Overview
1°) Program#1
2°) An M-Code Routine
3°) Program#2
Last Update:
>>>> The coordinates of Puck have been added to the Uranian satellites
( perturbations are not taken into account for Puck )
and several
constants given in reference [7] have been used.
>>>> In program#2, the position of Iapetus is also computed
-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 ) ------------Jup/Sat/Ura------------------ x (
West )
|
|
( South )
Data Registers: R00 thru R20 are used for temporay data storage and when the program stops:
Mimas - Enceladus - Tethys - Dione - Rhea - Titan - Hyperion - Iapetus ( with program#2 )
R01 = x1 R03 = x2
R05 = x3 R07 = x4
R09 = x5 R11 = x6
R13 = x7 R15
= x8
R02 = y1 R04 = y2
R06 = y3 R08 = y4
R10 = y5 R12 = y6
R14 = y7 R16
= y8
or Io - Europa - Ganymede - Callisto
or
Ariel - Umbriel -
Titania - Oberon - Miranda
- Puck
>>>> R19 = - sin DE
where DE is the planetocentric declination of the Earth.
Flags: F01 F02
F03 F04 F05 F06 F07 F08
-Flag nn is set when the distance Earth-Satellite n is shorter
than the distance Earth-Planet ( 0 < nn < 8 )
Subroutine: none if you have a Time
Module
"J0" otherwise .( cf for instance "Julian & Gregorian Calendars
for the HP-41" )
1°) Program#1
-Two M-code routines are used: Z+Z and Z-Z
-They may be replaced by XEQ "Z+Z" and XEQ "Z-Z"
respectively ( cf "Complex Functions for the HP-41" )
or, more directly, by X<>Y ST+ T
RDN + and X<>Y ST-T RDN
- respectively.
-If you have a Time module, lines 09-10 may be replaced by the 3 lines
1.012 DDAYS -
-Lines 144-798-1012 are three-byte GTOs
-If you don't have an HP-41CX, replace lines 408-409 by
CF 01 CF 02 CF 03 CF 04 CF 05
CF 06 CF 07
| 01 LBL "STL"
02 DEG 03 STO 20 04 RDN 05 HR 06 24 07 / 08 X<>Y 09 XEQ "J0" 10 + 11 E6 12 / 13 STO 00 14 985609 15 * 16 3 17 - 18 STO 01 19 SIN 20 192 21 * 22 RCL 01 23 ST+ X 24 SIN 25 ST+ X 26 + 27 7703 28 - 29 1 30 % 31 RCL 01 32 + 33 STO 02 34 1 35 RCL 01 36 COS 37 60 38 / 39 - 40 STO 08 41 RCL 00 42 16172 43 * 44 STO 05 45 76 46 - 47 SIN 48 STO 07 49 RCL 00 50 1116 51 * 52 STO 14 53 7 54 - 55 SIN 56 GTO IND 20 57 LBL 02 58 81 59 * 60 RCL 00 61 33460 62 * 63 STO 15 64 43 65 - 66 STO 03 67 SIN 68 636 69 * 70 + 71 RCL 03 72 ST+ X 73 SIN 74 20 75 * 76 + 77 RCL 15 78 RCL 14 79 - 80 60 81 - 82 STO 06 83 SIN 84 23 85 * 86 - 87 RCL 14 88 RCL 15 89 + 90 STO 10 91 50 92 - 93 SIN 94 21 95 SQRT 96 * 97 + 98 RCL 07 99 12 100 * 101 - 102 RCL 10 103 2 104 / 105 SIN 106 2 107 SQRT 108 * 109 + 110 9306 111 + 112 1 113 % 114 RCL 03 115 + 116 STO 04 117 9.56 118 RCL 03 119 COS 120 .53 121 * 122 - 123 RCL 03 124 ST+ X 125 COS 126 68 127 / 128 - 129 RCL 06 130 COS 131 53 132 / 133 + 134 STO 09 135 113.67 136 STO 10 137 169.53 138 STO 11 139 28.05 140 STO 12 141 2.49 142 STO 13 143 7 144 GTO 10 145 LBL 03 146 RCL 00 147 11731 148 * 149 STO 05 150 39 151 - 152 STO 03 153 SIN 154 CHS 155 531 156 * 157 RCL 00 158 233 159 * 160 STO 06 161 28 162 + 163 COS 164 86 165 * 166 - 167 RCL 05 168 RCL 06 169 - 170 19 171 + 172 STO 07 |
173 SIN
174 21 175 * 176 - 177 RCL 03 178 ST+ X 179 SIN 180 16 181 * 182 + 183 9998 184 RCL 00 185 * 186 51 187 - 188 COS 189 RCL 05 190 RCL 06 191 + 192 11 193 - 194 COS 195 + 196 RCL 06 197 ST+ X 198 40 199 + 200 SIN 201 - 202 1733 203 RCL 00 204 * 205 17 206 - 207 COS 208 - 209 4 210 * 211 + 212 RCL 00 213 71360 214 * 215 COS 216 RCL 05 217 RCL 06 218 ST+ X 219 - 220 COS 221 - 222 2 223 SQRT 224 * 225 + 226 RCL 05 227 ST+ X 228 RCL 06 229 - 230 70 231 + 232 COS 233 - 234 695 235 - 236 1 237 % 238 RCL 03 239 + 240 STO 04 241 1921 242 RCL 03 243 COS 244 89 245 * 246 + 247 RCL 07 248 COS 249 3 250 * 251 + 252 RCL 03 253 ST+ X 254 COS 255 ST+ X 256 - 257 1 258 % 259 STO 09 260 74.01 261 STO 10 262 12.35 263 CHS 264 STO 11 265 82.28 266 STO 12 267 .77 268 STO 13 269 6 270 GTO 10 271 LBL 01 272 RCL 00 273 83091 274 * 275 STO 15 276 20 277 + 278 STO 03 279 SIN 280 556 281 * 282 X<>Y 283 33 284 * 285 - 286 RCL 03 287 ST+ X 288 SIN 289 18 290 * 291 + 292 RCL 05 293 RCL 15 294 + 295 57 296 + 297 COS 298 6 299 * 300 - 301 RCL 15 302 RCL 14 303 - 304 29 305 + 306 COS 307 RCL 07 308 - 309 4 310 * 311 - 312 1431 313 + 314 1 315 % 316 RCL 03 317 + 318 STO 04 319 5209 320 RCL 03 321 COS 322 252 323 * 324 - 325 RCL 03 326 ST+ X 327 COS 328 6 329 * 330 - 331 .1 332 % 333 STO 09 334 100.46 335 STO 10 336 337.78 337 STO 11 338 2.22 339 STO 12 340 1.3 341 STO 13 342 4 343 LBL 10 344 STO 16 |
