},
6067     {     0.00000000094,  3.21490077835,     8671.96987044060},
6068     {     0.00000000086,  5.24456061569,    13119.72110282519},
6069     {     0.00000000089,  5.73824161119,    11371.70468975820},
6070     {     0.00000000106,  5.90729095013,     8432.76438481560},
6071     {     0.00000000098,  3.61325552038,      853.19638175200},
6072     {     0.00000000080,  2.97911637785,    26724.89941359840},
6073     {     0.00000000078,  0.95802015551,     3191.04922956520},
6074     {     0.00000000080,  5.90881737672,     6040.34724601740},
6075     {     0.00000000087,  2.51076876054,     1052.26838318840},
6076     {     0.00000000091,  3.00950021946,    12964.30070339100},
6077     {     0.00000000075,  1.32761316297,    17924.91069982040},
6078     {     0.00000000073,  5.00315639405,     1903.43681250120},
6079     {     0.00000000073,  4.09954161905,     3319.83703120740},
6080     {     0.00000000074,  2.58079983162,    10021.90459040220},
6081     {     0.00000000070,  5.37592930185,    12310.18132361080},
6082     {     0.00000000072,  2.54228814803,     5884.92684658320},
6083     {     0.00000000069,  3.48131994134,    13760.59871020740},
6084     {     0.00000000068,  3.24176355205,    16706.58525184800},
6085     {     0.00000000067,  4.69007678444,      522.57741809380},
6086     {     0.00000000070,  1.00588846894,    13362.46696045140},
6087     {     0.00000000070,  2.38386517904,    13916.01910964160},
6088     {     0.00000000069,  5.27194307948,     3980.50971301380},
6089     {     0.00000000074,  3.94650982500,    16173.37116840440},
6090     {     0.00000000077,  0.12291238953,    11216.28429032400},
6091     {     0.00000000062,  0.15391383953,    11081.21921028860},
6092     {     0.00000000065,  3.97651716363,    13358.92658845020},
6093     {     0.00000000074,  2.99585183104,    10021.76996979660},
6094     {     0.00000000080,  6.17370752997,     9380.95967271720},
6095     {     0.00000000061,  2.56972324319,      149.56319713460},
6096     {     0.00000000059,  3.80951935336,    10264.56588407340},
6097     {     0.00000000060,  4.79893452692,     1437.17561419860},
6098     {     0.00000000064,  0.24188540623,    18984.29263000960},
6099     {     0.00000000059,  6.09929610915,     5459.37628707820},
6100     {     0.00000000060,  2.26503107747,    28628.33622609960},
6101     {     0.00000000067,  2.07568987702,     1596.18644228460},
6102     {     0.00000000058,  5.26082962947,    13362.43245314700},
6103     {     0.00000000056,  1.88732579172,     9070.11887384880},
6104     {     0.00000000058,  0.87844749732,     5642.19824260920},
6105     {     0.00000000056,  1.18238857561,     6696.47732458460},
6106     {     0.00000000062,  3.98214740104,     3427.92063123960},
6107     {     0.00000000055,  5.72462334370,      433.71173787680},
6108     {     0.00000000056,  2.35545469122,    33716.96506586640},
6109     {     0.00000000055,  3.77399580108,    10213.28554621100},
6110     {     0.00000000055,  1.33171417253,     8982.81066930900},
6111     {     0.00000000056,  5.49808236951,    24093.27678917520},
6112     {     0.00000000053,  5.34430579198,     5099.26550511660},
6113     {     0.00000000063,  3.53402427573,     3205.54734666440},
6114     {     0.00000000066,  6.22551943489,     8270.29774868340},
6115     {     0.00000000055,  4.74960633412,     6660.86953400080},
6116     {     0.00000000054,  0.30483383119,    12721.57209941700},
6117     {     0.00000000067,  0.58592813080,     3335.08950239240},
6118     {     0.00000000054,  2.12825168465,    13171.00144068760},
6119     {     0.00000000055,  5.03409432626,     7255.56965173440},
6120     {     0.00000000051,  2.91157155859,    10404.73381232260},
6121     {     0.00000000068,  2.44228862715,     6158.64743530580},
6122     {     0.00000000049,  0.23351885884,     4379.63903749020},
6123     {     0.00000000068,  2.26299130022,     2766.26762836500},
6124     {     0.00000000050,  6.10119450350,     3253.30422216000},
6125     {     0.00000000048,  2.36328912422,     4032.77002792660},
6126     {     0.00000000060,  0.30397974651,     9225.53927328300},
6127     {     0.00000000049,  5.45150193687,    13207.02930736500},
6128     {     0.00000000048,  0.72695221239,    10028.95082710020},
6129     {     0.00000000061,  3.40242612458,    10551.52824519400},
6130     {     0.00000000049,  3.40240207389,     3304.58456002240},
6131     {     0.00000000047,  2.83602015531,     9808.53818466140},
6132     {     0.00000000047,  0.50228092595,    17395.21973472580},
6133     {     0.00000000047,  3.03745055781,     6144.42034130420},
6134     {     0.00000000051,  1.27412586850,     3344.49376205780},
6135     {     0.00000000050,  1.83471955356,    30376.35263916660},
6136     {     0.00000000046,  0.75336415193,    16062.18452611680},
6137     {     0.00000000048,  0.33255135928,     6702.00024889200},
6138     {     0.00000000056,  0.21744516383,    10022.81760116760},
6139     {     0.00000000046,  5.83138098160,     3364.49086444760},
6140     {     0.00000000044,  0.79889168525,     7107.82304427560},
6141     {     0.00000000051,  0.35982632787,     9468.26787725700},
6142     {     0.00000000044,  3.10598653755,    10235.13637553740},
