forked from Bill-Gray/lunar
-
Notifications
You must be signed in to change notification settings - Fork 0
/
cospar.txt
790 lines (653 loc) · 24.8 KB
/
cospar.txt
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
# Description of this file is at bottom.
Remap: 3001 10 4001 28 4002 29 5005 47 5014 48 5015 49 5016 50
Remap: 5001 11 5002 12 5003 13 5004 14 6001 15 6002 16 6003 17 6004 18
Remap: 6005 19 6006 20 6007 21 6008 22 6009 40
Remap: 6015 51 6016 52 6017 53 6018 54
Remap: 7001 23 7002 24 7003 25 7004 26 7005 27 7006 55 7007 56 7008 57
Remap: 7009 58 7010 59 7011 60 7012 61 7013 62 7014 63 7015 64
Remap: 8001 30 8003 71 8004 70 8005 68 8006 69 8007 67 8008 66
Remap: 9001 31 9002 109 9003 108 9004 173 9005 174
# Not actually in use yet:
Remap: 6010 175 6011 176 6012 177 6013 178 6014 179
Planet: p
Obj: 0 # Sun
r=695700
a0=286.13
d0=63.87
W=84.176+14.1844000d
# See Mercury under 'H' (Mars uses 'M')
Obj: 2 # Venus
r=6051.8
a0= 272.76
d0= 67.16
W2=160.20-85.7142857d # (k)
W=160.20-1.4813688d # (b)
# Earth: for reference only (see comment (m))
Obj: 3
r=6378.136,6356.7519
a0= 0.00-0.641T
d0= 90.00-0.557T
W= 190.147+360.9856235d
# See Mars under 'M'
Obj: 5 # Jupiter
r=71492,66854
a0= 268.056595-.006499T
d0= 64.495303+.002413T
W2= 43.3+870.270d # (System II)
W3= 284.95+870.536d # (d) (System III)
W= 67.1+877.900d # (System I)
Obj: 6 # Saturn
r=60268,54364
a0= 40.589-0.036T
d0= 83.537-0.004T
W2= 104.90+812d # (System II)
W3= 38.90+810.7939024d # (d) (System III)
W= 227.90+844.3d # (System I)
Obj: 7 # Uranus
r=25559,24973
a0= 257.311
d0=-15.175
W= 203.81-501.1600928d # (d)
# (See Neptune under 'N'; it has trig terms)
Obj: 9 # Pluto
r=1188.3
a0= 132.993
d0= -6.163
W= 302.695+56.3625225d # (e)
# Recommended values for the direction of the north pole of rotation and the
# prime meridian of the satellites (2000)
# a0, d0, T and d have the same meanings as in Table I (epoch 2000 January 1.5,
# i.e., JD 2451545.0 TCB).
Planet: H
H1=174.7910857 + 4.092335d
H2=349.5821714 + 8.184670d
H3=164.3732571 + 12.277005d
H4=339.1643429 + 16.369340d
H5=153.9554286 + 20.461675d
Obj: 1 # Mercury
r=2440.53,2438.26
a0=281.0103-0.0328T
d0= 61.4155-0.0049T
W=329.5988+6.1385108d+0.01067257 sin H1 -0.00112309 sin H2 -0.00011040 sin H3 -0.00002539 sin H4 -0.00000571 sin H5
# (a) (l)
Planet: E
E1=125.045-0.0529921d
E2=250.089-0.1059842d
E3=260.008+13.0120009d
E4=176.625+13.3407154d
E5=357.529+0.9856003d
E6=311.589+26.4057084d
E7=134.963+13.0649930d
E8=276.617+0.3287146d
E9=34.226+1.7484877d
E10=15.134-0.1589763d
E11=119.743+0.0036096d
