Overview
-These programs combine the second routine listed in "Astronomical Ephemeris(IV)"
& the routine listed in "Jovian & Saturnian Satellites"
-There was not enough room to include the positions of the Moon &
Pluto.
-These programs may be used with an HP41CV without any module ( 2020 bytes / SIZE 016 ).
-"EPH" calculates the heliocentric & geocentric coordinates of the Sun and the major planets ( referred to the mean ecliptic & equinox of the date )
-"STL" computes the coordinates of Io Europa Ganymede Callisto if flag
F10 is clear
or Mimas Enceladus Tethys Dione Rhea Titan Hyperion if flag
F10 is set
-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------------------ x ( West
)
|
|
( South )
Program Listing
Data Registers: •
R00 = t = time in century since 2000/01/01 0h TT
( Register R00 is to be initialized before executing these programs
)
LBL "EPH" = LBL 10 LBL 01 LBL 02 LBL 04 LBL 05 LBL 06 LBL 07 LBL 08:
R01 = XSun R03 = geocentric
longitude ( deg )
R06 = heliocentric longitude ( deg )
R02 = YSun R04 = geocentric
latitude ( deg )
R07 = heliocentric latitude ( deg )
R05 = distance Earth-Planet ( AU )
R08 = distance Sun-Planet ( AU )
Flags: /
Subroutines: /
STL:
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: none for LBL 10 LBL 01 LBL 02 LBL 04 LBL 05 LBL 06 LBL 07 LBL 08:
STL:
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
Subroutines: /
-Lines 639 & 1051 are three-byte GTOs
-If you don't have an HP41CX , replace lines 567-568 by CF 01
CF 02 CF 03 CF 04 CF 05 CF 06 CF 07
| 01 LBL "EPH"
02 LBL 10 03 1 04 STO 09 05 1671 06 STO 10 07 48 08 + 09 STO 15 10 36000770 11 STO 06 12 80026 13 CHS 14 STO 12 15 77063 16 CHS 17 STO 13 18 CLST 19 STO 01 20 STO 02 21 STO 11 22 XEQ 13 23 RCL 05 24 P-R 25 STO 01 26 X<>Y 27 STO 02 28 RCL 05 29 RCL 04 30 RCL 03 31 RTN 32 LBL 01 33 .3871 34 STO 09 35 20563 36 STO 10 37 7005 38 STO 11 39 1556 40 STO 15 41 77456 42 STO 13 43 250205 44 STO 12 45 149474072 46 STO 06 47 48331 48 1186 49 XEQ 13 50 RTN 51 LBL 02 52 .7233 53 STO 09 54 677 55 STO 10 56 3395 57 STO 11 58 1402 59 STO 15 60 131564 61 STO 13 62 181179 63 STO 12 64 58519213 65 STO 06 66 76680 67 901 68 XEQ 13 69 RTN 70 LBL 04 71 XEQ 12 72 RCL 15 73 10 74 * 75 18 76 - 77 COS 78 16 79 * 80 STO 03 81 CLX 82 STO 04 83 STO 05 84 1.524 85 STO 09 86 9340 87 STO 10 88 1850 89 STO 11 90 9 91 - 92 STO 15 93 4829 94 CHS 95 STO 12 96 19141696 97 STO 06 98 23940 99 CHS 100 STO 13 101 49558 102 772 103 XEQ 14 104 RTN 105 LBL 05 106 XEQ 12 107 RCL 08 108 73 109 + 110 COS 111 RCL 10 112 RCL 07 