6143     {     0.00000000049,  0.14978113272,     2648.45482547300},
6144     {     0.00000000058,  4.51787450922,     6660.44945790720},
6145     {     0.00000000042,  5.40417232308,     3344.20285535160},
6146     {     0.00000000048,  2.42299327989,     4407.10790388980},
6147     {     0.00000000057,  3.84354136220,     6816.28993343500},
6148     {     0.00000000047,  1.49030680647,     6247.51311552280},
6149     {     0.00000000043,  5.14318704546,     7373.38245462640},
6150     {     0.00000000053,  5.94275298258,     8439.87793181640},
6151     {     0.00000000042,  0.14486089509,     1505.28780909299},
6152     {     0.00000000049,  5.57153056447,    17468.85519794540},
6153     {     0.00000000055,  6.26098836404,     3361.38782219220},
6154     {     0.00000000046,  3.07675286071,    12722.55242048520},
6155     {     0.00000000042,  4.74455545491,     3369.06161416760},
6156     {     0.00000000043,  4.97295184315,     3337.02199804800},
6157     {     0.00000000055,  3.80215638520,     3376.64029337720},
6158     {     0.00000000049,  4.43316054873,     9595.23908922340},
6159     {     0.00000000047,  1.97344701193,     1581.95934828300},
6160     {     0.00000000043,  0.38914582059,     6665.97238221460},
6161     {     0.00000000040,  1.06953099245,    23695.12778576700},
6162     {     0.00000000039,  1.54137978685,     2818.03500860600},
6163     {     0.00000000039,  3.79055778605,    33318.81606245820},
6164     {     0.00000000037,  5.27208151144,    20752.66436247540},
6165     {     0.00000000041,  1.82257882538,    14158.74771361560},
6166     {     0.00000000039,  3.15412760412,    14469.58851248400},
6167     {     0.00000000041,  0.55705920174,     3346.13535100720},
6168     {     0.00000000040,  5.57723811162,     3863.18984479360},
6169     {     0.00000000038,  2.71525209390,     8584.66166590080},
6170     {     0.00000000049,  5.44994428603,     9638.94074787620},
6171     {     0.00000000036,  4.85483701684,    23141.55838292460},
6172     {     0.00000000038,  2.11687208088,    15664.03552270859},
6173     {     0.00000000035,  5.30700692772,     6677.63442474780},
6174     {     0.00000000047,  2.56845181850,      162.46663613220},
6175     {     0.00000000034,  0.52542487310,    10713.99488132620},
6176     {     0.00000000047,  1.37540278055,     3316.73398895200},
6177     {     0.00000000045,  3.09384709364,     6701.58017279840},
6178     {     0.00000000036,  5.41035019142,    20597.24396304120},
6179     {     0.00000000035,  0.84359386197,     6518.75821726740},
6180     {     0.00000000038,  2.22559377525,     3503.07906283200},
6181     {     0.00000000043,  1.70231864194,    12323.42309600880},
6182     {     0.00000000046,  4.97118367286,     9381.93999378540},
6183     {     0.00000000043,  0.95148893985,    34115.11406927460},
6184     {     0.00000000035,  5.73672778427,     6684.81528205140},
6185     {     0.00000000043,  2.34641544095,     5244.04923920100},
6186     {     0.00000000040,  5.92298266112,     3336.73109134180},
6187     {     0.00000000032,  2.93166446867,     9499.25986200560},
6188     {     0.00000000032,  5.16999042304,     5085.03841111500},
6189     {     0.00000000033,  4.25349328071,    36659.42848915800},
6190     {     0.00000000043,  1.50296327105,    27035.74021246680},
6191     {     0.00000000040,  5.84317493907,    16460.33352952499},
6192     {     0.00000000032,  4.13881058425,    31570.79964939120},
6193     {     0.00000000035,  5.50392428699,     8425.65083781480},
6194     {     0.00000000034,  1.60980125001,    12566.15169998280},
6195     {     0.00000000034,  3.68494085870,     8827.39026987480},
6196     {     0.00000000031,  3.75179356135,     4845.90023579280},
6197     {     0.00000000030,  4.87421522701,     1692.16566950240},
6198     {     0.00000000037,  1.12999386856,    18052.92954315780},
6199     {     0.00000000031,  2.73132541218,    12295.95422960920},
6200     {     0.00000000030,  0.60227284998,    20354.51535906720},
6201     {     0.00000000030,  3.56474503430,    16304.91313009080},
6202     {     0.00000000030,  0.00488152861,    11243.68584642080},
6203     {     0.00000000039,  3.34380105325,    29978.20363575840},
6204     {     0.00000000028,  3.12073820291,    11925.27409260060},
6205     {     0.00000000027,  2.53950067771,    19004.64794940840},
6206     {     0.00000000028,  2.80254457895,     3607.21946842160},
6207     {     0.00000000032,  4.04412731190,     6680.24453233140},
6208     {     0.00000000028,  5.05697601811,    17412.05193577560},
6209     {     0.00000000029,  5.85207825749,    31172.65064598300},
6210     {     0.00000000033,  5.16379108102,    10596.18207843420},
6211     {     0.00000000027,  1.49309168626,     8186.51266249260},
6212     {     0.00000000027,  2.25111298175,       76.26607127560},
6213     {     0.00000000029,  1.82581479324,     3333.56619000180},
6214     {     0.00000000026,  5.61633953268,    14054.60730802600},
6215     {     0.00000000025,  4.87224086763,     3077.52850332700},
6216     {     0.00000000025,  4.33552142677,    17085.95866572220},
6217     {     0.00000000027,  0.80699664558,    20735.83216142559},
6218     {     0.00000000025,  5.15192817935,    11766.26326451460},
