Overview
1°) Sun+Moon+Planets
2°) The Moon ( better precision )
3°) Sun+Planets ( better precision
)
-The following program calculates the geocentric and heliocentric longitudes
and latitudes of the Sun, the Moon and the major planets,
including Pluto & Xena ( Lilah or Eris or more exactly:
Asteroid
136199 Eris (2003 UB313) )
-They are referred to the mean equinox of the date.
-For the Sun and the planets ( except Pluto & Xena ), truncated
series from the VSOP87 theory are used,
with improvements from the new theories VSOP09 & TOP10 for
Uranus and Neptune.
-The coordinates of Pluto & Xena are obtained by a least-squares
fit of DE406, thanks to my HP48.
-For the Moon, cf "Astronomical Algorithms".
-Accuracy is not so good as that of "Astronomical Ephemeris(I)" - more
terms have been neglected - but the whole program is shorter.
-The errors can reach 1 arcminute in the heliocentric longitude in
the 1st program, perhaps 0°012 in paragraphs 2 & 3.
-The results are valid between 1000 and 3000 for the Sun, the Moon,
Mercury, Venus and Mars.
-Over the time-span [1700-2300] for Jupiter, Saturn, Uranus and Neptune.
-[1880-2100] for Pluto and [1900-2100] for the "tenth planet" ( dwarf
planet )
• PLUTO
L = 238°927 + 1465°671 T
i = 17°140
a = 39.489
omegabar = -135°925 + 13°971 T
e = 0.249
OMEGA = omegabar + 246°232
-After solving Kepler's equation with these orbital elements, the following corrections are added:
dL = 0
max error ~ 0°0153
dB = -0°004 + 0°086 T
max error ~ 0°0066
between 1880 and 2100
dR = -0.001 + 0.021 T
max error ~ 0.011
• XENA
L = 20°862 + 655.265 T
i = 43°867
a = 68.049
omegabar = OMEGA + 151.210
e = 0.43364
OMEGA = 36.039 + 13.970 T
-After solving Kepler's equation with these orbital elements, the following corrections are added:
dL = 0°014 - 1°175 T + 3°080 T^2
max error ~ 0°0067
dB = -0°124 T + 1°358 T^2 + 26°587 T^3
max error ~ 0°0032
between 1900 and 2100
dR = 0.008 - 0.960 T - 11.605 T^2
max error ~ 0.010
-For these 2 "Plutinos", "SUN" may probably be used a few years outside
the intervals, but not many years...
Data Registers
-Registers R00 thru R15 are used.
R00 = T = time since 2000/01/01 0h TT is to be initialized before
executing this program (
Unit = 1000 years = 365250 days )
R01, R02 contain the Sun's rectangular ecliptic coordinates.
So, first execute "SUN" if you want to get correct geocentric
coordinates.
R03 = geocentric longitude in decimal degrees
R04 = geocentric latitude ------------------
R05 = distance to the Earth in Astronomical Units ( parallax
in sexagesimal degree for the Moon )
R06 = heliocentric longitude in decimal degrees = L
R07 = heliocentric latitude ------------------- =
B
R08 = radius vector in Astronomical Units
= R
R09 = semi-major axis
R10 = eccentricity
R11 = inclination over the ecliptic.
R12 = mean longitude - 13.971 T
R13 = longitude of the perihelion
R14 = longitude of the ascending node
R03 R04 & R05 are also used for corrections in the longitude,
latitude and radius vector.
R15 = temporary data storage ( actually, R15 is not used
for the Sun, Mercury, Venus, Mars , Pluto and Xena )
>>>> The HP-41 must be set in DEG mode.
1°) Sun + Moon + Planets
| 01 LBL "SUN"
02 1 03 STO 09 04 RCL 00 05 359993.727 06 RCL 00 07 33 08 / 09 + 10 * 11 80.026 12 - 13 STO 12 14 CLX 15 46 16 * 17 17195 18 + 19 * 20 77063 21 - 22 STO 13 23 RDN 24 CHS 25 42 26 - 27 * 28 1671 29 + 30 STO 10 31 CLST 32 STO 01 33 STO 02 34 STO 11 35 XEQ 13 36 RCL 05 37 P-R 38 STO 01 39 X<>Y 40 STO 02 41 RCL 05 42 RCL 04 43 RCL 03 44 RTN 45 LBL 03 46 RCL 00 47 359990.5 48 RCL 00 49 65 50 / 51 - 52 * 53 2.96 54 - 55 STO 12 56 CLX 57 19 58 * 59 CHS 60 445267111 61 + 62 % 63 68.25 64 - 65 STO 13 66 ST+ X 67 STO 14 68 CLX 69 87 70 * 71 477198868 72 + 73 % 74 128.43 75 + 76 STO 07 77 ST+ X 78 STO 08 79 CLX 80 37 81 * 82 483202018 83 - 84 % 85 86.66 86 - 87 STO 09 88 ST+ X 89 STO 06 90 6036 91 RCL 14 92 RCL 07 93 - 94 STO 03 95 COS 96 58 97 * 