113 - 114 41 115 + 116 SIN 117 - 118 509 119 SQRT 120 * 121 RCL 09 122 75 123 - 124 SIN 125 37 126 * 127 + 128 RCL 06 129 RCL 11 130 - 131 61 132 - 133 SIN 134 42 135 * 136 + 137 RCL 10 138 33 139 - 140 SIN 141 56 142 * 143 + 144 RCL 11 145 7 146 - 147 SIN 148 329 149 * 150 - 151 STO 03 152 CLX 153 STO 04 154 STO 05 155 5.203 156 STO 09 157 1303 158 STO 11 159 4849 160 STO 10 161 1613 162 STO 15 163 34310 164 STO 12 165 3036303 166 STO 06 167 14331 168 STO 13 169 100464 170 1021 171 XEQ 14 172 RTN 173 LBL 06 174 XEQ 12 |
175 RCL 07
176 RCL 11 177 + 178 50 179 - 180 SIN 181 45 182 * 183 RCL 09 184 14 185 + 186 COS 187 118 188 * 189 + 190 RCL 07 191 RCL 11 192 - 193 30 194 + 195 COS 196 228 197 * 198 + 199 RCL 11 200 7 201 - 202 SIN 203 810 204 * 205 + 206 STO 03 207 RCL 09 208 ST+ X 209 STO 13 210 33 211 + 212 COS 213 20 214 * 215 RCL 07 216 RCL 11 217 + 218 20 219 + 220 COS 221 18 222 * 223 - 224 STO 04 225 RCL 13 226 60 227 - 228 COS 229 19 230 * 231 STO 05 232 9.543 233 STO 09 234 5553 235 RCL 00 236 35 237 * 238 - 239 STO 10 240 2489 241 STO 11 242 1964 243 STO 15 244 50061 245 STO 12 246 1223511 247 STO 06 248 93057 249 STO 13 250 113666 251 877 252 XEQ 14 253 RTN 254 LBL 07 255 XEQ 12 256 RCL 06 257 RCL 12 258 - 259 10 260 - 261 COS 262 RCL 12 263 RCL 04 264 - 265 COS 266 - 267 15 268 * 269 RCL 05 270 RCL 12 271 + 272 11 273 - 274 COS 275 RCL 12 276 RCL 03 277 - 278 51 279 - 280 COS 281 + 282 40 283 * 284 + 285 RCL 03 286 73 287 + 288 SIN 289 RCL 04 290 39 291 + 292 SIN 293 + 294 35 295 * 296 - 297 RCL 14 298 ST+ X 299 19 300 + 301 STO 11 302 SIN 303 209 304 * 305 - 306 RCL 05 307 62 308 - 309 SIN 310 858 311 * 312 + 313 STO 03 314 CLX 315 STO 04 316 RCL 11 317 COS 318 34 319 * 320 STO 05 321 19.192 322 STO 09 323 45955 324 CHS 325 STO 12 326 429864 327 STO 06 328 4630 329 STO 10 330 773 331 STO 11 332 1486 333 STO 15 334 172993 335 STO 13 336 74005 337 521 338 XEQ 14 339 RTN 340 LBL 08 341 XEQ 12 342 RCL 04 343 50 344 - 345 COS 346 24 347 * 348 RCL 14 |
349 RCL 05
350 - 351 11 352 - 353 COS 354 22 355 * 356 + 357 RCL 14 358 7 359 + 360 SIN 361 71 362 * 363 + 364 RCL 05 365 28 366 + 367 COS 368 584 369 * 370 + 371 STO 03 372 CLX 373 STO 04 374 RCL 14 375 COS 376 17 377 * 378 CHS 379 STO 05 380 30.07 381 STO 09 382 899 383 STO 10 384 1770 385 RCL 00 386 9 387 * 388 - 389 STO 11 390 1426 391 STO 15 392 55654 393 CHS 394 STO 12 395 219883 396 STO 06 397 48124 398 STO 13 399 131784 400 1102 401 GTO 14 402 LBL 12 403 102 404 RCL 00 405 2.06 406 * 407 STO 15 408 * 409 STO 14 410 208 411 LASTX 