E12=239.961+0.1643573d
E13=25.053+12.9590088d
Obj: 3001 # Earth's moon
r=1737.4
a0=269.9949 +0.0031T -3.8787 sin E1 -0.1204 sin E2 +0.0700 sin E3 -0.0172 sin E4 +0.0072 sin E6 -0.0052 sin E10 +0.0043 sin E13
d0=66.5392 +0.0130T +1.5419 cos E1 +0.0239 cos E2 -0.0278 cos E3 +0.0068 cos E4 -0.0029 cos E6 +0.0009 cos E7 +0.0008 cos E10 -0.0009 cos E13
W=38.3213 +13.17635815d -1.4e-12d2 +3.5610 sin E1 +0.1208 sin E2 -0.0642 sin E3 +0.0158 sin E4 +0.0252 sin E5 -0.0066 sin E6 -0.0047 sin E7 -0.0046 sin E8 +0.0028 sin E9 +0.0052 sin E10 +0.0040 sin E11 +0.0019 sin E12 -0.0044 sin E13
Planet: M
M1 = 190.72646643 + 15917.10818695T
M2 = 21.46892470 + 31834.27934054T
M3 = 332.86082793 + 19139.89694742T
M4 = 394.93256437 + 38280.79631835T
M5 = 189.63271560 + 41215158.18420050T # + 12.71192322 T2
M6 = 121.46893664 + 660.22803474T
M7 = 231.05028581 + 660.99123540T
M8 = 251.37314025 + 1320.50145245T
M9 = 217.98635955 + 38279.96125550T
M10 = 196.19729402 + 19139.83628608T
M11 = 79.398797 + 0.5042615T
M12 = 166.325722 + 0.5042615T
M13 = 95.391654 + 0.5042615T
Obj: 4001 # Phobos (s)
r=13.0,11.4,9.1
a0 = 317.67071657 -0.10844326T -1.78428399 sin M1 +0.02212824 sin M2
d0 = 52.88627266 -0.06134706T -1.07516537 cos M1 +0.00668626 cos M2
W = 34.9964842535 +1128.84475928d + 12.72192797 T2 + 1.42421769 sin M1 - 0.02273783 sin M2 + 1.145 sin M5
Obj: 4002 # Deimos (s)
r=7.8,6.0,5.1
a0 = 316.65705808 -0.10518014T +3.09217726 sin M6 + 0.22980637 sin M7
d0 = 53.50992033 -0.0597909T + 1.83936044 cos M6 + 0.14325320 cos M7
W = 79.39932954 +285.16188899d - 2.73954829 sin M6 - 0.39968606 sin M7
Obj: 4 # Mars
r=3396.19,3376.20
a0= 317.269202 − 0.10927547T + 0.419057 sin M11
d0= 54.432516 - 0.05827105T + 1.591274 cos M12
W= 176.049863 + 350.891982443297d + 0.584542 sin M13 # (c) See 2018 Jul 17 comments
Planet: J
J1=73.32+91472.9T
J2=24.62+45137.2T
J3=283.90+4850.7T
J4=355.80+1191.3T
J5=119.90+262.1T
J6=229.80+64.3T
J7=352.35+2382.6T
J8=113.35+6070.0T
Obj: 5016 # XVI Metis
r=30,20,17
a0=268.05 -0.009T
d0=64.49 +0.003T
W=346.09 +1221.2547301d
Obj: 5015 # XV Adrastea
r=10,8,7
a0=268.05 -0.009T
d0=64.49 +0.003T
W=33.29 +1206.9986602d
Obj: 5005 # V Amalthea
r=125,73,64
a0=268.05 -0.009T -0.84 sin J1 +0.01 sin 2J1
d0=64.49 +0.003T -0.36 cos J1
W=231.67 +722.6314560d +0.76 sin J1 -0.01 sin 2J1
Obj: 5014 # XIV Thebe
r=58,49,42
a0=268.05 -0.009T -2.11 sin J2 +0.04 sin 2J2
d0=64.49 +0.003T -0.91 cos J2 +0.01 cos 2J2
W=8.56 +533.7004100d +1.91 sin J2 -0.04 sin 2J2
Obj: 5001 # Io
r=1829.4,1819.4,1815.7
a0=268.05 -0.009T +0.094 sin J3 +0.024 sin J4