98 - 99 RCL 14 100 COS 101 46 102 * 103 - 104 RCL 08 105 COS 106 9 107 * 108 - 109 RCL 14 110 RCL 08 111 - 112 STO 15 113 COS 114 RCL 07 115 COS 116 82 117 * 118 - 119 4 120 * 121 + 122 RCL 14 123 RCL 12 124 - 125 STO 11 126 COS 127 RCL 07 128 RCL 14 129 + 130 STO 10 131 COS 132 + 133 3 134 * 135 - 136 1 137 % 138 1/X 139 ASIN 140 HMS 141 STO 05 142 RCL 07 143 RCL 09 144 - 145 SIN 146 281 147 * 148 RCL 07 149 RCL 09 150 + 151 SIN 152 278 153 * 154 + 155 RCL 09 156 RCL 14 157 + 158 SIN 159 173 160 * 161 + 162 RCL 03 163 RCL 09 164 - 165 SIN 166 55 167 * 168 + 169 RCL 03 170 RCL 09 171 + 172 SIN 173 46 174 * 175 + 176 RCL 14 177 RCL 09 178 - 179 SIN 180 33 181 * 182 + 183 RCL 08 184 RCL 09 185 - 186 SIN 187 17 188 * 189 + 190 RCL 09 191 RCL 10 192 + 193 SIN 194 RCL 08 195 RCL 09 196 + 197 SIN 198 + 199 9 200 * 201 + 202 RCL 09 203 RCL 11 204 + 205 SIN 206 RCL 09 207 SIN 208 641 209 * 210 - 211 8 212 * 213 + 214 STO 04 215 RCL 07 216 SIN 217 6289 218 * 219 RCL 14 220 SIN 221 658 222 * 223 + 224 RCL 08 225 SIN 226 214 227 * 228 + 229 RCL 06 230 SIN 231 114 232 * 233 + 234 RCL 15 235 SIN 236 59 237 * 238 + 239 RCL 03 240 RCL 12 241 - |
242 SIN
243 57 244 * 245 + 246 RCL 10 247 SIN 248 53 249 * 250 + 251 RCL 11 252 SIN 253 46 254 * 255 + 256 RCL 12 257 RCL 07 258 - 259 SIN 260 41 261 * 262 - 263 RCL 03 264 SIN 265 98 266 * 267 RCL 07 268 RCL 06 269 - 270 SIN 271 - 272 13 273 * 274 + 275 RCL 06 276 RCL 07 277 + 278 SIN 279 RCL 14 280 ST+ X 281 RCL 07 282 - 283 SIN 284 + 285 11 286 * 287 + 288 RCL 03 289 ST+ X 290 SIN 291 9 292 * 293 + 294 RCL 03 295 RCL 12 296 + 297 SIN 298 8 299 * 300 - 301 RCL 12 302 RCL 14 303 + 304 SIN 305 7 306 * 307 - 308 RCL 12 309 SIN 310 RCL 00 311 37 312 - 313 * 314 RCL 13 315 SIN 316 7 317 * 318 - 319 RCL 07 320 RCL 12 321 + 322 SIN 323 6 324 * 325 - 326 RCL 06 327 RCL 14 328 + 329 SIN 330 3 331 * 332 + 333 RCL 07 334 RCL 08 335 + 336 SIN 337 ST+ X 338 + 339 5 340 * 341 + 342 RCL 00 343 ST+ X 344 158 345 - 346 RCL 00 347 * 348 4812678812 349 + 350 RCL 00 351 * 352 211728 353 + 354 + 355 E3 356 ST/ 04 357 / 358 360 359 MOD 360 STO 03 361 RCL 05 362 RCL 04 363 RCL 03 364 RTN 365 LBL 01 366 .3871 367 STO 09 368 RCL 00 369 1494726.751 370 RCL 00 371 33 372 / 373 + 374 * 375 250.205 376 + 377 STO 12 378 CLX 379 20 380 * 381 20563 382 + 383 STO 10 384 CLX 385 18 386 * 387 7005 388 + 389 STO 11 390 CLX 391 30 392 * 393 15564 394 + 395 * 396 77456 397 + 398 STO 13 399 CLX 400 18 401 * 402 11861 403 + 404 * 405 48331 406 XEQ 13 407 RTN 408 LBL 02 409 .7233 410 STO 09 411 RCL 00 412 585178.159 413 RCL 00 414 32 415 / 416 + 417 * 418 181.179 419 + 420 STO 12 421 CLX 422 48 423 * 424 CHS 425 677 426 + 427 STO 10 428 CLX 429 10 430 * 431 3395 432 + 433 STO 11 434 CLX 435 108 436 * 437 CHS 438 14022 439 + 440 * 441 131564 442 + 443 STO 13 444 CLX 445 41 446 * 447 9010 448 + 449 * 450 76680 451 XEQ 13 452 RTN 453 LBL 04 454 RCL 00 455 202 456 * 457 18 458 - 459 COS 460 16 461 * 462 161054 463 RCL 00 464 * 465 48 466 + 467 COS 468 130705 469 RCL 00 470 * 471 12 472 - 473 COS 474 - 475 44 476 SQRT 477 * 478 + 479 3 480 - 481 RCL 00 482 322108 |
483 *
484 COS 485 5 486 * 487 - 488 STO 03 489 CLX 490 STO 04 491 STO 05 492 1.524 493 STO 09 494 RCL 00 495 191402.993 496 RCL 00 497 32 498 / 499 + 500 * 501 4.829 502 - 503 STO 12 504 CLX 505 90 506 * 507 9340 508 + 509 STO 10 510 CLX 511 6 512 * 513 CHS 514 1850 515 + 516 STO 11 517 CLX 518 13 519 * 520 18410 521 + 522 * 523 23940 524 - 525 STO 13 526 CLX 527 7720 528 * 529 49558 530 XEQ 14 531 RTN 532 LBL 05 533 XEQ 12 534 RCL 06 535 RCL 11 536 + 537 STO 12 538 47 539 - 540 COS 541 12 542 * 543 RCL 11 544 15 545 + 546 COS 547 131 548 * 549 + 550 RCL 00 551 * 552 RCL 08 553 RCL 10 554 + 555 21 556 + 557 SIN 558 4 559 * 560 + 561 RCL 06 562 RCL 10 563 + 564 28 565 + 566 COS 567 RCL 10 568 RCL 07 569 - 570 25 571 + 572 COS 573 + 574 5 575 * 576 - 577 RCL 11 578 RCL 06 579 - 580 78 581 + 582 COS 583 16 