412 * 413 STO 12 414 19 415 RCL 15 416 * 417 STO 11 418 593 419 LASTX 420 * 421 STO 07 422 LASTX 423 880 424 * 425 STO 08 426 + 427 STO 06 428 LASTX 429 RCL 07 430 - 431 STO 09 432 + 433 STO 10 434 4 435 RCL 15 436 * 437 STO 05 438 ST+ X 439 STO 04 440 LASTX 441 31 442 * 443 STO 03 444 RTN 445 LBL 13 446 0 447 STO 03 448 STO 04 449 STO 05 450 RDN 451 LBL 14 452 RCL 00 453 ST* 06 454 ST* 15 455 * 456 + 457 STO 14 458 E5 459 ST/ 10 460 9 461 STO 08 462 RCL 12 463 RCL 06 464 + 465 E3 466 STO 06 467 ST/ 03 468 ST/ 04 469 ST/ 05 470 ST/ 11 471 ST/ 14 472 / 473 RCL 13 474 RCL 15 475 + 476 RCL 06 477 / 478 STO 13 479 - 480 ENTER 481 ENTER 482 LBL 11 483 SIN 484 RCL 10 485 R-D 486 * 487 + 488 DSE 08 489 GTO 11 490 STO 15 491 2 492 / 493 1 494 RCL 10 495 + 496 1 497 LASTX 498 - 499 / 500 SQRT 501 P-R 502 LASTX 503 / 504 R-P 505 RDN 506 ST+ X 507 1 508 RCL 15 509 COS 510 RCL 10 511 * 512 - 513 RCL 09 514 * 515 RCL 05 516 + 517 STO 08 518 CLX 519 RCL 14 520 - 521 RCL 13 522 + |
523 COS
524 RCL 11 525 LASTX 526 SIN 527 P-R 528 X<>Y 529 ASIN 530 RCL 04 531 + 532 STO 07 533 X<> Z 534 R-P 535 CLX 536 RCL 14 537 + 538 RCL 03 539 + 540 STO 06 541 RCL 08 542 X<>Y 543 RDN 544 P-R 545 R^ 546 X<>Y 547 P-R 548 RCL 02 549 ST+ Z 550 CLX 551 RCL 01 552 + 553 R-P 554 X<>Y 555 RDN 556 R-P 557 R^ 558 X<>Y 559 STO 05 560 X<> Z 561 STO 04 562 X<>Y 563 STO 03 564 RTN 565 LBL "STL" 566 XEQ 10 567 CLX 568 X<>F 569 FC? 10 570 GTO 12 571 XEQ 06 572 169.53 573 STO 11 574 28.05 575 STO 12 576 7 577 GTO 13 578 LBL 12 579 XEQ 05 580 337.78 581 STO 11 582 2.22 583 STO 12 584 4 585 LBL 13 586 STO M 587 RCL 00 588 3.6525 589 % 590 STO 00 591 38 592 * 593 RCL 11 594 + 595 RCL 03 596 - 597 STO O 598 SIN 599 RCL 04 600 COS 601 STO 14 602 * 603 RCL 12 604 SIN 605 STO 06 606 * 607 RCL 04 608 SIN 609 ST* 06 610 RCL 12 611 COS 612 STO 03 613 * 614 + 615 X<> O 616 RCL 14 617 CHS 618 P-R 619 X<>Y 620 RCL 03 621 * 622 RCL 06 623 + 624 X<>Y 625 R-P 626 X<>Y 627 STO 01 628 RCL 05 629 173 E6 630 / 631 ST- 00 632 RCL O 633 ASIN 634 COS 635 E3 636 / 637 STO N 638 FC? 10 639 GTO 13 640 16919949 641 RCL 00 642 * 643 240.7 644 + 645 562103 646 RCL 00 647 * 648 103.1 649 + 650 STO 10 651 SIN 652 9.12 653 * 654 + 655 29.9 656 RCL 00 657 52548 658 * 659 - 660 STO 12 661 RCL 10 662 + 663 SIN 664 .23 665 * 666 + 667 RCL 10 668 RCL 12 669 - 670 SIN 671 .21 672 * 673 - 674 RCL 00 675 5657028 676 * 677 76 678 + 679 STO 09 680 SIN 681 9 682 / 683 + 684 RCL 09 685 RCL 10 686 - 687 SIN 688 RCL 12 689 SIN 690 + 691 11 692 / 693 - 694 RCL 09 695 ST+ X 696 SIN |