d0=64.50 +0.003T +0.040 cos J3 +0.011 cos J4
W=200.39 +203.4889538d -0.085 sin J3 -0.022 sin J4
Obj: 5002 # Europa
r=1562.6,1560.3,1559.5
a0=268.08 -0.009T +1.086 sin J4 +0.060 sin J5 +0.015 sin J6 +0.009 sin J7
d0=64.51 +0.003T +0.468 cos J4 +0.026 cos J5 +0.007 cos J6 +0.002 cos J7
W=36.022 +101.3747235d -0.980 sin J4 -0.054 sin J5 -0.014 sin J6 -0.008 sin J7 # (a)
Obj: 5003 # Ganymede
r=2631.2
a0=268.20 -0.009T -0.037 sin J4 +0.431 sin J5 +0.091 sin J6
d0=64.57 +0.003T -0.016 cos J4 +0.186 cos J5 +0.039 cos J6
W=44.064 +50.3176081d +0.033 sin J4 -0.389 sin J5 -0.082 sin J6
Obj: 5004 # Callisto
r=2410.3
a0=268.72 -0.009T -0.068 sin J5 +0.590 sin J6 +0.010 sin J8
d0=64.83 +0.003T -0.029 cos J5 +0.254 cos J6 -0.004 cos J8
W=259.51 +21.5710715d +0.061 sin J5 -0.533 sin J6 -0.009 sin J8
Planet: S
S1=353.32+75706.7T
S2=28.72+75706.7T
S3=177.40-36505.5T
S4=300.00-7225.9T
S5=316.45+506.2T
S6=345.20-1016.3T
# S7=29.80-52.1T
Obj: 6018 # XVIII Pan
r=17.2,15.4,10.4
a0=40.6 -0.036T
d0=83.5 -0.004T
W=48.8 +626.0440000d
Obj: 6015 # XV Atlas
r=20.5,17.8,9.4
a0=40.58 -0.036T
d0=83.53 -0.004T
W=137.88 +598.3060000d
Obj: 6016 # XVI Prometheus
r=68.2,41.6,28.2
a0=40.58 -0.036T
d0=83.53 -0.004T
W=296.14 +587.289000d
Obj: 6017 # XVII Pandora
r=52.2,40.8,31.5
a0=40.58 -0.036T
d0=83.53 -0.004T
W=162.92 +572.7891000d
Obj: 6010 # X Janus
r=101.7,93.0,76.3
a0=40.58 -0.036T -1.623 sin S2 +0.023 sin 2S2
d0=83.52 -0.004T -0.183 cos S2 +0.001 cos 2S2
W=58.83 +518.2359876d +1.613 sin S2 -0.023 sin 2S2 # (j)
Obj: 6011 # XI Epimetheus
r=64.9,57.3,53.0
a0=40.58 -0.036T -3.153 sin S1 +0.086 sin 2S1
d0=83.52 -0.004T -0.356 cos S1 +0.005 cos 2S1
W=293.87 +518.4907239d +3.133 sin S1 -0.086 sin 2S1 # (j)
Obj: 6001 # I Mimas
r=207.8,196.7,190.6
a0=40.66 -0.036T +13.56 sin S3
d0=83.52 -0.004T -1.53 cos S3
W=337.46 +381.9945550d -13.48 sin S3 -44.85 sin S5 # (d)
Obj: 6002 # II Enceladus
r=256.6,251.4,248.3
a0=40.66 -0.036T
d0=83.52 -0.004T
W=2.82 +262.7318996d # (e)
Obj: 6003 # III Tethys
r=538.4,428.3,526.3
a0=40.66 -0.036T +9.66 sin S4
d0=83.52 -0.004T -1.09 cos S4
W=10.45 +190.6979085d -9.60 sin S4 +2.23 sin S5 # (f)
Obj: 6013 # XIII Telesto
r=16.3,11.8,9.8
a0=50.51 -0.036T
d0=84.06 -0.004T
W=56.88 +190.6979332d # (j)
Obj: 6014 # XIV Calypso
r=15.3,9.3,6.3
a0=36.41 -0.036T
d0=85.04 -0.004T
W=153.51 +190.69792373d # (j)
Obj: 6004 # IV Dione
r=563.4,561.3,559.6
a0=40.66 -0.036T
d0=83.52 -0.004T
W=357.00 +131.5349316d # (g)
Obj: 6012 # XII Helene
r=22.5,19.6,13.3
a0=40.85 -0.036T
d0=83.34 -0.004T
W=245.12 +131.6174056d
Obj: 6005 # V Rhea
r=765,763.1,762.4