584 * 585 - 586 RCL 08 587 73 588 + 589 COS 590 RCL 10 591 49 592 - 593 COS 594 - 595 509 596 SQRT 597 * 598 + 599 RCL 09 600 16 601 + 602 COS 603 37 604 * 605 - 606 RCL 12 607 29 608 + 609 COS 610 42 611 * 612 - 613 RCL 08 614 ST+ X 615 57 616 + 617 COS 618 56 619 * 620 - 621 RCL 11 622 7.3 623 + 624 SIN 625 329 626 * 627 + 628 STO 03 629 RCL 12 630 27 631 + 632 COS 633 5 634 * 635 CHS 636 STO 04 637 CLX 638 STO 05 639 RCL 00 640 1303 641 RCL 00 642 55 643 * 644 - 645 STO 11 646 CLX 647 45 648 / 649 * 650 RCL 06 651 + 652 34.31 653 + 654 STO 12 655 CLX 656 5.203 657 STO 09 658 INT 659 CHS 660 * 661 163 662 + 663 * 664 4849 665 + 666 STO 10 667 CLX 668 103 669 * 670 16126 671 + 672 * 673 14331 674 + 675 STO 13 676 CLX 677 40 678 * 679 10210 680 + 681 * 682 100464 683 XEQ 14 684 RTN 685 LBL 06 686 XEQ 12 687 RCL 11 688 68 689 - 690 COS 691 67 692 * 693 RCL 00 694 * 695 RCL 09 696 73 697 + 698 COS 699 11 700 * 701 + 702 RCL 11 703 RCL 07 704 - 705 STO 13 706 63 707 + 708 COS 709 23 710 * 711 - 712 RCL 09 713 ST+ X 714 STO 12 715 50 716 - 717 COS 718 62 719 * 720 - 721 RCL 11 722 14.7 723 + |
724 COS
725 323 726 * 727 - 728 RCL 00 729 * 730 RCL 03 731 RCL 07 732 + 733 COS 734 6 735 * 736 - 737 RCL 03 738 17 739 + 740 COS 741 7 742 * 743 + 744 RCL 11 745 RCL 03 746 - 747 SIN 748 RCL 11 749 ST+ X 750 15 751 + 752 SIN 753 + 754 8 755 * 756 - 757 RCL 08 758 ST+ X 759 54 760 + 761 COS 762 RCL 08 763 29 764 - 765 COS 766 + 767 RCL 10 768 25 769 + 770 COS 771 + 772 9 773 * 774 + 775 RCL 13 776 2 777 / 778 SIN 779 14 780 * 781 - 782 RCL 13 783 40 784 - 785 COS 786 45 787 * 788 - 789 RCL 09 790 14 791 + 792 COS 793 118 794 * 795 + 796 RCL 12 797 30 798 + 799 COS 800 228 801 * 802 + 803 RCL 11 804 7.2 805 + 806 SIN 807 810 808 * 809 - 810 STO 03 811 RCL 10 812 28 813 - 814 COS 815 6 816 * 817 RCL 12 818 33 819 + 820 COS 821 20 822 * 823 + 824 RCL 13 825 20 826 - 827 COS 828 18 829 * 830 - 831 STO 04 832 RCL 09 833 17 834 + 835 SIN 836 5 837 * 838 RCL 08 839 20 840 - 841 COS 842 8 843 * 844 + 845 RCL 12 846 60 847 - 848 COS 849 19 850 * 851 + 852 STO 05 853 9.543 854 STO 09 855 RCL 00 856 347 857 RCL 00 858 6 859 * 860 + 861 * 862 CHS 863 5553 864 + 865 STO 10 866 RDN 867 X^2 868 19 869 / 870 RCL 07 871 + 872 50.061 873 + 874 STO 12 875 CLX 876 37 877 * 878 CHS 879 2489 880 + 881 STO 11 882 CLX 883 84 884 * 885 19638 886 + 887 * 888 93057 889 + 890 STO 13 891 CLX 892 12 893 * 894 CHS 895 8771 896 + 897 * 898 113666 899 XEQ 14 900 RTN 901 LBL 07 902 XEQ 12 903 RCL 05 904 8 905 - 906 SIN 907 14 908 * 909 RCL 00 910 * 911 RCL 14 912 RCL 15 913 + 914 60 915 - 916 COS 917 4 918 * 919 + 920 RCL 07 921 RCL 12 922 - 923 28 924 + 925 COS 926 RCL 15 927 RCL 13 928 - 929 11 930 - 931 COS 932 - 933 6 934 * 935 + 936 RCL 11 937 RCL 03 938 - 939 SIN 940 7 941 * 942 + 943 RCL 14 944 9 945 + 946 SIN 947 10 948 * 949 - 950 RCL 12 951 RCL 15 952 + 953 70 954 + 955 COS 956 12 957 * 958 - 959 RCL 06 960 RCL 12 961 - 962 10 963 - 964 COS |
965 RCL 04
966 RCL 12 967 + 968 COS 969 - 970 15 971 * 972 + 973 RCL 03 974 17 975 + 976 COS 977 RCL 04 978 51 979 + 980 COS 981 + 982 35 983 * 984 - 985 RCL 13 986 ST+ X 987 STO 04 988 11 989 - 990 COS 991 RCL 03 992 RCL 12 993 + 994 51 995 - 996 COS 997 + 998 40 999 * 1000 + 1001 RCL 15 1002 71 1003 - 1004 COS 1005 209 1006 * 1007 - 1008 RCL 05 1009 27.8 1010 - 1011 COS 1012 858 1013 * 1014 - 1015 STO 03 1016 RCL 15 1017 33 1018 + 1019 COS 1020 RCL 04 1021 SIN 1022 - 1023 6 1024 * 1025 STO 04 1026 RCL 15 1027 19 1028 + 1029 COS 1030 34 1031 * 1032 STO 05 1033 19.192 1034 STO 09 1035 RCL 00 1036 8 1037 RCL 00 1038 4 1039 * 1040 + 1041 * 1042 773 1043 + 1044 STO 11 1045 CLX 1046 27 1047 * 1048 CHS 1049 4630 1050 + 1051 STO 10 1052 RDN 1053 X^2 1054 33 1055 / 1056 45.955 1057 - 1058 ST+ 12 1059 CLX 1060 21 1061 * 1062 14863 1063 + 1064 * 1065 172993 1066 + 1067 STO 13 1068 CLX 1069 18 1070 * 1071 134 1072 + 1073 * 1074 5211 1075 + 1076 * 1077 74005 