Overview
-This program calculates the coordinates x and y of the first 7 satellites
of Saturn if flag F10 is set, or of the first 4 satellites of Jupiter
if flag F10 is clear.
-Actually, it combines "IEGC" & "METDRTH" ( cf "Satellites
of Jupiter" & "Saturnian Satellites" )
-However, "IEGC" has been re-written so that the same types of formulas
are used.
-Moreover, the inclinations of the orbits on the equatorial plane are
now taken into account
for Mimas, Tethys, Rhea, Titan, Hyperion and Europe, Ganymede,
Callisto
-Thus, the y-values are obtained more accurately.
-The x-axis coincides with the equator of the planet.
-The center of the Planet is the origin and x , y are measured in equatorial
radii.
y ( North )
|
|
|
( East ) --------------Sat/Jup------------------ x ( West
)
|
|
( South )
Data Registers: R00 thru R19 are used for temporay data storage and when the program stops:
Io - Europa - Ganymede - Callisto if CF 10
R01 = x1 R03 = x2
R05 = x3 R07 = x4
R02 = y1 R04 = y2
R06 = y3 R08 = y4
or Mimas - Enceladus - Tethys - Dione - Rhea - Titan - Hyperion if SF 10
R01 = x1 R03 = x2
R05 = x3 R07 = x4
R09 = x5 R11 = x6
R13 = x7
R02 = y1 R04 = y2
R06 = y3 R08 = y4
R10 = y5 R12 = y6
R14 = y7
R19 = - sin DE where DE is the planetocentric declination of the Earth.
Flags: F01 F02
F03 F04 F05 F06 F07
-Flag nn is set when the distance Earth-Satellite n is shorter
than the distance Earth-Planet ( 0 < nn < 8 )
CF 10 for the Satellites of Jupiter
SF 10 for the Satellites of Saturn
Subroutine: none if you have a Time
Module
"J0" otherwise .( cf for instance "Julian & Gregorian Calendars
for the HP-41" )
Program listing
-If you have a Time module, replace lines 07-08 by
the 3 lines 1.012 DDAYS
-
-Lines 46-267-680 are three-byte GTOs
-If you don't have an HP-41CX, replace lines 264-265 by CF 01
CF 02 CF 03 CF 04 CF 05 CF 06 CF 07
| 01 LBL "STL"
02 DEG 03 HR 04 24 05 / 06 X<>Y 07 XEQ "J0" 08 + 09 E6 10 / 11 STO 00 12 985609 13 * 14 3 15 - 16 STO 01 17 SIN 18 192 19 * 20 RCL 01 21 ST+ X 22 SIN 23 ST+ X 24 + 25 10297 26 + 27 1 28 % 29 RCL 01 30 + 31 STO 02 32 1 33 RCL 01 34 COS 35 60 36 / 37 - 38 STO 08 39 RCL 00 40 1116 41 * 42 7 43 - 44 SIN 45 FC? 10 46 GTO 01 47 81 48 * 49 RCL 00 50 33460 51 * 52 43 53 - 54 STO 03 55 SIN 56 636 57 * 58 + 59 RCL 03 60 ST+ X 61 SIN 62 20 63 * 64 + 65 RCL 00 66 16172 67 * 68 STO 15 69 ST+ X 70 60 71 - 72 STO 06 73 SIN 74 23 75 * 76 - 77 RCL 00 78 34576 79 * 80 50 81 - 82 SIN 83 5 84 * 85 + 86 RCL 15 87 76 88 - 89 SIN 90 12 91 * 92 - 93 9306 94 + 95 1 96 % 97 RCL 03 98 + 99 STO 04 100 9.57 101 RCL 03 102 COS 103 .53 104 * 105 - 106 RCL 03 107 ST+ X 108 COS 109 68 110 / 111 - 112 RCL 06 113 COS 114 53 115 / 116 + 117 STO 09 118 113.67 119 RCL 00 120 14 121 * |