a0=40.38 -0.036T +3.10 sin S6
d0=83.55 -0.004T -0.35 cos S6
W=235.16 +79.6900478d -3.08 sin S6 # (h)
Obj: 6006 # VI Titan
r=2575.15,2574.78,2574.47
a0=39.4827
d0=83.4279
W=186.5855+22.5769768d
# Previous (pre-2009 resolution) version:
# a0=36.41 -0.036T +2.66 sin S7
# d0=83.94 -0.004T -0.30 cos S7
# W=189.64 +22.5769768d -2.64 sin S7
Obj: 6008 # VIII Iapetus
r=745.7,712.1
a0=318.16 -3.949T
d0=75.03 -1.143T
W=350.20 +4.5379572d # (i)
Obj: 6009 # IX Phoebe
r=109.4,108.5,101.8
a0=356.90
d0=77.80
W=178.58 +931.639d
Planet: U
U1=115.75+54991.87T
U2=141.69+41887.66T
U3=135.03+29927.35T
U4=61.77+25733.59T
U5=249.32+24471.46T
U6=43.86+22278.41T
U7=77.66+20289.42T
U8=157.36+16652.76T
U9=101.81+12872.63T
U10=138.64+8061.81T
U11=102.23-2024.22T
U12=316.41+2863.96T
U13=304.01-51.94T
U14=308.71-93.17T
U15=340.82-75.32T
U16=259.14-504.81T
Obj: 7006 # VI Cordelia
r=13
a0=257.31 -0.15 sin U1
d0=-15.18 +0.14 cos U1
W=127.69 -1074.5205730d -0.04 sin U1
Obj: 7007 # VII Ophelia
r=15
a0=257.31 -0.09 sin U2
d0=-15.18 +0.09 cos U2
W=130.35 -956.4068150d -0.03 sin U2
Obj: 7008 # VIII Bianca
r=21
a0=257.31 -0.16 sin U3
d0=-15.18 +0.16 cos U3
W=105.46 -828.3914760d -0.04 sin U3
Obj: 7009 # IX Cressida
r=31
a0=257.31 -0.04 sin U4
d0=-15.18 +0.04 cos U4
W=59.16 -776.5816320d -0.01 sin U4
Obj: 7010 # X Desdemona
r=27
a0=257.31 -0.17 sin U5
d0=-15.18 +0.16 cos U5
W=95.08 -760.0531690d -0.04 sin U5
Obj: 7011 # XI Juliet
r=42
a0=257.31 -0.06 sin U6
d0=-15.18 +0.06 cos U6
W=302.56 -730.1253660d -0.02 sin U6
Obj: 7012 # XII Portia
r=54
a0=257.31 -0.09 sin U7
d0=-15.18 +0.09 cos U7
W=25.03 -701.4865870d -0.02 sin U7
Obj: 7013 # XIII Rosalind
r=27
a0=257.31 -0.29 sin U8
d0=-15.18 +0.28 cos U8
W=314.90 -644.6311260d -0.08 sin U8
Obj: 7014 # XIV Belinda
r=33
a0=257.31 -0.03 sin U9
d0=-15.18 +0.03 cos U9
W=297.46 -577.3628170d -0.01 sin U9
Obj: 7015 # XV Puck
r=77
a0=257.31 -0.33 sin U10
d0=-15.18 +0.31 cos U10
W=91.24 -472.5450690d -0.09 sin U10
Obj: 7001 # I Ariel
r=581.1,577.9,577.7
a0=257.43 +0.29 sin U13
d0=-15.10 +0.28 cos U13
W=156.22 -142.8356681d +0.05 sin U12 +0.08 sin U13
Obj: 7002 # II Umbriel
r=584.7
a0=257.43 +0.21 sin U14
d0=-15.10 +0.20 cos U14
W=108.05 -86.8688923d -0.09 sin U12 +0.06 sin U14
Obj: 7003 # III Titania
r=788.9
a0=257.43 +0.29 sin U15
d0=-15.10 +0.28 cos U15
W=77.74 -41.3514316d +0.08 sin U15
Obj: 7004 # IV Oberon
r=761.4
a0=257.43 +0.16 sin U16
d0=-15.10 +0.16 cos U16
W=6.77 -26.7394932d +0.04 sin U16
Obj: 7005 # V Miranda
r=240.4,234.2,232.9
a0=257.43 +4.41 sin U11 -0.04 sin 2U11
d0=-15.08 +4.25 cos U11 -0.02 cos 2U11