1078 XEQ 14 1079 RTN 1080 LBL 08 1081 XEQ 12 1082 RCL 06 1083 RCL 13 1084 - 1085 COS 1086 RCL 05 1087 SIN 1088 RCL 00 1089 * 1090 - 1091 9 1092 * 1093 RCL 07 1094 RCL 13 1095 - 1096 16 1097 + 1098 COS 1099 RCL 05 1100 RCL 13 1101 - 1102 STO 06 1103 13 1104 - 1105 SIN 1106 - 1107 5 1108 * 1109 + 1110 RCL 15 1111 RCL 13 1112 - 1113 11 1114 - 1115 COS 1116 22 1117 * 1118 + 1119 RCL 04 1120 50 1121 + 1122 COS 1123 24 1124 * 1125 + 1126 RCL 14 1127 7 1128 + 1129 SIN 1130 71 1131 * 1132 + 1133 RCL 05 1134 27.8 1135 - 1136 COS 1137 584 1138 * 1139 + 1140 STO 03 1141 RCL 14 1142 54 1143 + 1144 SIN 1145 RCL 06 1146 21 1147 - 1148 COS 1149 + 1150 CHS 1151 9 1152 * 1153 STO 04 1154 RCL 14 1155 COS 1156 17 1157 * 1158 CHS 1159 STO 05 1160 30.07 1161 STO 09 1162 RCL 00 1163 1770 1164 RCL 00 1165 93 1166 * 1167 - 1168 STO 11 1169 RDN 1170 X^2 1171 32 1172 / 1173 RCL 13 1174 + 1175 55.654 1176 - 1177 STO 12 1178 CLX 1179 6 1180 * 1181 899 1182 + 1183 STO 10 1184 CLX 1185 38 1186 * 1187 14263 1188 + 1189 * 1190 48124 1191 + 1192 STO 13 1193 CLX 1194 26 1195 * 1196 11022 1197 + 1198 * 1199 131784 1200 XEQ 14 1201 RTN 1202 LBL 09 1203 CLX 1204 STO 03 1205 RCL 00 |
1206 86
1207 * 1208 4 1209 - 1210 STO 04 1211 RCL 00 1212 21 1213 * 1214 STO 05 1215 39.489 1216 STO 09 1217 24900 1218 STO 10 1219 17140 1220 STO 11 1221 RCL 00 1222 1451.7 1223 * 1224 238.927 1225 + 1226 STO 12 1227 RCL 00 1228 13971 1229 * 1230 135925 1231 - 1232 STO 13 1233 246232 1234 XEQ 14 1235 RTN 1236 LBL 10 1237 RCL 00 1238 1358 1239 RCL 00 1240 26587 1241 * 1242 + 1243 * 1244 124 1245 - 1246 * 1247 STO 04 1248 CLX 1249 3080 1250 * 1251 1175 1252 - 1253 * 1254 14 1255 + 1256 STO 03 1257 CLX 1258 11605 1259 * 1260 CHS 1261 960 1262 - 1263 * 1264 8 1265 + 1266 STO 05 1267 CLX 1268 641.294 1269 * 1270 20.862 1271 + 1272 STO 12 1273 68.049 1274 STO 09 1275 43364 1276 STO 10 1277 43867 1278 STO 11 1279 RCL 00 1280 13970 1281 * 1282 187249 1283 + 1284 STO 13 1285 151210 1286 CHS 1287 GTO 14 1288 LBL 12 1289 30349.057 1290 RCL 00 1291 * 1292 STO 06 1293 12221.14 1294 LASTX 1295 * 1296 STO 07 1297 - 1298 STO 08 1299 LASTX 1300 - 1301 STO 09 1302 RCL 08 1303 + 1304 STO 10 1305 RCL 07 1306 ST+ X 1307 - 1308 STO 11 1309 4284.673 1310 RCL 00 1311 * 1312 STO 12 1313 2184.856 1314 LASTX 1315 * 1316 STO 13 1317 - 1318 STO 14 1319 ST+ X 1320 STO 15 1321 RCL 12 1322 - 1323 STO 05 1324 ST+ X 1325 STO 04 1326 RCL 07 1327 RCL 12 1328 3 1329 * 1330 - 1331 STO 03 1332 RTN 1333 LBL 13 1334 0 1335 STO 03 1336 STO 04 1337 STO 05 1338 RDN 1339 LBL 14 1340 + 1341 E3 1342 ST/ 03 1343 ST/ 04 1344 ST/ 05 1345 ST/ 11 1346 ST/ 13 1347 / 1348 STO 14 1349 E5 1350 ST/ 10 1351 12 1352 STO 08 1353 RCL 12 1354 RCL 13 1355 - 1356 RCL 00 1357 13.971 1358 * 1359 + 1360 360 1361 MOD 1362 ENTER 1363 ENTER 1364 LBL 11 1365 SIN 1366 RCL 10 1367 R-D 1368 * 1369 + 1370 DSE 08 1371 GTO 11 1372 2 1373 / 1374 1 1375 RCL 10 1376 + 1377 1 1378 LASTX 1379 - 1380 / 1381 SQRT 1382 P-R 1383 LASTX 1384 / 1385 R-P 1386 RDN 1387 ST+ X 1388 1 1389 R^ 1390 ST+ X 1391 COS 1392 RCL 10 1393 * 1394 - 1395 RCL 09 1396 * 1397 RCL 05 1398 + 1399 STO 08 1400 CLX 1401 RCL 14 1402 - 1403 RCL 13 1404 + 1405 COS 1406 RCL 11 1407 LASTX 1408 SIN 1409 P-R 1410 X<>Y 1411 ASIN 1412 RCL 04 1413 + 1414 STO 07 1415 X<> Z 1416 R-P 1417 CLX 1418 RCL 14 1419 + 1420 RCL 03 1421 + 1422 STO 06 1423 RCL 08 1424 X<>Y 1425 RDN 1426 P-R 1427 R^ 1428 X<>Y 1429 P-R 1430 RCL 02 1431 ST+ Z 1432 CLX 1433 RCL 01 1434 + 1435 R-P 1436 X<>Y 1437 RDN 1438 R-P 1439 R^ 1440 X<>Y 1441 STO 05 1442 X<> Z 1443 STO 04 1444 X<>Y 1445 STO 03 1446 END |
( 2194 bytes / SIZE 016 )
| STACK | INPUTS | OUTPUTS |
| Z | / | distance to the earth ( AU )* |
| Y | / | geocentric latitude ( deg ) |
| X | / | geocentric longitude ( deg ) |
* parallax in ° ' " for the Moon
Example: T = 0.1
i-e 2100/01/01 0h TT
• XEQ "SUN" >>>>
Long = -79°389
= R03
R01 = X = 0.181078
RDN Lat = 0
= R04 and
R02 = Y = -0.966557
RDN Dist = 0.983372 AU