6219     {     0.00000000024,  4.12825907026,     4193.80880845180},
6220     {     0.00000000024,  4.31275606947,    14584.29827312060},
6221     {     0.00000000024,  2.19374141743,        3.52311834900},
6222     {     0.00000000024,  4.96463811748,    26087.90314157420},
6223     {     0.00000000027,  4.99613391588,     3877.41693879520},
6224     {     0.00000000029,  2.40082338888,     3312.16323923200},
6225     {     0.00000000024,  3.11953483056,    13149.15061136120},
6226     {     0.00000000030,  5.66813524124,     3281.23856478620},
6227     {     0.00000000026,  6.15978676797,      419.48464387520},
6228     {     0.00000000022,  2.11310905377,    20995.39296644940},
6229     {     0.00000000022,  5.24071820165,    12935.85151592320},
6230     {     0.00000000021,  1.72081702579,     2803.80791460440},
6231     {     0.00000000021,  4.18626331979,      187.92514776260},
6232     {     0.00000000022,  2.34227094593,     7322.10246078180},
6233     {     0.00000000021,  2.91971393449,    12168.00269657460},
6234     {     0.00000000023,  0.93103820963,     6261.74020952440},
6235     {     0.00000000022,  6.06510562418,    15110.46611986620},
6236     {     0.00000000020,  5.98993383835,    24150.08005134500},
6237     {     0.00000000022,  2.68877932276,     3546.79797513700},
6238     {     0.00000000023,  0.86323712599,    30774.50164257480},
6239     {     0.00000000020,  0.72774754977,    13553.89797291080},
6240     {     0.00000000022,  3.09244912137,    13362.38239649640},
6241     {     0.00000000020,  0.33937394936,     5989.06725217280},
6242     {     0.00000000025,  4.69237538534,     3347.65866339780},
6243     {     0.00000000025,  3.51209525616,    15265.88651930040},
6244     {     0.00000000026,  3.36529647088,    21265.52312652020},
6245     {     0.00000000021,  3.15458479593,    26637.59120905859},
6246     {     0.00000000019,  5.02104925490,     3029.77162783140},
6247     {     0.00000000019,  6.15294842048,    18208.34994259200},
6248     {     0.00000000023,  2.63078161726,    24491.42579258340},
6249     {     0.00000000025,  2.94366934698,    13362.51701710200},
6250     {     0.00000000020,  0.86927302126,     3399.98628861340},
6251     {     0.00000000018,  4.37088769243,     3651.45322556820},
6252     {     0.00000000022,  4.79007467235,    11614.43329373220},
6253     {     0.00000000019,  5.80539564686,    21795.21409161479},
6254     {     0.00000000017,  2.62698055094,     6872.67311951120},
6255     {     0.00000000020,  4.13854946023,    16699.53901514999},
6256     {     0.00000000018,  2.69537794731,    27682.14074415640},
6257     {     0.00000000017,  2.35800085725,     7788.36365908440},
6258     {     0.00000000016,  5.12979256980,     1744.42598441520},
6259     {     0.00000000019,  4.36117042303,    11780.49035851620},
6260     {     0.00000000017,  3.98180845854,    18606.49894600020},
6261     {     0.00000000020,  5.29535152048,    13936.79450513400},
6262     {     0.00000000018,  0.90866227881,    27433.88921587499},
6263     {     0.00000000018,  1.15898054343,      220.41264243880},
6264     {     0.00000000021,  1.07415905494,    11769.85369316640},
6265     {     0.00000000018,  3.61054156740,     9485.03276800400},
6266     {     0.00000000020,  5.54806425258,    14128.24277124560},
6267     {     0.00000000015,  4.19346479448,    23937.85638974100},
6268     {     0.00000000019,  2.49025671313,    24341.52831745660},
6269     {     0.00000000015,  6.22588872744,     8799.98871377800},
6270     {     0.00000000014,  2.27829337274,     4447.75123238460},
6271     {     0.00000000015,  1.86263855445,     2921.12778282460},
6272     {     0.00000000014,  3.59449757262,     3074.00538497800},
6273     {     0.00000000016,  4.04109191506,     3134.42687826260},
6274     {     0.00000000018,  1.50064662425,    19406.67828817460},
6275     {     0.00000000014,  4.63902518517,    11527.12508919240},
6276     {     0.00000000019,  5.20657856071,    32920.66705904999},
6277     {     0.00000000018,  5.05191310629,     3603.69635007260},
6278 ];
6279 
6280 
6281 static const ln_vsop[RADIUS_R3] mars_radius_r3 = [
6282     {     0.00001113108,  5.14987305093,     3340.61242669980},
6283     {     0.00000424447,  5.61343952053,     6681.22485339960},
6284     {     0.00000100044,  5.99727457548,    10021.83728009940},
6285     {     0.00000019606,  0.07631453783,    13362.44970679920},
6286     {     0.00000003478,  0.42912010211,    16703.06213349900},
6287     {     0.00000004693,  3.14159265359,        0.00000000000},
6288     {     0.00000002870,  0.44692002393,     3344.13554504880},
6289     {     0.00000002428,  3.02114808809,     3185.19202726560},
6290     {     0.00000000687,  0.80560442666,     6684.74797174860},
6291     {     0.00000000578,  0.77849309402,    20043.67456019880},
6292     {     0.00000000540,  3.86818792995,     1059.38193018920},
6293     {     0.00000000468,  4.52509679627,     3496.03282613400},
6294     {     0.00000000487,  1.60861075208,     3583.34103067380},
6295     {     0.00000000362,  4.42325508671,     2787.04302385740},
6296     {     0.00000000397,  5.72008479880,     3149.16416058820},
6297     {     0.00000000299,  0.75708428385,     3738.76143010800},