W=30.70 -254.6906892d -1.27 sin U12 +0.15 sin 2U12 +1.15 sin U11 -0.09 sin 2U11
Planet: N
N0=357.85+52.316T
N1=323.92+62606.6T
N2=220.51+55064.2T
N3=354.27+46564.5T
N4=75.31+26109.4T
N5=35.36+14325.4T
N6=142.61+2824.6T
N7=177.85+52.316T
Obj: 8 # Neptune
r=24764,24341
a0= 299.36+0.70 sin N0
d0= 43.46-0.51 cos N0
W= 249.978 + 541.1397757d -0.48 sin N0 # (d) (2018 Jul 17)
Obj: 8003 # III Naiad
r=29
a0=299.36 +0.70 sin N0 -6.49 sin N1 +0.25 sin 2N1
d0=43.36 -0.51 cos N0 -4.75 cos 2N1 +0.09 cos 2N1
W=254.06 +1222.8441209d -0.48 sin N0 +4.40 sin N1 -0.27 sin 2N1
Obj: 8004 # IV Thalassa
r=40
a0=299.36 +0.70 sin N0 -0.28 sin N2
d0=43.45 -0.51 cos N0 -0.21 cos N2
W=102.06 +1155.7555612d -0.48 sin N0 +0.19 sin N2
Obj: 8005 # V Despina
r=74
a0=299.36 +0.70 sin N0 -0.09 sin N3
d0=43.45 -0.51 cos N0 -0.07 cos N3
W=306.51 +1075.7341562d -0.49 sin N0 +0.06 sin N3
Obj: 8006 # VI Galatea
r=79
a0=299.36 +0.70 sin N0 -0.07 sin N4
d0=43.43 -0.51 cos N0 -0.05 cos N4
W=258.09 +839.6597686d -0.48 sin N0 +0.05 sin N4
Obj: 8007 # VII Larissa
r=96
a0=299.36 +0.70 sin N0 -0.27 sin N5
d0=43.41 -0.51 cos N0 -0.20 cos N5
W=179.41 +649.0534470d -0.48 sin N0 +0.19 sin N5
Obj: 8008 # VIII Proteus
r=208
a0=299.27 +0.70 sin N0 -0.05 sin N6
d0=42.91 -0.51 cos N0 -0.04 cos N6
W=93.38 +320.7654228d -0.48 sin N0 +0.04 sin N6
Obj: 8001 # I Triton
r=1352.6
a0=299.36 -32.35 sin N7 -6.28 sin 2N7 -2.08 sin 3N7 -0.74 sin 4N7 -0.28 sin 5N7 -0.11 sin 6N7 -0.07 sin 7N7 -0.02 sin 8N7 -0.01 sin 9N7
d0=41.17 +22.55 cos N7 +2.10 cos 2N7 +0.55 cos 3N7 +0.16 cos 4N7 +0.05 cos 5N7 +0.02 cos 6N7 +0.01 cos 7N7
W=296.53 -61.2572637d +22.25 sin N7 +6.73 sin 2N7 +2.05 sin 3N7 +0.74 sin 4N7 +0.28 sin 5N7 +0.11 sin 6N7 +0.05 sin 7N7 +0.02 sin 8N7 +0.01 sin 9N7
Planet: P
Obj: 9001 # Charon/Pluto I
r=606.0
a0= 132.993
d0= -6.163
W=122.695 +56.3625225d
Obj: 9002 # Nix/Pluto II = S/2005 P 2 (n)
r=48.7,33.2,31.1
a0= 132.993
d0= -6.163
W=272.24 +14.483934d
Obj: 9003 # Hydra/Pluto III = S/2005 P 1 (n)
r=50.9,36.1,30.9
a0= 132.993
d0= -6.163
W=57.19 +9.422837d
Obj: 9004 # Kerberos/Pluto IV = S/2011 (134340) 1 (n)
r=19,10,9
a0= 132.993
d0= -6.163
W=90.19 +11.1913026d
Obj: 9005 # Styx/Pluto V = S/2012 (134340) 1 (n)
r=16,9,8
a0= 132.993
d0= -6.163
W=11.7 +17.8551357d
Obj: -1 # Ceres (r), (t)
r=487.3,487.3,446
a0=291.42763
d0=66.76033
W=170.309 +952.1532635d
Obj: -2 # Pallas
r=568,532,448
a0= 33
d0= -3
W= 38 + 1105.8036d
Obj: -4 # Vesta
r=289,280,229
a=309.031 # +/- 0.01 (p)
d=42.235 # +/- 0.01
W=285.39+1617.3329428d
Obj: -21 # Lutetia
r=62.0,50.5,46.5
a0=52 # +/- 5
d0=12 # +/- 5