= R05
• the Moon R/S or XEQ
03 >>>> Long = 157°405
= R03
RDN Lat = 1°096
= R04
RDN Paral. = 0°59'01"
= R05
• Mercury R/S or
XEQ 01 >>>> Long = -71°982
= R03
R06 = -54°797 = L
RDN Lat = -2°113
= R04 and
R07 = -6°791 = B
RDN Dist = 1.38605 AU
= R05
R08 = 0.43213 AU = R
• Venus
R/S or XEQ 02 >>>> Long
= -39°924
= R03
R06 = 19°729
RDN Lat = -1°852
= R04 and
R07 = -2°876
RDN Dist = 1.1257 AU
= R05
R08 = 0.7252 AU
• Mars
R/S or XEQ 04 >>>>
Long = 29°544
= R03
R06 = 67°576
RDN Lat = 0°950
= R04 and
R07 = 0°548
RDN Dist = 0.870 AU
= R05
R08 = 1.510 AU
• Jupiter R/S
or XEQ 05 >>>> Long =
-158°790
= R03
R06 = 191°001
RDN Lat = 1°279
= R04 and
R07 = 1°301
RDN Dist = 5.550 AU
= R05
R08 = 5.455 AU
• Saturn R/S
or XEQ 06 >>>> Long = -154°359
= R03
R06 = 199°998
RDN Lat = 2°422
= R04 and
R07 = 2°474
RDN Dist = 9.875 AU
= R05
R08 = 9.667 AU
• Uranus R/S or
XEQ 07 >>>> Long =
17°739
= R03
R06 = 20°538
RDN Lat = -0°630
= R04 and
R07 = -0°625
RDN Dist = 19.835 AU
= R05
R08 = 19.981 AU
• Neptune R/S or XEQ
08 >>>> Long = 167°292
= R03
R06 = 165°578
RDN Lat = 0°965
= R04 and
R07 = 0°952
RDN Dist = 29.797 AU
= R05
R08 = 30.200 AU
• Pluto R/S
or XEQ 09 >>>> Long
= 32°398
= R03
R06 = 33°515
RDN Lat = -16°921
= R04 and
R07 = -16°793
RDN Dist = 48.583 AU
= R05
R08 = 48.941 AU
• Xena R/S
or XEQ 10 >>>> Long
= 43°192
= R03
R06 = 43°761
RDN Lat = 6°180
= R04 and
R07 = 6°141
RDN Dist = 83.419 AU
= R05
R08 = 83.950 AU
Notes:
-As you can see, there is not enough room to execute SIZE 016 !!
-This is not a problem if you have an HEPAX module or a CLONIX/NOVRAM.
( cf http://www.clonix41.org
)
-Otherwise, the program may be split in 2 parts:
-For example, since the Moon's coordinates are computed without any
XEQ, lines 45 to 364 may form a single program called, say LBL "MO"
which can be stored in X-memory.
-To execute it without using GETP, place it as the first file
in X-memory and use the following method,
given by Keith Jarett in "HP41 Extended Functions Made Easy"
| 01 LBL "EXM"
02 190 03 CLA 04 XTOA 05 RDN 06 ASTO b 07 END |
-Unfortunately, this method cannot be employed for the whole program
because it must lie enterily
within the Extended Functions/Memory module, so no more than
124 registers.
-A few lines may be added after line 01 of this "SUN" program to allow
execution from another program, for example: GTO IND X
LBL 00
-Then place 0 in X-register to compute the position of the Sun, 1 for
Mercury, ..... , 10 for Xena/Lilah/Eris
2°) The Moon
-In this variant, the periodic terms whose amplitude is > 0°003
are taken into account.
| 01 LBL "MO"
02 RCL 00 03 359990.5 04 RCL 00 05 65 06 / 07 - 08 * 09 2.96 10 - 11 STO 12 12 CLX 13 19 14 * 15 CHS 16 445267111 17 + 18 % 19 68.25 20 - 21 STO 13 22 ST+ X 23 STO 14 24 CLX 25 87 26 * 27 477198868 28 + 29 % 30 128.43 31 + 32 STO 07 33 ST+ X 34 STO 08 35 CLX 36 37 37 * 38 483202018 39 - 40 % 41 86.66 42 - 43 STO 09 44 ST+ X 45 STO 06 46 6036 47 RCL 14 48 RCL 07 49 - 50 STO 03 51 COS 52 58 53 * 54 - 55 RCL 14 56 COS 57 46 58 * 59 - 60 RCL 08 61 COS 62 9 63 * 64 - 65 RCL 14 66 RCL 08 |
67 -
68 STO 15 69 COS 70 RCL 07 71 COS 72 82 73 * 74 - 75 4 76 * 77 + 78 RCL 14 79 RCL 12 80 - 81 STO 11 82 COS 83 RCL 07 84 RCL 14 85 + 86 STO 10 87 COS 88 + 89 3 90 * 91 - 92 1 93 % 94 1/X 95 ASIN 96 HMS 97 STO 05 98 RCL 07 99 RCL 09 100 - 101 SIN 102 281 103 * 104 RCL 07 105 RCL 09 106 + 107 SIN 108 278 109 * 110 + 111 RCL 09 112 RCL 14 113 + 114 SIN 115 173 116 * 117 + 118 RCL 03 119 RCL 09 120 - 121 SIN 122 55 123 * 124 + 125 RCL 03 126 RCL 09 127 + 128 SIN 129 46 130 * 131 + 132 RCL 14 |
133 RCL 09
134 - 135 SIN 136 33 137 * 138 + 139 RCL 08 140 RCL 09 141 - 142 SIN 143 17 144 * 145 + 146 RCL 09 147 RCL 10 148 + 149 SIN 150 RCL 08 151 RCL 09 152 + 153 SIN 154 + 155 9 156 * 157 + 158 RCL 09 159 RCL 11 160 + 161 SIN 162 RCL 09 163 SIN 164 641 165 * 166 - 167 8 168 * 169 + 170 RCL 15 171 RCL 09 172 + 173 SIN 174 RCL 10 175 RCL 09 176 - 177 SIN 178 + 179 4 180 * 181 + 182 RCL 12 183 RCL 14 184 + 185 RCL 09 186 + 187 SIN 188 PI 189 * 190 - 191 STO 04 192 RCL 07 193 SIN 194 6289 195 * 196 RCL 14 197 SIN 198 658 |