6298     {     0.00000000352,  5.55622002342,     4136.91043351620},
6299     {     0.00000000316,  3.37609906858,     6525.80445396540},
6300     {     0.00000000234,  2.13923292630,     3097.88382272579},
6301     {     0.00000000214,  4.20457486315,     3341.59274776800},
6302     {     0.00000000214,  0.56472270648,      155.42039943420},
6303     {     0.00000000201,  2.35183535764,     1592.59601363280},
6304     {     0.00000000206,  0.96951658721,     1990.74501704100},
6305     {     0.00000000231,  5.82604761072,     2388.89402044920},
6306     {     0.00000000163,  4.15852184076,     4535.05943692440},
6307     {     0.00000000148,  3.28924896754,     2957.71589447660},
6308     {     0.00000000155,  5.12396546072,      796.29800681640},
6309     {     0.00000000154,  1.13809634337,    10025.36039844840},
6310     {     0.00000000158,  3.76267616455,     1194.44701022460},
6311     {     0.00000000134,  5.57743966517,     3894.18182954220},
6312     {     0.00000000145,  3.02382693331,     3337.08930835080},
6313     {     0.00000000147,  4.25259909424,     4399.99435688900},
6314     {     0.00000000100,  4.26399779787,     1589.07289528380},
6315     {     0.00000000091,  6.12313839857,     6489.77658728800},
6316     {     0.00000000100,  1.12570940535,    23384.28698689860},
6317     {     0.00000000100,  1.17079212321,     7079.37385680780},
6318     {     0.00000000076,  6.00434755125,      529.69096509460},
6319     {     0.00000000076,  5.93213294948,     7477.52286021600},
6320     {     0.00000000069,  1.70323063297,     9492.14631500480},
6321     {     0.00000000069,  3.69074496365,     8962.45534991020},
6322     {     0.00000000068,  0.15861692654,     3870.30339179440},
6323     {     0.00000000061,  4.14189658327,     4292.33083295040},
6324     {     0.00000000063,  1.94108069224,     6923.95345737360},
6325     {     0.00000000060,  4.28936601254,    12303.06777661000},
6326     {     0.00000000065,  1.11375145336,     6151.53388830500},
6327     {     0.00000000075,  4.71644556135,     3347.72597370060},
6328     {     0.00000000056,  2.74147961496,     4933.20844033260},
6329     {     0.00000000053,  4.77467577413,     6127.65545055720},
6330     {     0.00000000050,  2.57807944338,     3340.59517304760},
6331     {     0.00000000049,  3.72534850744,     9866.41688066520},
6332     {     0.00000000050,  4.60885064189,     3340.62968035200},
6333     {     0.00000000042,  6.14743017903,     7234.79425624200},
6334     {     0.00000000042,  3.43563949713,     5486.77784317500},
6335     {     0.00000000044,  4.47908248027,      426.59819087600},
6336     {     0.00000000040,  0.79167327114,        7.11354700080},
6337     {     0.00000000045,  6.24183361898,     2274.11694950980},
6338     {     0.00000000038,  1.09272124839,     9623.68827669120},
6339     {     0.00000000042,  4.60964038446,     6682.20517446780},
6340     {     0.00000000038,  6.18558685622,     5729.50644714900},
6341     {     0.00000000038,  4.61315601536,     7740.60678358880},
6342     {     0.00000000036,  3.14996505800,      639.89728631400},
6343     {     0.00000000040,  1.47221984696,    13365.97282514820},
6344     {     0.00000000034,  2.44888174358,     2288.34404351140},
6345     {     0.00000000033,  4.07561553526,     3532.06069281140},
6346     {     0.00000000033,  4.00337366796,      191.44826611160},
6347     {     0.00000000034,  2.61360044785,     4690.47983635860},
6348     {     0.00000000042,  2.12093492483,    12832.75874170460},
6349     {     0.00000000032,  4.50887364887,     7875.67186362420},
6350     {     0.00000000032,  1.57458654370,    10419.98628350760},
6351     {     0.00000000042,  4.64340929626,    15643.68020330980},
6352     {     0.00000000034,  5.06656541832,     6681.24210705180},
6353     {     0.00000000036,  0.28987292152,     3723.50895892300},
6354     {     0.00000000033,  4.52563219188,     4929.68532198360},
6355     {     0.00000000034,  2.74382990905,     6677.70173505060},
6356     {     0.00000000029,  4.82292532787,     6836.64525283380},
6357     {     0.00000000031,  1.25306031255,      242.72860397400},
6358     {     0.00000000040,  1.33261257095,     5331.35744374080},
6359     {     0.00000000034,  3.03578748114,     6681.20759974740},
6360     {     0.00000000028,  5.44161669691,    10021.85453375160},
6361     {     0.00000000028,  3.41041355991,    10021.82002644720},
6362     {     0.00000000029,  1.44701292203,    26724.89941359840},
6363     {     0.00000000027,  0.23446626513,     9830.38901398780},
6364     {     0.00000000031,  3.55930404825,     8969.56889691100},
6365     {     0.00000000027,  0.62554177429,     6681.29216370240},
6366     {     0.00000000028,  0.66108605606,     6283.07584999140},
6367     {     0.00000000026,  2.93963456706,     2544.31441988340},
6368     {     0.00000000028,  3.02947324104,     2281.23049651060},
6369     {     0.00000000026,  0.06758130889,    10818.13528691580},
6370     {     0.00000000033,  5.38463358374,      553.56940284240},
6371     {     0.00000000026,  1.18522107539,     8955.34180290940},
6372     {     0.00000000030,  5.72396134501,     3339.63210563160},
6373     {     0.00000000032,  2.01050754787,     5884.92684658320},