697 7
698 / 699 + 700 RCL 09 701 3 702 * 703 SIN 704 RCL 09 705 RCL 10 706 + 707 SIN 708 + 709 15 710 / 711 + 712 RCL 09 713 4 714 * 715 SIN 716 25 717 / 718 + 719 STO 08 720 193.84 721 RCL 00 722 51135 723 * 724 - 725 STO 07 726 206 727 P-R 728 RCL 07 729 RCL 12 730 - 731 49 732 P-R 733 X<>Y 734 ST+ T 735 RDN 736 + 737 RCL 07 738 RCL 10 739 + 740 5 741 P-R 742 X<>Y 743 ST- T 744 RDN 745 - 746 RCL 07 747 RCL 10 748 - 749 3 750 P-R 751 X<>Y 752 ST- T 753 RDN 754 - 755 RCL 07 756 RCL 09 757 + 758 2 759 P-R 760 X<>Y 761 ST- T 762 RDN 763 - 764 RCL 07 765 RCL 09 766 - 767 2 768 SQRT 769 P-R 770 X<>Y 771 ST+ T 772 RDN 773 + 774 R-P 775 2 E3 776 / 777 STO 13 778 RCL 08 779 RCL Z 780 STO 02 781 - 782 1 783 P-R 784 RCL 13 785 - 786 R-P 787 CLX 788 SIGN 789 P-R 790 STO 15 791 X<>Y 792 RCL 13 793 ST* 15 794 ST- Z 795 ASIN 796 COS 797 * 798 X<>Y 799 R-P 800 X<>Y 801 ST+ 02 802 RCL 00 803 6510 804 * 805 221 806 - 807 12 808 P-R 809 1 810 ST+ Z 811 10^X 812 - 813 RCL 00 814 1412 815 * 816 8 817 + 818 3 819 P-R 820 X<>Y 821 ST+ T 822 RDN 823 + 824 R-P 825 X<>Y 826 RCL 02 827 + 828 SIN 829 * 830 X<> 02 831 2457 832 RCL 10 833 COS 834 9 835 * 836 - 837 1 838 RCL 15 839 - 840 * 841 XEQ 14 842 RCL 00 843 22576976 844 * 845 43.62 846 - 847 79 848 RCL 00 849 302 850 * 851 + 852 SIN 853 12 854 / 855 - 856 15.7 857 RCL 00 858 1401 859 * 860 STO 04 861 - 862 + 863 STO 10 864 SIN 865 11 866 SQRT 867 * 868 - 869 RCL 10 870 ST+ X 871 SIN |
872 17
873 / 874 + 875 STO 02 876 15 877 RCL 04 878 + 879 6 880 P-R 881 1 882 ST+ Z 883 CLX 884 11 885 - 886 R-P 887 X<>Y 888 RCL 02 889 + 890 SIN 891 * 892 X<> 02 893 2028 894 RCL 10 895 COS 896 59 897 * 898 + 899 XEQ 14 900 79690048 901 RCL 00 902 * 903 761 904 SQRT 905 - 906 51 907 RCL 00 908 27525 909 * 910 + 911 + 912 SIN 913 6 914 * 915 STO 02 916 CLX 917 875 918 XEQ 14 919 131534932 920 RCL 00 921 * 922 71.19 923 + 924 5 925 RCL 00 926 84305 927 * 928 - 929 + 930 SIN 931 4 932 / 933 - 934 626 935 XEQ 14 936 190697912 937 RCL 00 938 * 939 53.08 940 + 941 38.6 942 RCL 00 943 13968 944 * 945 - 946 STO 03 947 SIN 948 43.4 949 * 950 RCL 03 951 3 952 * 953 SIN 954 2 955 SQRT 956 / 957 + 958 STO 15 959 21 960 / 961 - 962 139 963 RCL 00 964 197809 965 * 966 + 967 + 968 SIN 969 16 970 * 971 STO 02 972 CLX 973 489 974 XEQ 14 975 262731903 976 RCL 00 977 * 978 11 979 + 980 RCL 00 981 88773 982 * 983 63 984 + 985 SIN 986 4 987 / 988 + 989 RCL 00 990 253657 991 * 992 44 993 - 994 SIN 995 5 996 / 997 + 998 49 999 RCL 00 1000 337962 1001 * 1002 - 1003 + 1004 SIN 1005 .55 1006 * 1007 - 1008 395 1009 XEQ 14 1010 RCL 15 1011 70.74 1012 - 1013 RCL 00 1014 381994499 1015 * 1016 + 1017 RCL 00 1018 E6 1019 STO 02 1020 772 1021 + 1022 * 1023 79 1024 - 1025 - 1026 STO 15 1027 SIN 1028 10 1029 LN 1030 * 1031 - 1032 227 1033 RCL 02 1034 460 1035 - 1036 RCL 00 1037 * 1038 + 1039 + 1040 SIN 1041 24 1042 * 1043 STO 02 1044 CLX 1045 308 1046 RCL 15 |