345 ST+ X
346 STO 17 347 RCL 04 348 RCL 02 349 - 350 RCL 09 351 P-R 352 RCL 08 353 + 354 R-P 355 RCL 04 356 RCL 10 357 - 358 SIN 359 RCL 13 360 SIN 361 * 362 RCL 09 363 * 364 STO 07 365 R-P 366 STO 01 367 ST/ 07 368 RCL 11 369 R^ 370 RCL 02 371 + 372 - 373 STO 19 374 SIN 375 RCL 12 376 SIN 377 STO 05 378 * 379 RCL 07 380 ST* 05 381 RCL 12 382 COS 383 STO 03 384 * 385 + 386 X<> 19 387 1 388 CHS 389 P-R 390 X<>Y 391 RCL 03 392 * 393 RCL 05 394 + 395 X<>Y 396 R-P 397 X<>Y 398 X<> 01 399 1731 E5 400 / 401 ST- 00 402 RCL 19 403 ASIN 404 COS 405 .1 406 % 407 STO 18 408 CLX 409 X<>F 410 GTO IND 20 411 LBL 02 412 16919949 413 RCL 00 414 * 415 240.7 416 + 417 562103 418 RCL 00 419 * 420 103.1 421 + 422 STO 10 423 SIN 424 9.12 425 * 426 + 427 29.9 428 RCL 00 429 52548 430 * 431 - 432 STO 12 433 RCL 10 434 + 435 SIN 436 .23 437 * 438 + 439 RCL 10 440 RCL 12 441 - 442 SIN 443 .21 444 * 445 - 446 RCL 00 447 5657028 448 * 449 76.2 450 + 451 STO 09 452 SIN 453 9 454 / 455 + 456 RCL 09 457 RCL 10 458 - 459 SIN 460 RCL 12 461 SIN 462 + 463 11 464 / 465 - 466 RCL 09 467 ST+ X 468 SIN 469 7 470 / 471 + 472 RCL 09 473 3 474 * 475 SIN 476 RCL 09 477 RCL 10 478 + 479 SIN 480 + 481 15 482 / 483 + 484 RCL 09 485 4 486 * 487 SIN 488 25 489 / 490 + 491 RCL 09 492 5 493 * 494 SIN 495 41 496 / 497 + 498 STO 08 499 193.84 500 RCL 00 501 51135 502 * 503 - 504 STO 07 505 206 506 P-R 507 RCL 07 508 RCL 12 509 - 510 49 511 P-R 512 Z+Z 513 RCL 07 514 RCL 10 515 + 516 5 |
517 P-R
518 Z-Z 519 RCL 07 520 RCL 10 521 - 522 3 523 P-R 524 Z-Z 525 RCL 07 526 RCL 09 527 + 528 2 529 P-R 530 Z-Z 531 RCL 07 532 RCL 09 533 - 534 2 535 SQRT 536 P-R 537 Z+Z 538 R-P 539 2 E3 540 / 541 STO 13 542 RCL 08 543 RCL Z 544 STO 02 545 - 546 1 547 P-R 548 RCL 13 549 - 550 R-P 551 CLX 552 SIGN 553 P-R 554 STO 15 555 X<>Y 556 RCL 13 557 ST* 15 558 ST- Z 559 ASIN 560 COS 561 * 562 X<>Y 563 R-P 564 X<>Y 565 ST+ 02 566 RCL 00 567 6510 568 * 569 221 570 - 571 12 572 P-R 573 1 574 ST+ Z 575 10^X 576 - 577 RCL 00 578 1412 579 * 580 8 581 + 582 3 583 P-R 584 Z+Z 585 XEQ 11 586 2457 587 RCL 10 588 COS 589 9 590 * 591 - 592 1 593 RCL 15 594 - 595 * 596 XEQ 13 597 RCL 00 598 22576976 599 * 600 43.62 601 - 602 79 603 RCL 00 604 302 605 * 606 + 607 SIN 608 12 609 / 610 - 611 20 612 RCL 00 613 1401 614 * 615 STO 04 616 + 617 SIN 618 28 619 / 620 + 621 STO Y 622 164.3 623 RCL 04 624 + 625 - 626 STO 10 627 SIN 628 3.31 629 * 630 + 631 RCL 10 632 ST+ X 633 SIN 634 17 635 / 636 + 637 STO 02 638 15 639 RCL 04 640 + 641 6 642 P-R 643 1 644 CHS 645 11 646 Z-Z 647 XEQ 11 648 2028 649 RCL 10 650 COS 651 59 652 * 653 - 654 XEQ 13 655 79690048 656 RCL 00 657 * 658 27.59 659 - 660 51 661 RCL 00 662 27525 663 * 664 + 665 + 666 SIN 667 6 668 * 669 STO 02 670 CLX 671 875 672 XEQ 13 673 131534932 674 RCL 00 675 * 676 71.19 677 + 678 5 679 RCL 00 680 84305 681 * 682 - 683 + 684 SIN 685 4 686 / 687 - 688 626 |
689 XEQ 13
690 190697912 691 RCL 00 692 * 693 53.08 694 + 695 38.6 696 RCL 00 697 13968 698 * 699 - 700 STO 03 701 SIN 702 43.4 703 * 704 RCL 03 705 3 706 * 707 SIN 708 .71 709 * 710 + 711 STO 15 712 21 713 / 714 - 715 139 716 RCL 00 717 197809 718 * 719 + 720 + 721 SIN 722 19 723 * 724 STO 02 725 CLX 726 489 727 XEQ 13 728 262731903 729 RCL 00 730 * 731 11 732 + 733 RCL 00 734 88773 735 * 736 63 737 + 738 SIN 739 4 740 / 741 + 742 RCL 00 743 253657 744 * 745 44 746 - 747 SIN 748 5 749 / 750 + 751 49 752 RCL 00 753 337962 754 * 755 - 756 + 757 SIN 758 .55 759 * 760 - 761 395 762 XEQ 13 763 RCL 15 764 70.74 765 - 766 RCL 00 767 381994499 768 * 769 + 770 78.4 771 RCL 00 772 1000772 773 * 774 - 775 + 776 STO 15 777 SIN 778 2.31 779 * 780 - 781 227 782 RCL 00 783 999540 784 * 785 + 786 + 787 SIN 788 28 789 * 790 STO 02 791 CLX 792 308 793 RCL 15 794 COS 795 6 796 * 797 + 798 GTO 13 799 LBL 03 800 155.24 801 RCL 00 802 472544545 803 * 804 - 805 31.09 806 CHS 807 RCL 00 808 221389 809 * 810 + 811 - 812 SIN 813 6 814 * 815 STO 02 816 CLX 817 336 818 XEQ 13 819 343.71 820 RCL 00 821 254690657 822 * 823 - 824 222 825 RCL 00 826 78540 827 * 828 - 829 STO 15 830 SIN 831 1.5 832 * 833 - 834 RCL 15 835 ST+ X 836 SIN 837 .19 838 * 839 + 840 77 841 RCL 00 842 55720 843 * 844 + 845 + 846 SIN 847 .15 848 * 849 + 850 276 851 RCL 00 852 55433 853 * 854 - 855 + 856 SIN 857 77 858 * 859 STO 02 860 CLX |