6374     {     0.00000000027,  3.74433763737,     6298.32832117640},
6375     {     0.00000000026,  1.03437538808,     6681.15754309680},
6376     {     0.00000000024,  0.07873299732,      382.89653222320},
6377     {     0.00000000027,  0.62459992026,     3553.91152213780},
6378     {     0.00000000024,  3.46652790647,     8031.09226305840},
6379     {     0.00000000027,  4.97242136909,     3767.21061757580},
6380     {     0.00000000021,  0.34500515713,      398.14900340820},
6381     {     0.00000000022,  0.16000431895,     6674.11130639880},
6382     {     0.00000000025,  4.80981908946,     7632.94325965020},
6383     {     0.00000000020,  1.03308861369,     7210.91581849420},
6384     {     0.00000000019,  1.00795666182,     7064.12138562280},
6385     {     0.00000000020,  5.08085454093,     6688.33840040040},
6386     {     0.00000000024,  4.53131373076,     1748.01641306700},
6387     {     0.00000000021,  1.00067762870,     6894.52394883760},
6388     {     0.00000000021,  2.68399619671,    10018.31416175040},
6389     {     0.00000000018,  0.24311256346,     3981.49003408200},
6390     {     0.00000000023,  3.25718834734,     5621.84292321040},
6391     {     0.00000000018,  5.22850479583,     3333.49887969900},
6392     {     0.00000000017,  0.65399461894,     3340.54511639700},
6393     {     0.00000000016,  2.23166601637,    10264.56588407340},
6394     {     0.00000000016,  3.99319122882,      951.71840625060},
6395     {     0.00000000017,  0.24322966235,     3340.67973700260},
6396     {     0.00000000015,  0.68756621158,     2699.73481931760},
6397     {     0.00000000015,  0.79676193982,     6438.49624942560},
6398     {     0.00000000019,  3.09984967041,     8273.82086703240},
6399     {     0.00000000018,  5.49826928276,     2146.16541647520},
6400     {     0.00000000014,  4.64772091449,     2118.76386037840},
6401     {     0.00000000015,  2.35470306373,     5092.15195811580},
6402     {     0.00000000014,  4.97209858575,    11081.21921028860},
6403     {     0.00000000017,  0.37871098191,    10575.40668294180},
6404     {     0.00000000014,  0.53224061765,     1066.49547719000},
6405     {     0.00000000014,  1.08680225227,     6040.34724601740},
6406     {     0.00000000015,  4.55907710983,     8270.29774868340},
6407     {     0.00000000016,  5.13375747116,     9468.26787725700},
6408     {     0.00000000013,  0.53705768941,     5088.62883976680},
6409     {     0.00000000013,  0.11088343011,      213.29909543800},
6410     {     0.00000000013,  1.73016080294,     8671.96987044060},
6411     {     0.00000000012,  3.99880295457,    13207.02930736500},
6412     {     0.00000000012,  4.09699657905,     6041.32756708560},
6413     {     0.00000000013,  5.63225993860,     3178.14579056760},
6414     {     0.00000000011,  3.61924209254,    11773.37681151540},
6415     {     0.00000000013,  4.97777304006,    10022.81760116760},
6416     {     0.00000000011,  2.29245339567,     2914.01423582380},
6417     {     0.00000000011,  0.17994697060,     9070.11887384880},
6418     {     0.00000000012,  5.15200495439,    10973.55568635000},
6419     {     0.00000000014,  6.05434498977,      640.87760738220},
6420     {     0.00000000011,  1.75779397460,     4562.46099302120},
6421     {     0.00000000012,  1.46467398653,    12964.30070339100},
6422     {     0.00000000010,  3.56966848964,    15113.98923821520},
6423     {     0.00000000009,  4.80839551981,     3325.35995551480},
6424     {     0.00000000010,  1.23311080707,     3360.96774609859},
6425     {     0.00000000009,  1.93544907019,    13760.59871020740},
6426     {     0.00000000010,  0.49076916855,     2810.92146160520},
6427     {     0.00000000010,  2.49016534434,    16173.37116840440},
6428     {     0.00000000009,  3.62373278148,     5614.72937620960},
6429     {     0.00000000009,  2.29700488106,     8429.24126646660},
6430     {     0.00000000009,  2.52785501283,     3427.92063123960},
6431     {     0.00000000009,  5.57605456632,     3355.86489788480},
6432     {     0.00000000008,  3.38386554244,     8827.39026987480},
6433     {     0.00000000008,  1.67431441943,    16706.58525184800},
6434     {     0.00000000008,  3.62389227844,    12310.18132361080},
6435     {     0.00000000008,  2.25791643317,      151.89728108520},
6436     {     0.00000000008,  3.08029498940,     6254.62666252360},
6437     {     0.00000000010,  2.86769411066,     3320.25710730100},
6438     {     0.00000000008,  3.03420706487,     1751.53953141600},
6439     {     0.00000000007,  0.11237624686,     3127.31333126180},
6440     {     0.00000000009,  4.92065236724,    11216.28429032400},
6441     {     0.00000000007,  3.67458682256,     3980.50971301380},
6442 ];
6443 
6444 
6445 static const ln_vsop[RADIUS_R4] mars_radius_r4 = [
6446     {     0.00000019551,  3.58210746512,     3340.61242669980},
6447     {     0.00000016322,  4.05115851142,     6681.22485339960},
6448     {     0.00000005848,  4.46381646580,    10021.83728009940},
6449     {     0.00000001533,  4.84332951095,    13362.44970679920},
6450     {     0.00000000375,  1.50951652931,     3185.19202726560},
6451     {     0.00000000340,  5.20519444932,    16703.06213349900},
6452     {     0.00000000152,  5.16376141170,     3344.13554504880},