199 *
200 + 201 RCL 08 202 SIN 203 214 204 * 205 + 206 RCL 06 207 SIN 208 114 209 * 210 + 211 RCL 15 212 SIN 213 59 214 * 215 + 216 RCL 03 217 RCL 12 218 - 219 SIN 220 57 221 * 222 + 223 RCL 10 224 SIN 225 53 226 * 227 + 228 RCL 11 229 SIN 230 46 231 * 232 + 233 RCL 12 234 RCL 07 235 - 236 SIN 237 41 238 * 239 - 240 RCL 03 241 SIN 242 98 243 * 244 RCL 07 245 RCL 06 246 - 247 SIN 248 - 249 13 250 * 251 + 252 RCL 06 253 RCL 07 254 + 255 SIN 256 RCL 14 257 ST+ X 258 RCL 07 259 - 260 SIN 261 + 262 11 263 * 264 + |
265 RCL 03
266 ST+ X 267 SIN 268 9 269 * 270 + 271 RCL 03 272 RCL 12 273 + 274 SIN 275 8 276 * 277 - 278 RCL 12 279 RCL 14 280 + 281 SIN 282 7 283 * 284 - 285 RCL 12 286 SIN 287 RCL 00 288 37 289 - 290 * 291 RCL 13 292 SIN 293 7 294 * 295 - 296 RCL 07 297 RCL 12 298 + 299 SIN 300 6 301 * 302 - 303 RCL 06 304 RCL 14 305 + 306 SIN 307 3 308 * 309 + 310 RCL 07 311 RCL 08 312 + 313 SIN 314 ST+ X 315 + 316 RCL 13 317 RCL 07 318 - 319 SIN 320 - 321 RCL 12 322 RCL 13 323 + 324 SIN 325 + 326 5 327 * 328 + 329 RCL 10 330 RCL 12 |
331 -
332 SIN 333 RCL 08 334 RCL 14 335 + 336 SIN 337 + 338 RCL 14 339 ST+ X 340 SIN 341 + 342 RCL 03 343 RCL 08 344 - 345 SIN 346 + 347 RCL 00 348 23 349 * 350 1 351 - 352 R-D 353 SIN 354 - 355 4 356 * 357 + 358 RCL 12 359 RCL 08 360 - 361 SIN 362 RCL 03 363 RCL 06 364 - 365 SIN 366 + 367 3 368 * 369 - 370 RCL 00 371 ST+ X 372 158 373 - 374 RCL 00 375 * 376 4812678812 377 + 378 RCL 00 379 * 380 211728 381 + 382 + 383 E3 384 ST/ 04 385 / 386 360 387 MOD 388 STO 03 389 RCL 05 390 RCL 04 391 RCL 03 392 END |
( 515 bytes / SIZE 016 )
| STACK | INPUTS | OUTPUTS |
| Z | / | parallax ( ° ' " ) |
| Y | / | geocentric latitude ( deg ) |
| X | / | geocentric longitude ( deg ) |
Example: T = 0.1
i-e 2100/01/01 0h TT
XEQ "MO" >>>> Long = 157°398
= R03
RDN Lat = 1°096
= R04
RDN Paral. = 0°59'01"
= R05
3°) Sun + Planets
-Like for the Moon, the periodic terms whose amplitude is > 0°003
are taken into account + a few smaller terms here and there...
-For Pluto, the following correction to the heliocentric longitude
has also been added after solving Kepler's equation:
dL = 0°007 Cos ( 28897 T + 65 ) + 0°004 Cos ( 10769 T +76 )
-The maximum error in longitude for this planet is now 0°009 between
the years 1880 and 2110.
| 01 LBL "SUN"
02 1 03 STO 09 04 RCL 00 05 359993.727 06 RCL 00 07 33 08 / 09 + 10 * 11 80.026 12 - 13 STO 12 14 CLX 15 46 16 * 17 17195 18 + 19 * 20 77063 21 - 22 STO 13 23 RDN 24 CHS 25 42 26 - 27 * 28 1671 29 + 30 STO 10 31 CLX 32 STO 01 33 STO 02 34 STO 11 35 XEQ 13 36 RCL 05 37 P-R 38 STO 01 39 X<>Y 40 STO 02 41 RCL 05 42 RCL 04 43 RCL 03 44 RTN 45 LBL 01 46 .3871 47 STO 09 48 RCL 00 49 1494726.751 50 RCL 00 51 33 52 / 53 + 54 * 55 250.205 56 + 57 STO 12 58 CLX 59 20 60 * 61 20563 62 + 63 STO 10 64 CLX 65 18 66 * 67 7005 68 + 69 STO 11 70 CLX 71 30 72 * 73 15564 74 + 75 * 76 77456 77 + 78 STO 13 79 CLX 80 18 81 * 82 11861 83 + 84 * 85 48331 86 XEQ 13 87 RTN 88 LBL 02 89 .7233 90 STO 09 91 RCL 00 92 585178.159 93 RCL 00 94 32 95 / 96 + 97 * 98 181.179 99 + 100 STO 12 101 CLX 102 48 103 * 104 CHS 105 677 106 + 107 STO 10 108 CLX 109 10 110 * 111 3395 112 + 113 STO 11 114 CLX 115 108 116 * 117 CHS 118 14022 119 + 120 * 121 131564 122 + 123 STO 13 124 CLX 125 41 126 * 127 9010 128 + 129 * 130 76680 131 XEQ 13 132 RTN 133 LBL 04 134 RCL 00 135 202 136 * 137 18 138 - 139 COS 140 16 141 * 142 161054 143 RCL 00 144 * 145 48 146 + 147 COS 148 7 149 * 150 + 151 130705 152 RCL 00 153 * 154 12 155 - 156 COS 157 6 158 * 159 - 160 RCL 00 161 22812 162 * 163 21 164 + 165 COS 166 RCL 00 167 322108 168 * 169 11 170 + 171 COS 172 - 173 4 174 * 175 + 176 3 177 - 178 STO 03 179 CLX 180 STO 04 181 STO 05 182 1.524 183 STO 09 184 RCL 00 185 191402.993 186 RCL 00 187 32 188 / 189 + 190 * 191 4.829 192 - 193 STO 12 194 CLX 195 90 196 * 197 9340 198 + 199 STO 10 200 CLX 201 6 202 * 203 CHS 204 1850 205 + 206 STO 11 207 CLX 208 13 209 * 210 18410 211 + 212 * 213 23940 214 - 215 STO 13 216 CLX 217 7720 218 * 219 49558 220 XEQ 14 221 RTN 222 LBL 05 223 XEQ 12 224 RCL 06 225 RCL 11 226 + 227 STO 12 |