861 508
862 XEQ 13 863 205.86 864 RCL 00 865 26739484 866 * 867 - 868 STO 02 869 RCL 00 870 1112 871 * 872 28 873 + 874 STO 13 875 4 876 LN 877 P-R 878 RCL 00 879 5707 880 * 881 82 882 + 883 STO 14 884 .7 885 P-R 886 Z-Z 887 RCL 00 888 2484383 889 * 890 49 891 + 892 CHS 893 STO 04 894 1 895 P-R 896 Z-Z 897 XEQ 12 898 230 899 RCL 00 900 752 901 * 902 - 903 STO 20 904 .9 905 P-R 906 RCL 00 907 5045 908 * 909 59 910 X<>Y 911 - 912 STO 05 913 1.2 914 P-R 915 Z-Z 916 XEQ 11 917 1 918 RCL 03 919 COS 920 RCL 06 921 * 922 - 923 2283 924 * 925 XEQ 13 926 284.15 927 RCL 00 928 41351419 929 * 930 - 931 STO 02 932 RCL 14 933 .8 934 P-R 935 RCL 13 936 1.2 937 P-R 938 Z+Z 939 RCL 04 940 .8 941 P-R 942 Z+Z 943 XEQ 12 944 RCL 05 945 2 946 SQRT 947 P-R 948 RCL 20 949 .8 950 P-R 951 Z+Z 952 XEQ 11 953 1 954 RCL 03 955 COS 956 RCL 06 957 * 958 - 959 1707 960 * 961 XEQ 13 962 337.24 963 RCL 00 964 86868875 965 * 966 - 967 RCL 15 968 SIN 969 27 970 / 971 - 972 168 973 RCL 00 974 7783 975 * 976 + 977 + 978 STO 03 979 SIN 980 .45 981 * 982 + 983 10 984 CHS 985 RCL 00 986 7205 987 * 988 + 989 - 990 SIN 991 ST+ X 992 STO 02 993 CLX 994 1041 995 RCL 03 996 COS 997 4 998 * 999 - 1000 XEQ 13 1001 53.38 1002 RCL 00 1003 142835651 1004 * 1005 - 1006 RCL 15 1007 SIN 1008 .1 1009 * 1010 + 1011 747 1012 GTO 13 1013 LBL 11 1014 R-P 1015 X<>Y 1016 RCL 02 1017 + 1018 SIN 1019 * 1020 X<> 02 1021 RTN 1022 LBL 12 1023 R-P 1024 E3 1025 / 1026 STO 06 1027 R-D 1028 ST+ X 1029 X<>Y 1030 RCL 02 1031 + 1032 STO 03 |
1033 SIN
1034 * 1035 ST+ 02 1036 RTN 1037 LBL 01 1038 RCL 00 1039 21571071 1040 * 1041 90.6 1042 + 1043 STO 14 1044 13.93 1045 RCL 00 1046 1840 1047 * 1048 + 1049 STO 12 1050 - 1051 STO 15 1052 SIN 1053 .84 1054 * 1055 + 1056 19 1057 RCL 00 1058 1759 1059 * 1060 + 1061 + 1062 SIN 1063 RCL 14 1064 SIN 1065 ST+ X 1066 - 1067 4 1068 * 1069 STO 02 1070 CLX 1071 2633 1072 RCL 15 1073 COS 1074 19 1075 * 1076 - 1077 XEQ 13 1078 RCL 00 1079 50317609 1080 * 1081 217.13 1082 + 1083 STO 13 1084 88 1085 RCL 00 1086 7127 1087 * 1088 - 1089 + 1090 STO 14 1091 SIN 1092 6 1093 / 1094 + 1095 RCL 13 1096 RCL 12 1097 - 1098 SIN 1099 11 1100 / 1101 + 1102 101374725 1103 RCL 00 1104 * 1105 184.3 1106 + 1107 STO 12 1108 RCL 13 1109 - 1110 STO 15 1111 SIN 1112 14 1113 / 1114 - 1115 81 1116 RCL 00 1117 7177 1118 * 1119 - 1120 - 1121 SIN 1122 PI 1123 * 1124 STO 02 1125 CLX 1126 1497 1127 RCL 14 1128 COS 1129 ST+ X 1130 - 1131 XEQ 13 1132 RCL 12 1133 RCL 15 1134 ST+ X 1135 STO 15 1136 SIN 1137 6 1138 % 1139 + 1140 + 1141 205 1142 RCL 00 1143 32631 1144 * 1145 - 1146 - 1147 SIN 1148 8 1149 * 1150 STO 02 1151 CLX 1152 939 1153 RCL 15 1154 ST+ 15 1155 COS 1156 9 1157 * 1158 - 1159 XEQ 13 1160 RCL 12 1161 3 1162 * 1163 RCL 13 1164 90 1165 + 1166 ST+ X 1167 - 1168 RCL 15 1169 SIN 1170 .47 1171 * 1172 + 1173 590 1174 RCL 15 1175 COS 1176 6 1177 SQRT 1178 * 1179 - 1180 LBL 13 1181 RCL 01 1182 ST+ Z 1183 CLX 1184 E2 1185 / 1186 ST* 02 1187 P-R 1188 X>0? 1189 SF IND 16 1190 RCL 19 1191 * 1192 ENTER 1193 CLX 1194 X<> 02 1195 RCL 18 1196 * 1197 + 1198 STO IND 17 1199 DSE 17 1200 X<>Y 1201 STO IND 17 1202 DSE 16 1203 DSE 17 1204 END |
( 1974 bytes / SIZE 021 )
| STACK | INPUTS | OUTPUTS |
| Z | YYYY.MNDD | / |
| Y | HH.MNSS(TT) | y1 |
| X | 1 or 2 or 3 | x1 |
X = 1 for the Satellites
of Jupiter
---Execution time = 44s---
X = 2 for the Satellites
of Saturn
---Execution time = 84s---
X = 3 for the Satellites
of Uranus
---Execution time = 68s---
Example:
On 2018/01/24 at 16h41m TT
• Jovian Satellites
2018.0124 ENTER^
16.41
ENTER^
1 XEQ "STL"
>>>> x1 = -0.150 X<>Y
y1 = -0.329 and in
registers R01 thru R08:
Io - Europa - Ganymede - Callisto
x1 = -0.150 x2
= 1.752 x3
= -14.350 x4
= 9.880 DE
= -3°21
y1 = -0.329 y2
= -0.593 y3
= -0.278 y4
= -1.317
-Flags F01 to F04 are clear: all these 4 satellites are more distant
to the Earth than Jupiter.