6453     {     0.00000000126,  2.19183723061,     3496.03282613400},
6454     {     0.00000000148,  0.00000000000,        0.00000000000},
6455     {     0.00000000088,  0.10430359862,     3583.34103067380},
6456     {     0.00000000071,  5.56060980870,    20043.67456019880},
6457     {     0.00000000050,  5.56346631885,     6684.74797174860},
6458     {     0.00000000048,  2.91926298132,     2787.04302385740},
6459     {     0.00000000057,  1.86870004051,     6525.80445396540},
6460     {     0.00000000034,  3.63370917313,     3097.88382272579},
6461     {     0.00000000021,  2.30993179224,     1059.38193018920},
6462     {     0.00000000020,  4.04278354592,     4136.91043351620},
6463     {     0.00000000018,  4.17438755890,     3149.16416058820},
6464     {     0.00000000017,  5.90833786763,    23384.28698689860},
6465     {     0.00000000014,  1.98185426243,      155.42039943420},
6466     {     0.00000000013,  4.43167860883,     7477.52286021600},
6467     {     0.00000000017,  5.93839376025,    10025.36039844840},
6468     {     0.00000000015,  4.58867012625,     6489.77658728800},
6469     {     0.00000000014,  2.22119368504,     9866.41688066520},
6470     {     0.00000000013,  3.24667481494,     6127.65545055720},
6471     {     0.00000000013,  0.48623714297,     6923.95345737360},
6472     {     0.00000000012,  5.44223670746,     3738.76143010800},
6473     {     0.00000000016,  2.67418088918,     4399.99435688900},
6474     {     0.00000000014,  0.78383138857,     3894.18182954220},
6475     {     0.00000000011,  2.64507772215,     3341.59274776800},
6476     {     0.00000000012,  4.34268478367,     2388.89402044920},
6477     {     0.00000000012,  2.52802901788,     6836.64525283380},
6478     {     0.00000000009,  2.81895333303,     4292.33083295040},
6479     {     0.00000000012,  5.83109172622,     7079.37385680780},
6480     {     0.00000000009,  0.76993290644,     1592.59601363280},
6481     {     0.00000000008,  3.56780948809,      796.29800681640},
6482     {     0.00000000008,  2.59620253825,     4535.05943692440},
6483     {     0.00000000008,  3.91827119997,     6438.49624942560},
6484     {     0.00000000009,  2.21473599227,     1194.44701022460},
6485     {     0.00000000008,  1.21128945285,     4690.47983635860},
6486     {     0.00000000007,  3.08488687971,     2544.31441988340},
6487     {     0.00000000008,  5.72388554390,     1990.74501704100},
6488     {     0.00000000008,  3.00192257768,     3532.06069281140},
6489     {     0.00000000008,  4.44918099254,     3339.63210563160},
6490     {     0.00000000008,  3.21999751217,     3347.72597370060},
6491     {     0.00000000007,  1.16933312219,     4933.20844033260},
6492     {     0.00000000008,  5.12244052839,     3723.50895892300},
6493     {     0.00000000006,  4.60069136817,     5729.50644714900},
6494     {     0.00000000006,  1.82718202907,     2957.71589447660},
6495     {     0.00000000006,  3.00923601434,     6682.20517446780},
6496     {     0.00000000005,  2.74887623421,     1589.07289528380},
6497     {     0.00000000005,  2.01586492272,     5486.77784317500},
6498     {     0.00000000005,  6.17623487651,    13365.97282514820},
6499     {     0.00000000006,  3.96856230146,     2146.16541647520},
6500     {     0.00000000005,  2.80833888276,     3337.08930835080},
6501     {     0.00000000004,  2.92720462940,     7875.67186362420},
6502     {     0.00000000004,  4.02001405595,     3333.49887969900},
6503 ];
6504 
6505 
6506 static const ln_vsop[RADIUS_R5] mars_radius_r5 = [
6507     {     0.00000000475,  2.47621038205,     6681.22485339960},
6508     {     0.00000000270,  2.90961348988,    10021.83728009940},
6509     {     0.00000000116,  1.76766655427,     3340.61242669980},
6510     {     0.00000000097,  3.31315004582,    13362.44970679920},
6511     {     0.00000000049,  6.28284800757,     3185.19202726560},
6512     {     0.00000000027,  3.69297278191,    16703.06213349900},
6513     {     0.00000000013,  3.67011956659,     3496.03282613400},
6514     {     0.00000000012,  4.88179002689,     3583.34103067380},
6515     {     0.00000000012,  3.14159265359,        0.00000000000},
6516     {     0.00000000009,  4.05335755845,    20043.67456019880},
6517     {     0.00000000009,  0.35575801457,     6525.80445396540},
6518     {     0.00000000006,  3.95186839136,     6684.74797174860},
6519     {     0.00000000005,  1.40424074649,     2787.04302385740},
6520     {     0.00000000005,  3.60327227648,     3344.13554504880},
6521     {     0.00000000004,  5.11981331029,     3097.88382272579},
6522     {     0.00000000004,  5.24603068590,     6923.95345737360},
6523     {     0.00000000002,  0.40954426011,     9866.41688066520},
6524 ];
6525 
6526 extern (C) {
6527 
6528 /*! \fn void ln_get_mars_equ_coords(double JD, struct ln_equ_posn *position);
6529 * \param JD julian Day
6530 * \param position Pointer to store position
6531 *
6532 * Calculates Mars equatorial position for given julian day.
6533 * This function includes calculations for planetary aberration and refers
6534 * to the FK5 reference frame.
6535 *
6536 * To get the complete equatorial coordinates, corrections for nutation
6537 * have to be applied.
6538 *
6539 * The position returned is accurate to within 0.1 arcsecs.
