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
|
# 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
a0=286.13
d0=63.87
W=84.176+14.1844000d
# See Mercury under 'H' (Mars uses 'M')
Obj: 2 # Venus
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
a0= 0.00-0.641T
d0= 90.00-0.557T
W= 190.147+360.9856235d
# See Mars under 'M'
Obj: 5 # Jupiter
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
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
a0= 257.311
d0=-15.175
W= 203.81-501.1600928d # (d)
# (See Neptune under 'N'; it has trig terms)
Obj: 9 # Pluto
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
a0=281.0103-0.0328T
d0= 61.4155-0.0049T
W=329.5488+6.1385018d+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
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)
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)
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
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
a0=268.05 -0.009T
d0=64.49 +0.003T
W=346.09 +1221.2547301d
Obj: 5015 # XV Adrastea
a0=268.05 -0.009T
d0=64.49 +0.003T
W=33.29 +1206.9986602d
Obj: 5005 # V Amalthea
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
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
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
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
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
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
a0=40.6 -0.036T
d0=83.5 -0.004T
W=48.8 +626.0440000d
Obj: 6015 # XV Atlas
a0=40.58 -0.036T
d0=83.53 -0.004T
W=137.88 +598.3060000d
Obj: 6016 # XVI Prometheus
a0=40.58 -0.036T
d0=83.53 -0.004T
W=296.14 +587.289000d
Obj: 6017 # XVII Pandora
a0=40.58 -0.036T
d0=83.53 -0.004T
W=162.92 +572.7891000d
Obj: 6010 # X Janus
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
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
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
a0=40.66 -0.036T
d0=83.52 -0.004T
W=2.82 +262.7318996d # (e)
Obj: 6003 # III Tethys
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
a0=50.51 -0.036T
d0=84.06 -0.004T
W=56.88 +190.6979332d # (j)
Obj: 6014 # XIV Calypso
a0=36.41 -0.036T
d0=85.04 -0.004T
W=153.51 +190.69792373d # (j)
Obj: 6004 # IV Dione
a0=40.66 -0.036T
d0=83.52 -0.004T
W=357.00 +131.5349316d # (g)
Obj: 6012 # XII Helene
a0=40.85 -0.036T
d0=83.34 -0.004T
W=245.12 +131.6174056d
Obj: 6005 # V Rhea
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
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
a0=318.16 -3.949T
d0=75.03 -1.143T
W=350.20 +4.5379572d # (i)
Obj: 6009 # IX Phoebe
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
a0= 132.993
d0= -6.163
W=122.695 +56.3625225d
Obj: 9002 # Nix/Pluto II = S/2005 P 2 (n)
a0= 132.993
d0= -6.163
W=272.24 +14.483934d
Obj: 9003 # Hydra/Pluto III = S/2005 P 1 (n)
a0= 132.993
d0= -6.163
W=57.19 +9.422837d
Obj: 9004 # Kerberos/Pluto IV = S/2011 (134340) 1 (n)
a0= 132.993
d0= -6.163
W=90.19 +11.1913026d
Obj: 9005 # Styx/Pluto V = S/2012 (134340) 1 (n)
a0= 132.993
d0= -6.163
W=11.7 +17.8551357d
Obj: -1 # Ceres (r)
a0=291.418 # +/- 0.03
d0=66.764 # +/- 0.03
W=170.650 +952.1532d # rate is +/- 0.00003 deg/day
Obj: -2 # Pallas
a0= 33
d0= -3
W= 38 + 1105.8036d
Obj: -4 # Vesta
a=309.031 # +/- 0.01 (p)
d=42.235 # +/- 0.01
W=285.39+1617.3329428d
Obj: -21 # Lutetia
a0=52 % +/- 5
d0=12 % +/- 5
W=94 + 1057.7515d
Obj: -243 # Ida
a0=168.76
d0=-87.12
W=274.05 + 1864.6280070d (2018 Jul 17)
Obj: -433 # Eros
a0=11.35 # +/- 0.02
d0=17.22 # +/- 0.02
W=326.07+1639.38864745d
Obj: -511 # Davida
a0=297
d0=5
W=268.1 +1684.4193549d
Obj: -951 # (951) Gaspra
a0 = 9.47
d0 = 26.70
W = 83.67 + 1226.9114850d
Obj: -2867 # (2867) Šteins
a0 = 90
d0 =-62
W = 93.94 + 1428.852332d
Obj: -25143 # (25143) Itokawa
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.
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.
|