• Saturnian Satellites
2018.0124 ENTER^
16.41
ENTER^
2 R/S
>>>> x1 = -2.812 X<>Y
y1 = 0.543 and in
registers R01 thru R14:
Mimas - Enceladus - Tethys - Dione - Rhea - Titan - Hyperion
x1 = -2.812 x2
= -0.239 x3
= -4.877 x4 = 4.342
x5 = -8.125 x6
= -9.839 x7 = 5.021
DE = 26°24
y1 = 0.543 y2
= -1.743 y3
= -0.193 y4 = 1.993
y5 = -1.389 y6
= -7.704 y7 = -10.076
-Flags F02 F03 F05 F06 F07
are set, whence Enceladus, Tethys, Rhea, Titan and Hyperion are closer
to the Earth than Saturn.
• Uranian Satellites
2018.0124 ENTER^
16.41
ENTER^
3 R/S
>>>> x1 = -2.061 X<>Y
y1 = 4.281 and in
registers R01 thru R12:
Ariel - Umbriel - Titania - Oberon - Miranda - Puck
x1 = -2.061 x2 = 9.149
x3 = 14.964 x4 = -8.449
x5 = 3.321 x15 = 0.728
DE = 36°60
y1 = 4.281 y2
= -2.982 y3 = 4.850
y4 = -12.660 y5 = -2.075
y15 = 1.957
-Flags F02 F04 F05 are set, so Umbriel, Oberon
and Miranda are closer to the Earth than Uranus.
Notes:
-The accuracy is of order of a few hundredths of the planet's radius.
-Hyperion's coordinates are less accurate than those of the other Saturnian
Satellites.
-For Hyperion, the series converge slowly and several terms should
be added to get more accurate results.
-To obtain a better accuracy, one should use more terms not only in
the series that give the satellites' position with respect to the planet,
but also in the series that give the position of the planet
itself with respect to the Earth ! I've used only the main terms ( lines
14 to 342 )
-If you don't want to compute the coordinates of the satellites of Jupiter,
delete lines 1038 to 1080 and lines 270 to 342
-If you don't want to compute the coordinates of the satellites of
Saturn, ----------- 411 to 798 ---------
57 to 144
-If you don't want to compute the coordinates of the satellites of
Uranus, ----------- 799 to 1012 --------- 145 to 270
( If you don't want to get the position of Puck, delete lines
800 to 818 and replace line 269 by 5 instead of 6 )
2°) An M-Code Routine
-The M-Code routine "VR" takes the eccentricity e < 1 in Y-register
and the mean anomaly M in X-register
-It returns the true anomaly v in X-register and r/a in Y-register
-The eccentric anomaly E is also given in T-register
-The angles must be expressed in decimal degrees.
-There is no check for alpha data
-VR is used in the version below
092 "R"
016 "V"
071 ?NCXQ
05C DEG
2A0 SETDEC
0F8 C=X
128 L=C
10E A=C ALL
0B8 C=Y
05E C= | C |
0E8 X=C
0AE A<>C ALL
0A8 Y=C
04E C
2BE
35C
050 =
21C
250
250
110 -10^(-6)
028 T=C
046 C=0 S&X
01D C=
060 A+C
2EE ?C#0 ALL
01B JNC+03
2FE ?C<0 ALL
01F JC+03
0B5 ?NCGO
0A2 DATAERROR
0B8 C=Y
loop
10E A=C ALL
0F8 C=X
070 polar
3C4 rectangular
1D5
078 conversion
2BE C=-C
00E A
35C =
162 1
01D C=
060 A+C
068 Z=C
0B0 C=N ALL
231 ?NCXQ
064 R-D
10E A=C ALL
0B8 C=Y
2BE C=-C
01D C=
061 A+C
138 C=L
025 C=
060 AB+C
078 C=Z
269 C=
060 AB/C
070 N=C ALL
0B8 C=Y
025 C=
060 AB+C
0A8 Y=C
0B0 C=N ALL
05E C=| C |
10E A=C ALL
046 C
270 =
038 T
01D C=
060 A+C
2FE ?C<0
2B3 JNC-42d
goto loop
0F8 C=X
068 Z=C
0B8 C=Y
028 T=C
10E A=C ALL
04E C
35C =
090 2
261 C=
060 A/C
070 C
209 =
048 tan(C°)
070 N=C ALL
078 C=Z
2BE C=-C
00E A
35C =
162 1
01D C=
060 A+C
05E C=| C |
128 L=C
078 C=Z
00E A
35C =
162 1
01D C=
060 A+C
0A8 Y=C
138 C=L
269 C=
060 AB/C
305 C=
060 sqrt(AB)
0B0 C=N ALL
13D C=
060 AB*C
070 C
2A9 =
040 atan(C°)
10E A=C ALL
01D C=
060 A+C
0E8 X=C
070 C
1F1 =
048 cos(C°)
10E A=C ALL
078 C=Z
135 C=
060 A*C
001 C=
060 AB+1
070 N=C ALL
0B8 C=Y
10E A=C ALL
138 C=L
135 C=
060 A*C
0B0 C=N
269 C=
060 AB/C
0A8 Y=C
3E0 RTN
( 139 words )
| STACK | INPUTS | OUTPUTS |
| T | / | E |
| Z | / | e |
| Y | e | r / a |
| X | M | v |
Example:
0.2 ENTER^
24 XEQ "VR" >>>> 35°94864074
X<>Y 0.826226700
-And the eccentric anomaly in T-register is E = 29°67281468
Notes:
-It may take several seconds...