6540 */
6541 export @nogc void ln_get_mars_equ_coords(double JD, ref ln_equ_posn position) nothrow
6542 {
6543 	ln_helio_posn h_sol, h_mars;
6544 	ln_rect_posn g_sol, g_mars;
6545 	double a,b,c;
6546 	double ra, dec, delta, diff, last, t = 0;
6547 
6548 	/* need typdef for solar heliocentric coords */
6549 	ln_get_solar_geom_coords(JD, h_sol);
6550 	ln_get_rect_from_helio(h_sol, g_sol);
6551 
6552 	do {
6553 		last = t;
6554 		ln_get_mars_helio_coords(JD - t, h_mars);
6555 		ln_get_rect_from_helio(h_mars, g_mars);
6556 
6557 		/* equ 33.10 pg 229 */
6558 		a = g_sol.X + g_mars.X;
6559 		b = g_sol.Y + g_mars.Y;
6560 		c = g_sol.Z + g_mars.Z;
6561 
6562 		delta = a*a + b*b + c*c;
6563 		delta = sqrt(delta);
6564 		t = delta * 0.0057755183;
6565 		diff = t - last;
6566 	} while (diff > 0.0001 || diff < -0.0001);
6567 
6568 	ra = atan2(b,a);
6569 	dec = c / delta;
6570 	dec = asin(dec);
6571 
6572 	/* back to hours, degrees */
6573 	position.ra = ln_range_degrees(ln_rad_to_deg(ra));
6574 	position.dec = ln_rad_to_deg(dec);
6575 }
6576 
6577 
6578 /*! \fn void ln_get_mars_helio_coords(double JD, struct ln_helio_posn *position)
6579 * \param JD Julian Day
6580 * \param position Pointer to store heliocentric position
6581 *
6582 * Calculate Mars heliocentric (refered to the centre of the Sun) coordinates
6583 * in the FK5 reference frame for the given julian day.
6584 * Longitude and Latitude are in degrees, whilst radius vector is in AU.
6585 */
6586 /* Chapter 31 Pg 206-207 Equ 31.1 31.2 , 31.3 using VSOP 87
6587 */
6588 @nogc void ln_get_mars_helio_coords(double JD, ref ln_helio_posn position) nothrow
6589 {
6590 	double t, t2, t3, t4, t5;
6591 	double L0, L1, L2, L3, L4, L5;
6592 	double B0, B1, B2, B3, B4, B5;
6593 	double R0, R1, R2, R3, R4, R5;
6594 
6595 	/* check cache first */
6596 	if(JD == cJD) {
6597 		/* cache hit */
6598 		position.L = cL;
6599 		position.B = cB;
6600 		position.R = cR;
6601 		return;
6602 	}
6603 
6604 	/* get julian ephemeris day */
6605 	t =(JD - 2451545.0) / 365250;
6606 	t2 = t * t;
6607 	t3 = t2 * t;
6608 	t4 = t3 * t;
6609 	t5 = t4 * t;
6610 
6611 	/* calc L series */
6612 	L0 = ln_calc_series(mars_longitude_l0, t);
6613 	L1 = ln_calc_series(mars_longitude_l1, t);
6614 	L2 = ln_calc_series(mars_longitude_l2, t);
6615 	L3 = ln_calc_series(mars_longitude_l3, t);
6616 	L4 = ln_calc_series(mars_longitude_l4, t);
6617 	L5 = ln_calc_series(mars_longitude_l5, t);
6618 	position.L = (L0 + L1 * t + L2 * t2 + L3 * t3 + L4 * t4 + L5 * t5);
6619 
6620 	/* calc B series */
6621 	B0 = ln_calc_series(mars_latitude_b0, t);
6622 	B1 = ln_calc_series(mars_latitude_b1, t);
6623 	B2 = ln_calc_series(mars_latitude_b2, t);
6624 	B3 = ln_calc_series(mars_latitude_b3, t);
6625 	B4 = ln_calc_series(mars_latitude_b4, t);
6626 	B5 = ln_calc_series(mars_latitude_b5, t);
6627 	position.B = (B0 + B1 * t + B2 * t2 + B3 * t3 + B4 * t4 + B5 * t5);
6628 
6629 
6630 	/* calc R series */
6631 	R0 = ln_calc_series(mars_radius_r0, t);
6632 	R1 = ln_calc_series(mars_radius_r1, t);
6633 	R2 = ln_calc_series(mars_radius_r2, t);
6634 	R3 = ln_calc_series(mars_radius_r3, t);
6635 	R4 = ln_calc_series(mars_radius_r4, t);
6636 	R5 = ln_calc_series(mars_radius_r5, t);
6637 	position.R = (R0 + R1 * t + R2 * t2 + R3 * t3 + R4 * t4 + R5 * t5);
6638 
6639 	/* change to degrees in correct quadrant */
6640 	position.L = ln_rad_to_deg(position.L);
6641 	position.B = ln_rad_to_deg(position.B);
6642 	position.L = ln_range_degrees(position.L);
6643 
6644 	/* change to fk5 reference frame */
6645 	ln_vsop87_to_fk5(position, JD);
6646 
6647 	/* save cache */
6648 	cJD = JD;
6649 	cL = position.L;
6650 	cB = position.B;
6651 	cR = position.R;
6652 }
6653 
6654 /*! \fn double ln_get_mars_earth_dist(double JD);
6655 * \brief Calculate the distance between Mars and the Earth in AU.
6656 * \param JD Julian Day
6657 * \return Distance in AU
6658 *
6659 * Calculates the distance in AU between the Earth and Mars for the given
6660 * julian day.
6661 */
6662 @nogc double ln_get_mars_earth_dist(double JD) nothrow
6663 {
6664 	ln_helio_posn h_mars, h_earth;
6665 	ln_rect_posn g_mars, g_earth;
6666 	double x, y, z;
6667 
6668 	/* get heliocentric positions */
6669 	ln_get_mars_helio_coords(JD, h_mars);
6670 	ln_get_earth_helio_coords(JD, h_earth);
6671 
6672 	/* get geocentric coords */
6673 	ln_get_rect_from_helio(h_mars, g_mars);
6674 	ln_get_rect_from_helio(h_earth, g_earth);
6675 
6676 	/* use pythag */
6677 	x = g_mars.X - g_earth.X;
6678 	y = g_mars.Y - g_earth.Y;
6679 	z = g_mars.Z - g_earth.Z;
6680 	x = x * x;
6681 	y = y * y;
6682 	z = z * z;
6683 
6684 	return sqrt(x + y + z);
6685 }
6686 
6687 /*! \fn double ln_get_mars_solar_dist(double JD);
6688 * \brief Calculate the distance between Mars and the Sun in AU
6689 * \param JD Julian Day.