228 47
229 - 230 COS 231 12 232 * 233 RCL 11 234 22 235 + 236 SIN 237 27 238 * 239 RCL 00 240 * 241 - 242 RCL 11 243 15 244 + 245 COS 246 131 247 * 248 + 249 RCL 00 250 * 251 RCL 06 252 39 253 - 254 COS 255 2 256 SQRT 257 * 258 + 259 RCL 11 260 ST+ X 261 75 262 - 263 COS 264 RCL 10 265 RCL 08 266 ST+ X 267 STO 13 268 + 269 60 270 + 271 COS 272 - 273 RCL 06 274 RCL 13 275 + 276 79 277 + 278 COS 279 - 280 RCL 10 281 RCL 06 282 - 283 76 284 - 285 COS 286 + 287 RCL 11 288 RCL 03 289 - 290 SIN 291 + 292 3 293 * 294 + 295 RCL 07 296 COS 297 RCL 08 298 RCL 10 299 + 300 21 301 + 302 SIN 303 + 304 4 305 * 306 + 307 RCL 06 308 RCL 10 309 + 310 28 311 + 312 COS 313 RCL 10 314 RCL 07 315 - 316 25 317 + 318 COS 319 + 320 5 321 * 322 - 323 RCL 11 324 RCL 06 325 - 326 STO 14 327 78 328 + 329 COS 330 16 331 * 332 - 333 RCL 08 334 73 335 + 336 COS 337 22 338 * 339 + 340 RCL 10 341 49 342 - 343 COS 344 23 345 * 346 - 347 RCL 09 348 15 349 + 350 COS 351 37 352 * 353 - 354 RCL 12 355 29 356 + 357 COS 358 42 359 * 360 - 361 RCL 13 362 57 363 + 364 COS 365 56 366 * 367 - 368 RCL 11 369 7.3 370 + 371 SIN 372 329 373 * 374 + 375 STO 03 376 RCL 14 377 18 378 - 379 COS 380 RCL 12 381 27 382 + 383 COS 384 - 385 17 386 SQRT 387 * 388 STO 04 389 RCL 13 390 147 391 + 392 COS 393 3 394 * 395 STO 05 396 RCL 00 397 1303 398 RCL 00 399 55 400 * 401 - 402 STO 11 403 CLX 404 45 405 / 406 * 407 RCL 06 408 + 409 34.31 410 + 411 STO 12 412 CLX 413 5.203 414 STO 09 415 INT 416 CHS 417 * 418 163 419 + 420 * 421 4849 422 + 423 STO 10 424 CLX 425 103 426 * 427 16126 428 + 429 * 430 14331 431 + 432 STO 13 433 CLX 434 40 435 * 436 10210 437 + 438 * 439 100464 440 XEQ 14 441 RTN 442 LBL 06 443 XEQ 12 444 RCL 11 445 68 446 - 447 COS 448 67 449 * 450 RCL 00 451 * 452 RCL 09 453 73 454 + |
455 COS
456 11 457 * 458 + 459 RCL 11 460 RCL 07 461 - 462 STO 13 463 63 464 + 465 COS 466 23 467 * 468 - 469 RCL 09 470 ST+ X 471 STO 14 472 50 473 - 474 COS 475 62 476 * 477 - 478 RCL 11 479 14.7 480 + 481 COS 482 323 483 * 484 - 485 RCL 00 486 * 487 RCL 06 488 14 489 + 490 COS 491 RCL 07 492 59 493 + 494 COS 495 - 496 RCL 11 497 ST+ X 498 STO 15 499 RCL 03 500 - 501 61 502 - 503 COS 504 - 505 RCL 07 506 RCL 12 507 - 508 ST+ X 509 79 510 - 511 COS 512 - 513 RCL 13 514 RCL 07 515 - 516 COS 517 - 518 RCL 11 519 RCL 14 520 + 521 36 522 + 523 COS 524 + 525 PI 526 * 527 + 528 RCL 03 529 RCL 07 530 + 531 COS 532 6 533 * 534 - 535 RCL 03 536 17 537 + 538 COS 539 RCL 11 540 RCL 03 541 - 542 SIN 543 - 544 RCL 15 545 75 546 - 547 COS 548 - 549 8 550 * 551 + 552 RCL 08 553 ST+ X 554 54 555 + 556 COS 557 RCL 08 558 29 559 - 560 COS 561 + 562 RCL 10 563 25 564 + 565 COS 566 + 567 9 568 * 569 + 570 RCL 13 571 2 572 / 573 SIN 574 14 575 * 576 - 577 RCL 13 578 40 579 - 580 COS 581 45 582 * 583 - 584 RCL 09 585 14 586 + 587 COS 588 118 589 * 590 + 591 RCL 14 592 30 593 + 594 COS 595 228 596 * 597 + 598 RCL 11 599 7.2 600 + 601 SIN 602 810 603 * 604 - 605 STO 03 606 RCL 08 607 49 608 - 609 COS 610 RCL 09 611 RCL 07 612 - 613 76 614 + 615 COS 616 + 617 3 618 * 619 RCL 09 620 ST+ X 621 42 622 + 623 SIN 624 8 625 * 626 RCL 00 627 * 628 - 629 RCL 10 630 28 631 - 632 COS 633 6 634 * 635 + 636 RCL 11 637 SIN 638 4 639 * 640 - 641 RCL 14 642 33 643 + 644 COS 645 20 646 * 647 + 648 RCL 13 649 20 650 - 651 COS 652 18 653 * 654 - 655 STO 04 656 RCL 09 657 17 658 + 659 SIN 660 5 661 * 662 RCL 13 663 50 664 + 665 COS 666 RCL 11 667 COS 668 + 669 4 670 * 671 - 672 RCL 08 673 20 674 - 675 COS 676 8 677 * 678 + 679 RCL 14 680 60 681 - |
682 COS