-If e < 0 , it's replaced by -e
-If e = 1 or e > 1 , there will be a DATA ERROR message.
3°) Program#2
-Same specifications as the first version in §1, except that the coordinates of Iapetus x8 & y8 are stored in R15 & R16
-Lines 144-948-1162 are three-byte GTOs
| 01 LBL "STL"
02 DEG 03 STO 20 04 RDN 05 HR 06 24 07 / 08 X<>Y 09 XEQ "J0" 10 + 11 E6 12 / 13 STO 00 14 985609 15 * 16 3 17 - 18 STO 01 19 SIN 20 192 21 * 22 RCL 01 23 ST+ X 24 SIN 25 ST+ X 26 + 27 7703 28 - 29 1 30 % 31 RCL 01 32 + 33 STO 02 34 1 35 RCL 01 36 COS 37 60 38 / 39 - 40 STO 08 41 RCL 00 42 16172 43 * 44 STO 05 45 76 46 - 47 SIN 48 STO 07 49 RCL 00 50 1116 51 * 52 STO 14 53 7 54 - 55 SIN 56 GTO IND 20 57 LBL 02 58 81 59 * 60 RCL 00 61 33460 62 * 63 STO 15 64 43 65 - 66 STO 03 67 SIN 68 636 69 * 70 + 71 RCL 03 72 ST+ X 73 SIN 74 20 75 * 76 + 77 RCL 15 78 RCL 14 79 - 80 60 81 - 82 STO 06 83 SIN 84 23 85 * 86 - 87 RCL 14 88 RCL 15 89 + 90 STO 10 91 50 92 - 93 SIN 94 21 95 SQRT 96 * 97 + 98 RCL 07 99 12 100 * 101 - 102 RCL 10 103 2 104 / 105 SIN 106 2 107 SQRT 108 * 109 + 110 9306 111 + 112 1 113 % 114 RCL 03 115 + 116 STO 04 117 9.56 118 RCL 03 119 COS 120 .53 121 * 122 - 123 RCL 03 124 ST+ X 125 COS 126 68 127 / 128 - 129 RCL 06 130 COS 131 53 132 / 133 + 134 STO 09 135 113.67 136 STO 10 137 169.53 138 STO 11 139 28.05 140 STO 12 141 2.49 142 STO 13 143 7 144 GTO 10 145 LBL 03 146 RCL 00 147 11731 148 * 149 STO 05 150 39 151 - 152 STO 03 153 SIN 154 CHS 155 531 156 * 157 RCL 00 158 233 159 * 160 STO 06 161 28 162 + 163 COS 164 86 165 * 166 - 167 RCL 05 168 RCL 06 169 - 170 19 171 + 172 STO 07 173 SIN 174 21 175 * 176 - 177 RCL 03 178 ST+ X 179 SIN 180 16 181 * 182 + 183 9998 184 RCL 00 185 * 186 51 187 - 188 COS 189 RCL 05 190 RCL 06 191 + 192 11 193 - |
194 COS
195 + 196 RCL 06 197 ST+ X 198 40 199 + 200 SIN 201 - 202 1733 203 RCL 00 204 * 205 17 206 - 207 COS 208 - 209 4 210 * 211 + 212 RCL 00 213 71360 214 * 215 COS 216 RCL 05 217 RCL 06 218 ST+ X 219 - 220 COS 221 - 222 2 223 SQRT 224 * 225 + 226 RCL 05 227 ST+ X 228 RCL 06 229 - 230 70 231 + 232 COS 233 - 234 695 235 - 236 1 237 % 238 RCL 03 239 + 240 STO 04 241 1921 242 RCL 03 243 COS 244 89 245 * 246 + 247 RCL 07 248 COS 249 3 250 * 251 + 252 RCL 03 253 ST+ X 254 COS 255 ST+ X 256 - 257 1 258 % 259 STO 09 260 74.01 261 STO 10 262 12.35 263 CHS 264 STO 11 265 82.28 266 STO 12 267 .77 268 STO 13 269 6 270 GTO 10 271 LBL 01 272 RCL 00 273 83091 274 * 275 STO 15 276 20 277 + 278 STO 03 279 SIN 280 556 281 * 282 X<>Y 283 33 284 * 285 - 286 RCL 03 287 ST+ X 288 SIN 289 18 290 * 291 + 292 RCL 05 293 RCL 15 294 + 295 57 296 + 297 COS 298 6 299 * 300 - 301 RCL 15 302 RCL 14 303 - 304 29 305 + 306 COS 307 RCL 07 308 - 309 4 310 * 311 - 312 1431 313 + 314 1 315 % 316 RCL 03 317 + 318 STO 04 319 5209 320 RCL 03 321 COS 322 252 323 * 324 - 325 RCL 03 326 ST+ X 327 COS 328 6 329 * 330 - 331 .1 332 % 333 STO 09 334 100.46 335 STO 10 336 337.78 337 STO 11 338 2.22 339 STO 12 340 1.3 341 STO 13 342 4 343 LBL 10 344 STO 22 345 ST+ X 346 STO 17 347 RCL 04 348 RCL 02 349 - 350 RCL 09 351 P-R 352 RCL 08 353 + 354 R-P 355 RCL 04 356 RCL 10 357 - 358 SIN 359 RCL 13 360 SIN 361 * 362 RCL 09 363 * 364 STO 07 365 R-P 366 STO 01 367 ST/ 07 368 RCL 11 369 R^ 370 RCL 02 371 + 372 - 373 STO 19 374 SIN 375 RCL 12 376 SIN 377 STO 05 378 * 379 RCL 07 380 ST* 05 381 RCL 12 382 COS 383 STO 03 384 * 385 + 386 X<> 19 |
387 1