W=94 + 1057.7515d
Obj: -52 # Europa
r=379,330,249
a0=257
d0=12 # no uncertainties given
W=55 + 1534.6472187d
Obj: -243 # Ida
r=26.8,12.0,7.6
a0=168.76
d0=-87.12
W=274.05 + 1864.6280070d (2018 Jul 17)
Obj: -433 # Eros
r=17.0,5.5,5.5
a0=11.35 # +/- 0.02
d0=17.22 # +/- 0.02
W=326.07+1639.38864745d
Obj: -511 # Davida
r=180,147,127
a0=297
d0=5
W=268.1 +1684.4193549d
Obj: -951 # (951) Gaspra
r=9.1,5.2,4.4
a0 = 9.47
d0 = 26.70
W = 83.67 + 1226.9114850d
Obj: -2867 # (2867) Šteins
r=3.24,2.73,2.04
a0 = 90
d0 =-62
W = 93.94 + 1428.852332d
Obj: -25143 # (25143) Itokawa
r=0.268,0.147,0.104
a0 = 90.53
d0 =-66.30
W = 0+ 712.143d # No central meridian defined yet
END (This is the for-real end! Everything after this is a comment.)
(a) The 182 meridian is defined by the crater Cilix.
(b) The 128 meridian is defined by the crater Anat.
(c) The 326 meridian is defined by the crater Saga.
(d) The 162 meridian is defined by the crater Palomides.
(e) The 5 meridian is defined by the crater Salih.
(f) The 299 meridian is defined by the crater Arete.
(g) The 63 meridian is defined by the crater Palinurus.
(h) The 340 meridian is defined by the crater Tore.
(i) The 276 meridian is defined by the crater Almeric.
(j) These equations are correct for the period of the Voyager encounters.
Because of precession they may not be accurate at other time periods.
(k) "System II" for Venus is a proposed system for tracking clouds.
See 8 Jan 2008 comments below.
(l) Mercury updated from this comment at
http://ssd.jpl.nasa.gov/?horizons_news :
Feb 07, 2008:
-- The Mercury rotation model was updated based on radar observations
reported by Margot et al., Science 316, 2007, and a 2007-Dec-2 memo:
alpha-0 (RA J2000) = 281.0097 -0.0328T
delta-0 (DEC J200) = 61.4143 - 0.0049T
W = 329.548 + 6.1385025d
... where T is time in Julian centuries (36525 days) from J2000 epoch,
and d is interval in days (86400 SI seconds) from J2000 epoch, with the
J2000 epoch being JD 2451545.0 Coordinate Time (2000-Jan-1.5)
(m) COSPAR data for the earth is provided for reference only. At least in
my code, the earth's orientation is actually computed using the IAU
precession and nutation models (see 'precess.cpp'). WGCCRE dropped this
model in their 2015 report.
(n) As far as I know, there is no "official" rotation model for Nix and
Hydra. I took the polar axis for Pluto and Charon, then came up with
values for the constant and linear term in W that produced near-zero
longitudes facing Pluto over the 2000-2020 period (the time span for
which I have Nix and Hydra ephemerides).