6690 * \return Distance in AU.
6691 *
6692 * Calculates the distance in AU between the Sun and Mars for the given
6693 * julian day.
6694 */
6695 @nogc double ln_get_mars_solar_dist(double JD) nothrow
6696 {
6697 	ln_helio_posn h_mars;
6698 
6699 	/* get heliocentric position */
6700 	ln_get_mars_helio_coords(JD, h_mars);
6701 
6702 	return h_mars.R;
6703 }
6704 
6705 /*! \fn double ln_get_mars_magnitude(double JD);
6706 * \brief Calculate the visible magnitude of Mars
6707 * \param JD Julian Day
6708 * \return Magnitude of Mars
6709 *
6710 * Calculate the visisble magnitude of Mars for given julian day.
6711 */
6712 @nogc double ln_get_mars_magnitude(double JD) nothrow
6713 {
6714 	double delta, r, i;
6715 
6716 	/* get distances */
6717 	r = ln_get_mars_solar_dist(JD);
6718 	delta = ln_get_mars_earth_dist(JD);
6719 
6720 	/* get phase */
6721 	i = ln_get_mars_phase(JD);
6722 
6723 	return -1.52 + 5.0 * log10(r * delta) + 0.016 * i;
6724 }
6725 
6726 /*! \fn double ln_get_mars_disk(double JD);
6727 * \brief Calculate the illuminated fraction of Mars disk
6728 * \param JD Julian Day.
6729 * \return Illuminated fraction of Mars disk (Value between 0 - 1)
6730 *
6731 * Calculates the illuminated fraction of Mars disk for given julian day.
6732 */
6733 /* Chapter 41 */
6734 @nogc double ln_get_mars_disk(double JD) nothrow
6735 {
6736 	double r, delta, R;
6737 
6738 	/* get distances */
6739 	R = ln_get_earth_solar_dist(JD);
6740 	r = ln_get_mars_solar_dist(JD);
6741 	delta = ln_get_mars_earth_dist(JD);
6742 
6743 	/* calc fraction angle */
6744 	return (((r + delta) * (r + delta)) - R * R) / (4 * r * delta);
6745 
6746 }
6747 
6748 /*! \fn double ln_get_mars_phase(double JD);
6749 * \brief Calculate the phase angle of Mars (Sun - Mars - Earth)
6750 * \param JD Julian Day
6751 * \return Phase angle of Mars (degrees)
6752 *
6753 * Calculates the phase angle of Mars for the given julian day.
6754 */
6755 /* Chapter 41 */
6756 @nogc double ln_get_mars_phase(double JD) nothrow
6757 {
6758 	double i, r, delta, R;
6759 
6760 	/* get distances */
6761 	R = ln_get_earth_solar_dist(JD);
6762 	r = ln_get_mars_solar_dist(JD);
6763 	delta = ln_get_mars_earth_dist(JD);
6764 
6765 	/* calc phase */
6766 	i = (r * r + delta * delta - R * R) / (2 * r * delta);
6767 	i = acos(i);
6768 	return ln_rad_to_deg(i);
6769 }
6770 
6771 
6772 /*! \fn double ln_get_mars_rst(double JD, struct ln_lnlat_posn *observer, struct ln_rst_time *rst);
6773 * \param JD Julian day
6774 * \param observer Observers position
6775 * \param rst Pointer to store Rise, Set and Transit time in JD
6776 * \return 0 for success, else 1 for circumpolar.
6777 *
6778 * Calculate the time the rise, set and transit (crosses the local meridian at upper culmination)
6779 * time of Mars for the given Julian day.
6780 *
6781 * Note: this functions returns 1 if Mars is circumpolar, that is it remains the whole
6782 * day either above or below the horizon.
6783 */
6784 @nogc int ln_get_mars_rst(double JD, const ref ln_lnlat_posn observer,
6785 	ref ln_rst_time rst) nothrow
6786 {
6787 	return ln_get_body_rst_horizon(JD, observer, &ln_get_mars_equ_coords,
6788 		LN_STAR_STANDART_HORIZON, rst);
6789 }
6790 
6791 
6792 /*! \fn double ln_get_mars_sdiam(double JD)
6793 * \param JD Julian day
6794 * \return Semidiameter in arc seconds
6795 *
6796 * Calculate the semidiameter of Mars in arc seconds for the
6797 * given julian day.
6798 */
6799 @nogc double ln_get_mars_sdiam(double JD) nothrow
6800 {
6801 	double So = 4.68; /* at 1 AU */
6802 	double dist;
6803 
6804 	dist = ln_get_mars_earth_dist(JD);
6805 	return So / dist;
6806 }
6807 
6808 /*! \fn void ln_get_mars_rect_helio(double JD, struct ln_rect_posn *position)
6809 * \param JD Julian day.
6810 * \param position pointer to return position
6811 *
6812 * Calculate Mars rectangular heliocentric coordinates for the
6813 * given Julian day. Coordinates are in AU.
6814 */
6815 @nogc void ln_get_mars_rect_helio(double JD, ref ln_rect_posn position) nothrow
6816 {
6817 	ln_helio_posn mars;
6818 
6819 	ln_get_mars_helio_coords(JD, mars);
6820 	ln_get_rect_from_helio(mars, position);
6821 }
6822 
6823 /*! \example mars.c
6824  *
6825  * Examples of how to use planetary functions.
6826  */
6827 
6828 }