1047 COS
1048 6 1049 * 1050 + 1051 GTO 14 1052 LBL 13 1053 RCL 00 1054 21572831 1055 STO 15 1056 * 1057 30 1058 + 1059 COS 1060 RCL 15 1061 1760 1062 - 1063 RCL 00 1064 * 1065 STO 02 1066 21 1067 + 1068 COS 1069 ST+ X 1070 - 1071 4 1072 * 1073 X<> 02 1074 90.6 1075 + 1076 RCL 15 1077 60 1078 X^2 1079 - 1080 RCL 00 1081 * 1082 77 1083 + 1084 STO 15 1085 SIN 1086 .84 1087 * 1088 + 1089 2633 1090 RCL 15 1091 COS 1092 19 1093 * 1094 - 1095 XEQ 14 1096 RCL 00 1097 50317609 1098 STO 15 1099 7177 1100 + 1101 * 1102 46 1103 + 1104 COS 1105 PI 1106 * 1107 STO 02 1108 RCL 00 1109 RCL 15 1110 * 1111 217.13 1112 + 1113 STO 13 1114 RCL 15 1115 7127 1116 - 1117 RCL 00 1118 * 1119 55 1120 - 1121 STO 14 1122 SIN 1123 6 1124 / 1125 + 1126 RCL 15 1127 1840 1128 - 1129 RCL 00 1130 * 1131 23 1132 + 1133 SIN 1134 11 1135 / 1136 - 1137 1497 1138 RCL 14 1139 COS 1140 ST+ X 1141 - 1142 XEQ 14 1143 RCL 00 1144 101407355 1145 STO 15 1146 * 1147 20 1148 - 1149 SIN 1150 8 1151 * 1152 STO 02 1153 RCL 15 1154 32631 1155 - 1156 RCL 00 1157 * 1158 184.3 1159 + 1160 ST- 13 1161 RCL 13 1162 ST+ X 1163 STO 13 1164 SIN 1165 6 1166 % 1167 + 1168 - 1169 939 1170 RCL 13 1171 ST+ 13 1172 COS 1173 9 1174 * 1175 - 1176 XEQ 14 1177 RCL 00 1178 203488956 1179 * 1180 61.37 1181 - 1182 RCL 13 1183 SIN 1184 .47 1185 * 1186 - 1187 590 1188 RCL 13 1189 COS 1190 6 1191 SQRT 1192 * 1193 - 1194 LBL 14 1195 E2 1196 / 1197 ST* 02 1198 X<>Y 1199 RCL 01 1200 + 1201 X<>Y 1202 P-R 1203 X>0? 1204 SF IND M 1205 RCL O 1206 * 1207 ENTER 1208 CLX 1209 X<> 02 1210 RCL N 1211 * 1212 + 1213 RCL M 1214 ST+ X 1215 RDN 1216 STO IND T 1217 DSE T 1218 X<>Y 1219 STO IND T 1220 DSE M 1221 END |
( 2020 bytes / SIZE 016 )
-------------------------------------------------------------------------EPH---------------------------------------------------------------------------
| STACK | INPUTS | OUTPUTS |
| Z | / | distance to the earth ( AU ) |
| Y | / | geocentric latitude ( deg ) |
| X | / | geocentric longitude ( deg ) |
Example: Calculate the position of the Sun
& the major planets on 2020/07/16 at 0h TT
7502 ENTER^ 36525 / STO 00
• the Sun XEQ "EPH"
or XEQ 10 >>>> Long = 113°942
= R03
R01 = X = -0.41247
RDN Lat = 0