122 -
123 STO 10 124 169.53 125 STO 11 126 28.05 127 STO 12 128 2.49 129 STO 13 130 7 131 GTO 02 132 LBL 01 133 RCL 00 134 83091 135 * 136 20 137 + 138 STO 03 139 SIN 140 556 141 * 142 X<>Y 143 33 144 * 145 - 146 RCL 03 147 ST+ X 148 SIN 149 18 150 * 151 + 152 1431 153 + 154 1 155 % 156 RCL 03 157 + 158 STO 04 159 5209 160 RCL 03 161 COS 162 252 163 * 164 - 165 RCL 03 166 ST+ X 167 COS 168 6 169 * 170 - 171 E3 172 / 173 STO 09 174 100.46 175 RCL 00 176 10 177 * 178 - 179 STO 10 180 337.78 181 STO 11 182 2.22 183 STO 12 184 1.3 185 STO 13 186 4 187 LBL 02 188 STO 16 189 ST+ X 190 STO 17 191 RCL 08 192 ENTER 193 X^2 194 RCL 09 195 X^2 196 + 197 RCL 02 198 RCL 04 199 - 200 STO 05 201 COS 202 RCL 08 203 * 204 RCL 09 205 * 206 ST+ X 207 - 208 SQRT 209 STO 01 210 / 211 RCL 05 212 SIN 213 * 214 ASIN 215 RCL 04 216 - 217 RCL 11 218 + 219 STO 19 220 SIN 221 RCL 12 222 SIN 223 STO 05 224 * 225 RCL 04 226 RCL 10 227 - 228 SIN 229 RCL 13 230 SIN 231 * 232 RCL 09 233 * 234 RCL 01 235 / 236 ST* 05 237 RCL 12 238 COS 239 STO 03 240 * 241 + 242 X<> 19 |
243 1
244 CHS 245 P-R 246 X<>Y 247 RCL 03 248 * 249 RCL 05 250 + 251 X<>Y 252 R-P 253 X<>Y 254 X<> 01 255 173 E6 256 / 257 ST- 00 258 RCL 19 259 ASIN 260 COS 261 E3 262 / 263 STO 18 264 CLX 265 X<>F 266 FC? 10 267 GTO 03 268 16919949 269 RCL 00 270 * 271 240.7 272 + 273 562103 274 RCL 00 275 * 276 103.1 277 + 278 STO 10 279 SIN 280 9.12 281 * 282 + 283 29.9 284 RCL 00 285 52548 286 * 287 - 288 STO 12 289 RCL 10 290 + 291 SIN 292 .23 293 * 294 + 295 RCL 10 296 RCL 12 297 - 298 SIN 299 .21 300 * 301 - 302 RCL 00 303 5657028 304 * 305 76.2 306 + 307 STO 09 308 SIN 309 9 310 / 311 + 312 RCL 09 313 RCL 10 314 - 315 SIN 316 RCL 12 317 SIN 318 + 319 11 320 / 321 - 322 RCL 09 323 ST+ X 324 SIN 325 7 326 / 327 + 328 RCL 09 329 3 330 * 331 SIN 332 RCL 09 333 RCL 10 334 + 335 SIN 336 + 337 15 338 / 339 + 340 RCL 09 341 4 342 * 343 SIN 344 25 345 / 346 + 347 STO 08 348 193.84 349 RCL 00 350 51135 351 * 352 - 353 STO 07 354 206 355 P-R 356 RCL 07 357 RCL 12 358 - 359 49 360 P-R 361 X<>Y 362 ST+ T 363 RDN |
364 +
365 RCL 07 366 RCL 10 367 + 368 5 369 P-R 370 X<>Y 371 ST- T 372 RDN 373 - 374 RCL 07 375 RCL 10 376 - 377 3 378 P-R 379 X<>Y 380 ST- T 381 RDN 382 - 383 RCL 07 384 RCL 09 385 + 386 2 387 P-R 388 X<>Y 389 ST- T 390 RDN 391 - 392 RCL 07 393 RCL 09 394 - 395 2 396 SQRT 397 P-R 398 X<>Y 399 ST+ T 400 RDN 401 + 402 R-P 403 2 E3 404 / 405 STO 13 406 RCL 08 407 RCL Z 408 STO 02 409 - 410 1 411 P-R 412 RCL 13 413 - 414 R-P 415 CLX 416 SIGN 417 P-R 418 STO 15 419 X<>Y 420 RCL 13 421 