Once the COSPAR folks come up with official values, I expect they
will be close to (but not exactly equal to) the results I've given.
Note: on 2015 May 12, I added similarly "unofficial" rotation models
for Pluto IV = Kerberos and Pluto V = Styx.
(o) (2013 May 17) Mercury updated to IAU 2009 version, with trig terms.
(p) (2013 Nov 26) Updated Vesta to use Dawn-based spin axis. The COSPAR
axes, which as you can see have much higher sigmas, are :
a=305.8 # +/- 3.1
d=41.4 # +/- 1.5
Note that W is unchanged here, though I'm sure Dawn got a better
rotation period and fiddled with the zero point a little.
(q) (2015 May 6) Follow-up to the above: Dawn _did_ get a better rotation
period and offset. I modified Vesta's W to use the value from
http://astropedia.astrogeology.usgs.gov/download/Docs/WGCCRE/IAU-WGCCRE-Coordinate-System-for-Vesta.pdf
(pole RA/dec didn't change).
(r) (2016 Oct 2) Updated Ceres to use Dawn measurements from
https://naif.jpl.nasa.gov/pub/naif/DAWN/kernels/pck/dawn_ceres_v05.tpc
(s) (2018 Mar 26) Updated Phobos & Deimos to use
ftp://ssd.jpl.nasa.gov/pub/eph/satellites/orientation/iom.392R-17-004.pdf
This has a small effect on Deimos and a larger one on Phobos, partly
because the sign for the sin(M1) term was reversed.
(t) Ceres now uses v06 from Dawn. See 2020 Oct 19 "news item" at
https://ssd.jpl.nasa.gov/?horizons_news .
Satellites for which no suitable data are yet available have been omitted
from this table. Nereid is not included in this table because it is not in
synchronous rotation.
Errata to the published version:
In Table 2, Page 87, of the 2000 report (Seidelmann, et al., 2002): For the
Moon, for "0.1204 E2", read "0.1204 sin E2".
DESCRIPTION OF THIS FILE
Comments can be added freely within the file. However, if you put
them after the actual data, the code doesn't have to dig through all
this text. That speeds things up very slightly.
The file is processed by 'cospar.cpp', which should give insight as
to what's going on here.
Some of my software used a numbering system in which sun=0, Mer-Plu
=1...9, Moon=10, Io...Callisto=11..14, and so on, with the numbering
reflecting the order in which objects were added. Now, I (mostly) use
the JPL/IAU scheme, in which numbered satellites have four digits, the
first specifying the planet, the remaining three the object number. So
5014 = Jupiter XIV, 803 = Neptune III. For backward compatibility, a
"remap" table is given at the top; some of my software uses this to
convert the old numbers to the JPL/IAU style.
All lines are considered comments until a line starting with 'Planet'
or 'Obj' is encountered. After a 'Planet' line, the code starts looking
for angular coefficients; after an 'Obj' line, it starts to look for
lines describing a0, d0, and W. Data are from
http://astrogeology.usgs.gov/Projects/WGCCRE/
with corrections/updates as described below. Asteroid rotation data is
given at the above sites, too, but that will have to wait for another day.
(8 Jan 2008) Added the proposed coordinate system for cloud observations of
Venus made in UV. This system has a rotational period of exactly 4.2 days,
and coincides with the "usual" system at J2000. Nothing official yet, and it
means several changes will eventually be needed in Guide: to display both
systems in 'more info', to ensure that features and radar-based bitmaps are
shown in System I while clouds are shown in System II, and probably more.
(8 Feb 2008) Altered Mercury rotation _very_ slightly, as described
at comment (l) above.
(29 Jan 2010) Added data for Nix and Hydra. See comment (n) above.
(2 Feb 2010) Revised the Sun, Jupiter, Pluto, Charon, and Phoebe in
accordance with the 'report of the IAU/IAG Working Group on cartographic
coordinates and rotational elements: 2006' (Celestial Mech Dyn Astr (2007)
98:155-180.) Also revised a0 and d0 for Nix and Hydra to match the new
Pluto/Charon values.