388 CHS 389 P-R 390 X<>Y 391 RCL 03 392 * 393 RCL 05 394 + 395 X<>Y 396 R-P 397 X<>Y 398 X<> 01 399 1731 E5 400 / 401 ST- 00 402 RCL 19 403 ASIN 404 COS 405 .1 406 % 407 STO 18 408 CLX 409 X<>F 410 CF 08 411 GTO IND 20 412 LBL 02 413 RCL 00 414 4537939 415 * 416 36.89 417 + 418 RCL 00 419 302 420 * 421 STO 06 422 77.7 423 + 424 SIN 425 11.05 426 * 427 + 428 RCL 06 429 ST+ X 430 9 431 - 432 SIN 433 14 434 / 435 - 436 RCL 00 437 33460 438 * 439 43 440 - 441 SIN 442 16 443 / 444 - 445 RCL 00 446 1401 447 * 448 STO 04 449 26 450 + 451 SIN 452 23 453 / 454 - 455 RCL 00 456 1803937 457 * 458 9 459 + 460 COS 461 24 462 / 463 - 464 RCL 00 465 67221 466 * 467 11 468 + 469 SIN 470 59 471 / 472 + 473 STO 05 474 293 475 ENTER 476 SIGN 477 P-R 478 RCL 00 479 310 480 * 481 195 482 + 483 29 484 P-R 485 Z+Z 486 RCL 04 487 16 488 - 489 1 490 P-R 491 Z+Z 492 R-P 493 E3 494 STO 08 495 / 496 X<>Y 497 STO 10 498 CHS 499 RCL 05 500 + 501 360 502 MOD 503 VR 504 ST+ 10 505 X<>Y 506 STO 07 507 184.6 508 132 509 P-R 510 287 511 RCL 06 512 - 513 68 514 P-R 515 Z+Z 516 R-P 517 RCL 08 518 / 519 ASIN 520 ST+ X 521 STO 02 522 X<>Y 523 STO 09 524 CHS 525 RCL 10 526 + 527 RCL 07 528 58.76 529 * 530 STO 05 531 SIGN 532 P-R 533 RCL Y 534 RCL 02 535 SIN 536 * 537 X<> 02 538 COS 539 R^ 540 * 541 X<>Y 542 R-P 543 X<> 09 544 + 545 RCL 01 546 + 547 1 548 P-R 549 STO 16 550 X<>Y 551 STO 21 552 RCL 02 553 ASIN 554 RCL 05 555 P-R 556 ST* 21 557 ST* 16 558 R^ 559 * 560 RCL 18 561 RCL 08 562 * 563 STO 09 564 * 565 X<>Y 566 STO 05 567 RCL 19 568 * 569 - 570 X>0? 571 SF 08 572 RCL 05 573 RCL 09 574 * 575 RCL 19 576 RCL 16 577 * 578 + 579 STO 16 |
580 16919949
581 RCL 00 582 * 583 240.7 584 + 585 562103 586 RCL 00 587 * 588 103.1 589 + 590 STO 10 591 SIN 592 9.12 593 * 594 + 595 29.9 596 RCL 00 597 52548 598 * 599 - 600 STO 12 601 RCL 10 602 + 603 SIN 604 .23 605 * 606 + 607 RCL 10 608 RCL 12 609 - 610 SIN 611 .21 612 * 613 - 614 RCL 00 615 5657028 616 * 617 76.2 618 + 619 STO 09 620 SIN 621 9 622 / 623 + 624 RCL 09 625 RCL 10 626 - 627 SIN 628 RCL 12 629 SIN 630 + 631 11 632 / 633 - 634 RCL 09 635 ST+ X 636 SIN 637 7 638 / 639 + 640 RCL 09 641 3 642 * 643 SIN 644 RCL 09 645 RCL 10 646 + 647 SIN 648 + 649 15 650 / 651 + 652 RCL 09 653 4 654 * 655 SIN 656 25 657 / 658 + 659 RCL 09 660 5 661 * 662 SIN 663 41 664 / 665 + 666 STO 08 667 193.84 668 RCL 00 669 51135 670 * 671 - 672 STO 07 673 206 674 P-R 675 RCL 07 676 RCL 12 677 - 678 49 679 P-R 680 Z+Z 681 RCL 07 682 RCL 10 683 + 684 5 685 P-R 686 Z-Z 687 RCL 07 688 RCL 10 689 - 690 3 691 P-R 692 Z-Z 693 RCL 07 694 RCL 09 695 + 696 2 697 P-R 698 Z-Z 699 RCL 07 700 RCL 09 701 - 702 2 703 SQRT 704 P-R 705 Z+Z 706 R-P 707 2 E3 708 / 709 RCL 08 710 RCL Z 711 STO 02 712 - 713 360 714 MOD 715 VR 716 ST+ 02 717 X<>Y 718 STO 03 719 RCL 00 720 6510 721 * 722 221 723 - 724 12 725 P-R 726 1 727 ST+ Z 728 10^X 729 - 730 RCL 00 731 1412 732 * 733 8 734 + 735 PI 736 P-R 737 Z+Z 738 XEQ 11 739 2457 740 RCL 10 741 COS 742 9 743 * 744 - 745 RCL 03 746 * 747 XEQ 13 748 RCL 00 749 22576976 750 * 751 43.62 752 - 753 79 754 RCL 06 755 + 756 SIN 757 12 758 / 759 - 760 20 761 RCL 04 762 + 763 SIN 764 28 765 / 766 + 767 STO Y 768 15.7 769 RCL 04 770 - 771 + 772 STO 10 |
773 SIN
774 11 775 SQRT 776 * 777 - 778 RCL 10 779 ST+ X 780 SIN 781 17 782 / 783 + 784 STO 02 785 15 786 RCL 04 787 + 788 6 789 P-R 790 1 791 CHS 792 11 793 Z-Z 794 XEQ 11 795 2028 796 RCL 10 797 COS 798 59 799 * 800 + 801 XEQ 13 802 79690048 803 RCL 00 804 * 805 27.59 806 - 807 51 808 RCL 00 809 27525 810 * 811 + 812 + 813 SIN 814 6 815 * 816 STO 02 817 CLX 818 875 819 XEQ 13 820 131534932 821 RCL 00 822 * 823 71.19 824 + 825 5 826 RCL 00 827 84305 828 * 829 - 830 + 831 SIN 832 4 833 / 834 - 835 626 836 XEQ 13 837 190697912 838 RCL 00 839 * 840 53.08 841 + 842 38.6 843 RCL 00 844 13968 845 * 846 - 847 STO 03 848 SIN 849 43.4 850 * 851 RCL 