ST* 15 422 ST- Z 423 ASIN 424 COS 425 * 426 X<>Y 427 R-P 428 X<>Y 429 ST+ 02 430 RCL 00 431 6510 432 * 433 221 434 - 435 12 436 P-R 437 1 438 ST+ Z 439 10^X 440 - 441 RCL 00 442 1412 443 * 444 8 445 + 446 3 447 P-R 448 X<>Y 449 ST+ T 450 RDN 451 + 452 R-P 453 X<>Y 454 RCL 02 455 + 456 SIN 457 * 458 X<> 02 459 2457 460 RCL 10 461 COS 462 9 463 * 464 - 465 1 466 RCL 15 467 - 468 * 469 XEQ 04 470 RCL 00 471 22576976 472 * 473 43.62 474 - 475 79 476 RCL 00 477 302 478 * 479 + 480 SIN 481 12 482 / 483 - 484 15.7 |
485 RCL 00
486 1401 487 * 488 STO 04 489 - 490 + 491 STO 10 492 SIN 493 11 494 SQRT 495 * 496 - 497 RCL 10 498 ST+ X 499 SIN 500 17 501 / 502 + 503 STO 02 504 15 505 RCL 04 506 + 507 6 508 P-R 509 1 510 ST+ Z 511 CLX 512 11 513 - 514 R-P 515 X<>Y 516 RCL 02 517 + 518 SIN 519 * 520 X<> 02 521 2028 522 RCL 10 523 COS 524 59 525 * 526 + 527 XEQ 04 528 79690048 529 RCL 00 530 * 531 761 532 SQRT 533 - 534 51 535 RCL 00 536 27525 537 * 538 + 539 + 540 SIN 541 6 542 * 543 STO 02 544 CLX 545 875 546 XEQ 04 547 131534932 548 RCL 00 549 * 550 71.19 551 + 552 5 553 RCL 00 554 84305 555 * 556 - 557 + 558 SIN 559 4 560 / 561 - 562 626 563 XEQ 04 564 190697912 565 RCL 00 566 * 567 53.08 568 + 569 38.6 570 RCL 00 571 13968 572 * 573 - 574 STO 03 575 SIN 576 43.4 577 * 578 RCL 03 579 3 580 * 581 SIN 582 2 583 SQRT 584 / 585 + 586 STO 15 587 21 588 / 589 - 590 139 591 RCL 00 592 197809 593 * 594 + 595 + 596 SIN 597 16 598 * 599 STO 02 600 CLX 601 489 602 XEQ 04 603 262731903 604 RCL 00 605 * |
606 11
607 + 608 RCL 00 609 88773 610 * 611 63 612 + 613 SIN 614 4 615 / 616 + 617 RCL 00 618 253657 619 * 620 44 621 - 622 SIN 623 5 624 / 625 + 626 49 627 RCL 00 628 337962 629 * 630 - 631 + 632 SIN 633 .55 634 * 635 - 636 395 637 XEQ 04 638 RCL 15 639 70.74 640 - 641 RCL 00 642 381994499 643 * 644 + 645 RCL 00 646 E6 647 STO 02 648 772 649 + 650 * 651 79 652 - 653 - 654 STO 15 655 SIN 656 10 657 LN 658 * 659 - 660 227 661 RCL 02 662 460 663 - 664 RCL 00 665 * 666 + 667 + 668 SIN 669 24 670 * 671 STO 02 672 CLX 673 308 674 RCL 15 675 COS 676 6 677 * 678 + 679 GTO 04 680 LBL 03 681 RCL 00 682 21572831 683 STO 15 684 * 685 30 686 + 687 COS 688 RCL 15 689 1760 690 - 691 RCL 00 692 * 693 STO 02 694 21 695 + 696 COS 697 ST+ X 698 - 699 4 700 * 701 X<> 02 702 90.6 703 + 704 RCL 15 705 60 706 X^2 707 - 708 RCL 00 709 * 710 77 711 + 712 STO 15 713 SIN 714 .84 715 * 716 + 717 2633 718 RCL 15 719 COS 720 19 721 * 722 - 723 XEQ 04 724 RCL 00 725 50317609 726 STO 15 |
727 7177