The 2006 report modified Jupiter's pole position, both constant and
linear terms, and also has some periodic terms. They don't add up
to more than .003 degree, so for the nonce, I've not added them:
a0 += .000117 sin Ja + .000938 sin Jb + .001432 sin Jc + .000030 sin Jd
+ .002150 sin Je
d0 += .000050 cos Ja + .000404 cos Jb + .000617 cos Jc - .000013 sin Jd
+ .000926 cos Je
where Ja = 99.360714 + .4850.4046T, Jb = 175.895369 + 1191.9605T,
Jc = 300.323162 + 252.5475T, Jd = 114.012305 + 6070.2476T,
Je = 49.511251 + 64.3000T
Note, though, that these _could_ be added in the same manner in which
periodic terms have been added for Neptune.
(23 May 2011) After comments from Jean-Claude Pelle, cleaned up some
spurious text that didn't interfere with my code, but _would_ confuse
other code and really shouldn't have been there. Un-commented data for
five Saturnian satellites Helene, Calypso, Telesto, Epimetheus, Janus.
Also, I had some hard-wired code that allowed for multiple systems
("system II and III") longitudes only for Jupiter and Saturn. This is now
fixed in 'cospar.cpp', and requires that the 'W=' line _must_ follow the
'W2=' and 'W3=' lines. (The idea is that if you ask for a system II result
for an object that has no W2 line, the code will eventually trickle down
to the W= line and use that instead.)
Also switched from Guide's semi-random numbering of objects to the JPL
one, wherein numbered satellites have four digits: one giving the planet,
the remaining three the IAU numbering. (With remapping given at the top so
that the "old" Guide-style numbering can be used.)
(2013 May 17) Modified Mercury to use the IAU 2009 model, complete with
rotation terms; Titan to use IAU 2009, i.e., no more trig terms.
(2013 Jul 13) Added COSPAR 2009 data for minor/"dwarf" planets from
http://astropedia.astrogeology.usgs.gov/download/Docs/WGCCRE/WGCCRE2009reprint.pdf
(2013 Aug 26) Because Pluto is now a "dwarf planet", the poles of it
and its satellites are flipped and W increases with time rather than
decreasing. I should have made those changes when switching to the 2009
rotation models, but failed to do so. This is now corrected (including
for Hydra and Nix, which have unofficial models as described above...
and so do Kerberos and Styx, as of 2015 May.) See the 2011 erratum to
the COSPAR 2009 data at
http://astropedia.astrogeology.usgs.gov/download/Docs/WGCCRE/WGCCRE-Erratum-2011reprint.pdf
for details.
(2015 Nov 17) The 2009 WGCCRE report mentions that the change in the
System III rotation rate, to 870.5366420 degrees/day, had some problems.
Further determinations didn't quite match up with it, and they decided to
go back to the old value of 870.536 degrees/day. That change has now been
made in this file. Also found that some of the trig terms for Mercury were
botched (used 'M' instead of 'H'), resulting in not getting any value at all.
(2018 Jul 17) Corrections based on the WGCCRE 2015 report, at
https://astrogeology.usgs.gov/search/map/Docs/WGCCRE/WGCCRE2015reprint
Mercury's rotation has the same general form as before, but various
coefficients have changed. I caught and corrected a spurious extra term in
W that caused a sub-arcsecond error.
Mars now includes five trig terms for the pole position and
six for W. One term for each has considerable amplitude; the others are
below an arcsecond and are omitted here. Small changes made for Phobos and
Deimos have been incorporated, again with some lesser terms dropped. The
quadratic bit for M5 is dropped, mostly because I've no straightforward
way of including it anyway (and it's small).
W for Neptune has changed, with the rotation rate increasing from 536.3128
degrees/day to 541.1397757 degrees/day, based on observations of two unusually
stable features : https://doi.org/10.1016/j.icarus.2011.05.013
(243) Ida was far off in previous WGCCRE reports (dec for pole off by 90
degrees!). It should now be correct.
WGCCRE has dropped orientation models for the earth and moon. I've not
used the former for some time (the IAU precession/nutation model is much more
accurate). I do still use the latter in situations where the accurate
alternative (orientations from DE-4xx) would be overkill.
(2022 Feb 02) Added some planetary radii, for future use.
(2022 Oct 06) Added still more planetary radii.