03 852 3 853 * 854 SIN 855 .71 856 * 857 + 858 STO 15 859 21 860 / 861 - 862 139 863 RCL 00 864 197809 865 * 866 + 867 + 868 SIN 869 19 870 * 871 STO 02 872 CLX 873 489 874 XEQ 13 875 262731903 876 RCL 00 877 * 878 11 879 + 880 RCL 00 881 88773 882 * 883 63 884 + 885 SIN 886 4 887 / 888 + 889 RCL 00 890 253657 891 * 892 44 893 - 894 SIN 895 5 896 / 897 + 898 49 899 RCL 00 900 337962 901 * 902 - 903 + 904 SIN 905 .55 906 * 907 - 908 395 909 XEQ 13 910 RCL 15 911 70.74 912 - 913 RCL 00 914 381994499 915 * 916 + 917 78.4 918 RCL 00 919 1000772 920 * 921 - 922 + 923 STO 15 924 SIN 925 2.31 926 * 927 - 928 227 929 RCL 00 930 999540 931 * 932 + 933 + 934 SIN 935 28 936 * 937 STO 02 938 CLX 939 308 940 RCL 15 941 COS 942 6 943 * 944 + 945 RCL 21 946 STO 15 947 RDN 948 GTO 13 949 LBL 03 950 155.24 951 RCL 00 952 472544545 953 * 954 - 955 31.09 956 CHS 957 RCL 00 958 221389 959 * 960 + 961 - 962 SIN 963 6 964 * 965 STO 02 |
966 CLX
967 336 968 XEQ 13 969 343.71 970 RCL 00 971 254690657 972 * 973 - 974 222 975 RCL 00 976 78540 977 * 978 - 979 STO 15 980 SIN 981 1.5 982 * 983 - 984 RCL 15 985 ST+ X 986 SIN 987 .19 988 * 989 + 990 77 991 RCL 00 992 55720 993 * 994 + 995 + 996 SIN 997 .15 998 * 999 + 1000 276 1001 RCL 00 1002 55433 1003 * 1004 - 1005 + 1006 SIN 1007 77 1008 * 1009 STO 02 1010 CLX 1011 508 1012 XEQ 13 1013 205.86 1014 RCL 00 1015 26739484 1016 * 1017 - 1018 STO 02 1019 RCL 00 1020 1112 1021 * 1022 28 1023 + 1024 STO 13 1025 4 1026 LN 1027 P-R 1028 RCL 00 1029 5707 1030 * 1031 82 1032 + 1033 STO 14 1034 .7 1035 P-R 1036 Z-Z 1037 RCL 00 1038 2484383 1039 * 1040 49 1041 + 1042 CHS 1043 STO 04 1044 1 1045 P-R 1046 Z-Z 1047 XEQ 12 1048 230 1049 RCL 00 1050 752 1051 * 1052 - 1053 STO 20 1054 .9 1055 P-R 1056 RCL 00 1057 5045 1058 * 1059 59 1060 X<>Y 1061 - 1062 STO 05 1063 1.2 1064 P-R 1065 Z-Z 1066 XEQ 11 1067 1 1068 RCL 03 1069 COS 1070 RCL 06 1071 * 1072 - 1073 2283 1074 * 1075 XEQ 13 1076 284.15 1077 RCL 00 1078 41351419 1079 * 1080 - 1081 STO 02 1082 RCL 14 1083 .8 1084 P-R 1085 RCL 13 1086 1.2 1087 P-R 1088 Z+Z 1089 RCL 04 1090 .8 1091 P-R 1092 Z+Z 1093 XEQ 12 1094 RCL 05 1095 2 1096 SQRT 1097 P-R 1098 RCL 20 1099 .8 1100 P-R 1101 Z+Z 1102 XEQ 11 1103 1 1104 RCL 03 1105 COS 1106 RCL 06 1107 * 1108 - 1109 1707 1110 * 1111 XEQ 13 1112 337.24 1113 RCL 00 1114 86868875 1115 * 1116 - 1117 RCL 15 1118 SIN 1119 27 1120 / 1121 - 1122 168 1123 RCL 00 1124 7783 1125 * 1126 + 1127 + 1128 STO 03 1129 SIN 1130 .45 1131 * 1132 + 1133 10 1134 CHS 1135 RCL 00 1136 7205 1137 * 1138 + 1139 - 1140 SIN 1141 ST+ X 1142 STO 02 1143 CLX 1144 1041 1145 RCL 03 1146 COS 1147 4 1148 * 1149 - 1150 XEQ 13 1151 53.38 1152 RCL 00 1153 142835651 1154 * 1155 - 1156 RCL 15 1157 SIN 1158 .1 1159 * |
1160 +
1161 747 1162 GTO 13 1163 LBL 11 1164 R-P 1165 X<>Y 1166 RCL 02 1167 + 1168 SIN 1169 * 1170 X<> 02 1171 RTN 1172 LBL 12 1173 R-P 1174 E3 1175 / 1176 STO 06 1177 R-D 1178 ST+ X 1179 X<>Y 1180 RCL 02 1181 + 1182 STO 03 1183 SIN 1184 * 1185 ST+ 02 1186 RTN 1187 LBL 01 1188 RCL 00 1189 21571071 1190 * 1191 90.6 1192 + 1193 STO 14 1194 13.93 1195 RCL 00 1196 1840 1197 * 1198 + 1199 STO 12 1200 - 1201 STO 15 1202 SIN 1203 .84 1204 * 1205 + 1206 19 1207 RCL 00 1208 1759 1209 * 1210 + 1211 + 1212 SIN 1213 RCL 14 1214 SIN 1215 ST+ X 1216 - 1217 4 1218 * 1219 STO 02 1220 CLX 1221 2633 1222 RCL 15 1223 COS 1224 19 1225 * 1226 - 1227 XEQ 13 1228 RCL 00 1229 50317609 1230 * 1231 217.13 1232 + 1233 STO 13 1234 88 1235 RCL 00 1236 7127 1237 * 1238 - 1239 + 1240 STO 14 1241 SIN 1242 6 1243 / 1244 + 1245 RCL 13 1246 RCL 12 1247 - 1248 SIN 1249 11 1250 / 1251 + 1252 101374725 1253 RCL 00 1254 * 1255 184.3 1256 + 1257 STO 12 1258 RCL 13 1259 - 1260 STO 15 1261 ST+ 15 1262 SIN 1263 14 1264 / 1265 - 1266 81 1267 RCL 00 1268 7177 1269 * 1270 - 1271 - 1272 SIN 1273 PI 1274 * 1275 STO 02 1276 CLX 1277 1497 1278 RCL 14 1279 COS 1280 ST+ X 1281 - 1282 XEQ 13 1283 RCL 12 1284 RCL 15 1285 SIN 1286 6 1287 % 1288 + 1289 + 1290 205 1291 RCL 00 1292 32631 1293 * 1294 - 1295 - 1296 SIN 1297 8 1298 * 1299 STO 02 1300 CLX 1301 939 1302 RCL 15 1303 ST+ 15 1304 COS 1305 9 1306 * 1307 - 1308 XEQ 13 1309 RCL 12 1310 3 1311 * 1312 RCL 13 1313 90 1314 + 1315 ST+ X 1316 - 1317 RCL 15 1318 SIN 1319 .47 1320 * 1321 + 1322 590 1323 RCL 15 1324 COS 1325 6 1326 SQRT 1327 * 1328 - 1329 LBL 13 1330 RCL 01 1331 ST+ Z 1332 CLX 1333 E2 1334 / 1335 ST* 02 1336 P-R 1337 X>0? 1338 SF IND 22 1339 RCL 19 1340 * 1341 ENTER 1342 CLX 1343 X<> 02 1344 RCL 18 1345 * 1346 + 1347 STO IND 17 1348 DSE 17 1349 X<>Y 1350 STO IND 17 1351 DSE 22 1352 DSE 17 1353 END |
( 2206 bytes / SIZE
023 )
| STACK | INPUTS | OUTPUTS |
| Z | YYYY.MNDD | / |
| Y | HH.MNSS(TT) | y1 |
| X | 1 or 2 or 3 | x1 |
X = 1 for the Satellites
of Jupiter
---Execution time = 44s---
X = 2 for the Satellites
of Saturn
---Execution time = 105s---
X = 3 for the Satellites
of Uranus
---Execution time = 68s---
Example:
On 2018/01/24 at 16h41m TT
• Jovian Satellites
2018.0124 ENTER^
16.41
ENTER^
1 XEQ "STL"
>>>> x1 = -0.150 X<>Y
y1 = -0.329 and in
registers R01 thru R08:
Io - Europa - Ganymede - Callisto
x1 = -0.150 x2
= 1.752 x3
= -14.350 x4
= 9.880 DE
= -3°21
y1 = -0.329 y2
= -0.593 y3
= -0.278 y4
= -1.317
-Flags F01 to F04 are clear: all these 4 satellites are more distant
to the Earth than Jupiter.
• Saturnian Satellites
2018.0124 ENTER^
16.41
ENTER^
2 R/S
>>>> x1 = -2.812 X<>Y
y1 = 0.543 and in
registers R01 thru R16:
Mimas - Enceladus - Tethys - Dione - Rhea - Titan - Hyperion - Iapetus
x1 = -2.812 x2
= -0.239 x3
= -4.877 x4 = 4.342
x5 = -8.125 x6
= -9.837 x7 = 5.013
x8 = -2.177
DE
= 26°24
y1 = 0.543 y2
= -1.743 y3
= -0.193 y4 = 1.993
y5 = -1.389 y6
= -7.705 y7 = -10.078
y8 = 11.220
-Flags F02 F03 F05 F06 F07
are set, whence Enceladus, Tethys, Rhea, Titan and Hyperion are closer
to the Earth than Saturn.
• Uranian Satellites
2018.0124 ENTER^
16.41
ENTER^
3 R/S
>>>> x1 = -2.061 X<>Y
y1 = 4.281 and in
registers R01 thru R12:
Ariel - Umbriel - Titania - Oberon - Miranda - Puck
x1 = -2.061 x2 = 9.149
x3 = 14.964 x4 = -8.449
x5 = 3.321 x15 = 0.728
DE = 36°60
y1 = 4.281 y2
= -2.982 y3 = 4.850
y4 = -12.660 y5 = -2.075
y15 = 1.957
-Flags F02 F04 F05 are set, so Umbriel, Oberon
and Miranda are closer to the Earth than Uranus.
Note:
-The precision of Iapetus coordinates is of the same order as Hyperion's
coordinates.
References:
[1] Jean Meeus - "Astronomical Algorithms" - Willmann-Bell
- ISBN 0-943396-61-1
[2] D. Harper & D.B. Taylor 1993 - "The orbits of the
Major Satellites of Saturn" - Astronomy & Astrophysics 268 ,
326-349
[3] A. Vienne & L. Duriez 1995 - "TASS1.6:
Ephemerides of the major Saturnian Satellites" - Astronomy & Astrophysics
297 , 588-605
[4] L. Duriez & A. Vienne 1997 - "Theory of motion
and Ephemerides of Hyperion" - Astronomy & Astrophysics 324 ,
366-380
[5] J. Laskar & R.A. Jacobson 1987 - "GUST86.
An Analytical Ephemeris of the Uranian Satellites" - Astronomy & Astrophysics
188 , 212-224
[6] D. Lazzaro 1991 - "Semi-analytical Theory for the motion
of Uranus' Satellites" - Astronomy & Astrophysics 250 , 253-265
[7] R. A. Jacobson 2014 - THE ORBITS OF THE URANIAN SATELLITES
AND RINGS, THE GRAVITY FIELD OF THE
URANIAN SYSTEM, AND THE ORIENTATION
OF THE POLE OF URANUS- The Astronomical Journal, 148:76 (13pp)