728 + 729 * 730 46 731 + 732 COS 733 PI 734 * 735 STO 02 736 RCL 00 737 RCL 15 738 * 739 217.13 740 + 741 STO 13 742 RCL 15 743 7127 744 - 745 RCL 00 746 * 747 55 748 - 749 STO 14 750 SIN 751 6 752 / 753 + 754 RCL 15 755 1840 756 - 757 RCL 00 758 * 759 23 760 + 761 SIN 762 11 763 / 764 - 765 1497 766 RCL 14 767 COS 768 ST+ X 769 - 770 XEQ 04 771 RCL 00 772 101407355 773 STO 15 774 * 775 20 776 - 777 SIN 778 8 779 * 780 STO 02 781 RCL 15 782 32631 783 - 784 RCL 00 785 * 786 184.3 787 + 788 ST- 13 789 RCL 13 790 ST+ X 791 STO 13 792 SIN 793 6 794 % 795 + 796 - 797 939 798 RCL 13 799 ST+ 13 800 COS 801 9 802 * 803 - 804 XEQ 04 805 RCL 00 806 203488956 807 * 808 61.37 809 - 810 RCL 13 811 SIN 812 .47 813 * 814 - 815 590 816 RCL 13 817 COS 818 6 819 SQRT 820 * 821 - 822 LBL 04 823 E2 824 / 825 ST* 02 826 X<>Y 827 RCL 01 828 + 829 X<>Y 830 P-R 831 X>0? 832 SF IND 16 833 RCL 19 834 * 835 ENTER 836 CLX 837 X<> 02 838 RCL 18 839 * 840 + 841 STO IND 17 842 DSE 17 843 X<>Y 844 STO IND 17 845 DSE 16 846 DSE 17 847 END |
( 1351 bytes / SIZE 020 )
| STACK | INPUTS | OUTPUTS |
| Y | YYYY.MNDD | y1 |
| X | HH.MNSS(TT) | x1 |
Execution time = 42s if CF 10 (
Moons of Jupiter )
Execution time = 82s if SF 10
( Moons of Saturn )
Example: On 2004/12/31 at 0h
TT
• CF 10 JUPITER
2004.1231 ENTER^
0 XEQ "STL"
>>>> x1 = -4.929
X<>Y y1 = 0.155
and in registers R01 thru R08:
Io - Europa - Ganymede - Callisto
x1 = -4.929 x2
= -4.834 x3
= -14.516 x4
= -8.557
DE = -2°69
y1 = 0.155
y2 = -0.306
y3 = -0.203
y4 = -1.076
-Flag F01 is set: Io is closer to the Earth than Jupiter.
• SF 10 SATURN
2004.1231 ENTER^
0 R/S
>>>> x1 = -0.289
X<>Y y1 = 1.169
and in registers R01 thru R14:
Mimas - Enceladus - Tethys - Dione - Rhea - Titan - Hyperion
x1 = -0.288 x2
= 3.911 x3
= 0.781 x4
= -0.103 x5 = -8.730
x6 = 3.585
x7 = 21.825
DE = -22°52
y1 = 1.170
y2 = -0.213
y3 = 1.778
y4 = 2.398 y5
= 0.255 y6
= 7.338 y7
= 3.645
-Flags F01 F03 F04 F05 F06 F07
are set, whence Mimas, Tethys, Dione, Rhea, Titan and Hyperion are
closer to the Earth than Saturn.
Notes:
-The accuracy is of order of a few hundredths of the planet's radius.
-Hyperion's coordinates are less accurate than the other ones.
-For Hyperion, the series converge slowly and several terms might be
added to get more accurate results.
-The complete series are available from ftp://ftp.imcce.fr
-But if you don't want to compute the position of Hyperion, delete
lines 268 to 469 and replace line 130 by 6
References:
[1] A. Vienne and L. Duriez 1995 "TASS1.6:
Ephemerides of the major Saturnian Satellites" Astronomy & Astrophysics
297 , 588-605
[2] L. Duriez and A. Vienne 1997 "Theory of motion
and Ephemerides of Hyperion" Astronomy & Astrophysics 324
, 366-380
[3] Jean Meeus - "Astronomical Algorithms" - Willmann-Bell
- ISBN 0-943396-61-1