= R04 and
R02 = Y = 0.92896
RDN Dist = 1.01641 AU
= R05
• Mercury R/S or
XEQ 01 >>>> Long = 96°092
= R03
R06 = -31°948 = L
RDN Lat = -3°790
= R04 and
R07 = -6°910 = B
RDN Dist = 0.7253 AU
= R05
R08 = 0.3985 AU = R
• Venus
R/S or XEQ 02 >>>> Long
= 72°336
= R03
R06 = -39°509
RDN Lat = -4°515
= R04 and
R07 = -3°042
RDN Dist = 0.4910 AU
= R05
R08 = 0.7281 AU
• Mars
R/S or XEQ 04 >>>>
Long = 10°297
= R03
R06 = -35°263
RDN Lat = -3°495
= R04 and
R07 = -1°843
RDN Dist = 0.7302 AU
= R05
R08 = 1.3841 AU
• Jupiter R/S
or XEQ 05 >>>> Long =
-67°891
= R03
R06 = -67°529
RDN Lat = -0.332
= R04 and
R07 = -0°266
RDN Dist = 4.141 AU
= R05
R08 = 5.157 AU
• Saturn R/S
or XEQ 06 >>>> Long = -61°010
= R03
R06 = -61°523
RDN Lat = -0°228
= R04 and
R07 = -0°205
RDN Dist = 8.985 AU
= R05
R08 = 9.998 AU
• Uranus R/S or
XEQ 07 >>>> Long =
40°330
= R03
R06 = 37°505
RDN Lat = -0°444
= R04 and
R07 = -0°450
RDN Dist = 20.051 AU
= R05
R08 = 19.788 AU
• Neptune R/S or XEQ
08 >>>> Long = -9°164
= R03
R06 = -10°795
RDN Lat = -1°075
= R04 and
R07 = -1°054
RDN Dist = 29.353 AU
= R05
R08 = 29.920 AU
--------------------------------------------------------------------------STL----------------------------------------------------------------------------
| STACK | INPUTS | OUTPUTS |
| Y | / | y1 |
| X | / | x1 |
Execution time = 74s if CF
10 ( 4 Moons of Jupiter )
Execution time = 111s if SF 10
( 7 Moons of Saturn )
Example: On 2004/12/31 at 0h
TT
• CF 10 JUPITER
1826 ENTER^ 36525 / STO 00
XEQ "STL" >>>> x1 = -4.930 X<>Y y1 = 0.155 and in registers R01 thru R08:
Io - Europa - Ganymede - Callisto
x1 = -4.930 x2
= -4.831 x3
= -14.514 x4
= -8.546
y1 = 0.155
y2 = -0.307
y3 = -0.203
y4 = -1.077
-Flag F01 is set: Io is closer to the Earth than Jupiter.
• SF 10 SATURN
1826 ENTER^ 36525 / STO 00
XEQ "STL" >>>> x1 = -0.287 X<>Y y1 = 1.169 and in registers R01 thru R14:
Mimas - Enceladus - Tethys - Dione - Rhea - Titan - Hyperion
x1 = -0.287 x2
= 3.911 x3
= 0.781 x4
= -0.104 x5 = -8.730
x6 = 3.579
x7 = 21.822
y1 = 1.169
y2 = -0.213
y3 = 1.777
y4 = 2.397 y5
= 0.254 y6
= 7.335 y7
= 3.646
-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 HP41 must be in DEG mode.
-"STL" uses the synthetic registers M N O to minimize the number of
data registers.
-But M N O might be replaced by R16-R17-R18.
-The first line may also be deleted to save a few bytes.
-If you have a TIME module, you could add HR 24
/ X<>Y 1.012 DDAYS - 36525
/ STO 00 after line 02
-In this case, place the date in Y-register & the time in X-register
before executing "EPH" or "STL"