683 19 684 * 685 + 686 STO 05 687 9.543 688 STO 09 689 RCL 00 690 347 691 RCL 00 692 6 693 * 694 + 695 * 696 CHS 697 5551 698 + 699 STO 10 700 RDN 701 X^2 702 19 703 / 704 RCL 07 705 + 706 50.061 707 + 708 STO 12 709 CLX 710 37 711 * 712 CHS 713 2489 714 + 715 STO 11 716 CLX 717 84 718 * 719 19638 720 + 721 * 722 93057 723 + 724 STO 13 725 CLX 726 12 727 * 728 CHS 729 8771 730 + 731 * 732 113666 733 XEQ 14 734 RTN 735 LBL 07 736 XEQ 12 737 RCL 05 738 8 739 - 740 SIN 741 14 742 * 743 RCL 00 744 * 745 RCL 12 746 65 747 + 748 COS 749 ST+ X 750 + 751 RCL 11 752 RCL 03 753 - 754 STO 11 755 RCL 12 756 - 757 27 758 - 759 COS 760 PI 761 * 762 - 763 RCL 14 764 RCL 15 765 + 766 60 767 - 768 COS 769 4 770 * 771 + 772 RCL 07 773 RCL 12 774 - 775 28 776 + 777 COS 778 RCL 15 779 RCL 13 780 - 781 12 782 - 783 COS 784 - 785 6 786 * 787 + 788 RCL 11 789 10 790 + 791 SIN 792 7 793 * 794 + 795 RCL 14 796 10 797 + 798 SIN 799 10 800 * 801 - 802 RCL 12 803 RCL 15 804 + 805 70 806 + 807 COS 808 12 809 * 810 - 811 RCL 06 812 RCL 12 813 - 814 STO 14 815 10 816 - 817 COS 818 RCL 04 819 RCL 12 820 + 821 COS 822 - 823 15 824 * 825 + 826 RCL 03 827 17 828 + 829 COS 830 RCL 04 831 51 832 + 833 COS 834 + 835 35 836 * 837 - 838 RCL 13 839 ST+ X 840 STO 06 841 11 842 - 843 COS 844 RCL 03 845 RCL 12 846 + 847 STO 07 848 51 849 - 850 COS 851 + 852 40 853 * 854 + 855 RCL 15 856 71 857 - 858 COS 859 209 860 * 861 - 862 RCL 05 863 27.8 864 - 865 COS 866 858 867 * 868 - 869 STO 03 870 RCL 15 871 33 872 + 873 COS 874 RCL 06 875 SIN 876 - 877 6 878 * 879 STO 04 880 RCL 15 881 19 882 + 883 COS 884 34 885 * 886 RCL 06 887 79 888 + 889 COS 890 RCL 07 891 41 892 + 893 COS 894 + 895 6 896 * 897 - 898 RCL 14 899 SIN 900 5 901 * 902 - 903 STO 05 904 19.192 905 STO 09 906 RCL 00 907 8 908 RCL 00 |
909 4
910 * 911 + 912 * 913 773 914 + 915 STO 11 916 CLX 917 27 918 * 919 CHS 920 4630 921 + 922 STO 10 923 RDN 924 X^2 925 33 926 / 927 45.955 928 - 929 ST+ 12 930 CLX 931 21 932 * 933 14863 934 + 935 * 936 172993 937 + 938 STO 13 939 CLX 940 18 941 * 942 134 943 + 944 * 945 5211 946 + 947 * 948 74005 949 XEQ 14 950 RTN 951 LBL 08 952 XEQ 12 953 RCL 06 954 RCL 13 955 ST- 07 956 ST- 15 957 - 958 STO 08 959 COS 960 RCL 05 961 SIN 962 RCL 00 963 * 964 - 965 9 966 * 967 RCL 07 968 16 969 + 970 COS 971 RCL 05 972 RCL 13 973 - 974 STO 06 975 13 976 - 977 SIN 978 - 979 5 980 * 981 + 982 RCL 15 983 11 984 - 985 COS 986 22 987 * 988 + 989 RCL 04 990 50 991 + 992 COS 993 24 994 * 995 + 996 RCL 14 997 7 998 + 999 SIN 1000 71 1001 * 1002 + 1003 RCL 05 1004 27.8 1005 - 1006 COS 1007 584 1008 * 1009 + 1010 STO 03 1011 RCL 14 1012 54 1013 + 1014 SIN 1015 RCL 06 1016 21 1017 - 1018 COS 1019 + 1020 CHS 1021 9 1022 * 1023 STO 04 1024 RCL 05 1025 63 1026 - 1027 COS 1028 8 1029 * 1030 RCL 07 1031 16 1032 + 1033 SIN 1034 3 1035 * 1036 - 1037 RCL 08 1038 SIN 1039 RCL 15 1040 79 1041 + 1042 COS 1043 + 1044 5 1045 * 1046 - 1047 RCL 14 1048 6 1049 + 1050 COS 1051 17 1052 * 1053 - 1054 STO 05 1055 30.07 1056 STO 09 1057 RCL 00 1058 1770 1059 RCL 00 1060 93 1061 * 1062 - 1063 STO 11 1064 RDN 1065 X^2 1066 32 1067 / 1068 RCL 13 1069 + 1070 55.654 1071 - 1072 STO 12 1073 CLX 1074 6 1075 * 1076 899 1077 + 1078 STO 10 1079 CLX 1080 38 1081 * 1082 14263 1083 + 1084 * 1085 48124 1086 + 1087 STO 13 1088 CLX 1089 26 1090 * 1091 11022 1092 + 1093 * 1094 131784 1095 XEQ 14 1096 RTN 1097 LBL 09 1098 RCL 00 1099 28897 1100 * 1101 65 1102 + 1103 COS 1104 7 1105 * 1106 RCL 00 1107 10769 1108 * 1109 76 1110 + 1111 COS 1112 4 1113 * 1114 + 1115 STO 03 1116 RCL 00 1117 86 1118 * 1119 4 1120 - 1121 STO 04 1122 RCL 00 1123 21 1124 * 1125 STO 05 1126 39.489 1127 STO 09 1128 24900 1129 STO 10 1130 17140 1131 STO 11 1132 RCL 00 1133 1451.7 1134 * 1135 238.927 |
1136 +
1137 STO 12 1138 RCL 00 1139 13971 1140 * 1141 135925 1142 - 1143 STO 13 1144 246232 1145 XEQ 14 1146 RTN 1147 LBL 10 1148 RCL 00 1149 1358 1150 RCL 00 1151 26587 1152 * 1153 + 1154 * 1155 124 1156 - 1157 * 1158 STO 04 1159 CLX 1160 3080 1161 * 1162 1175 1163 - 1164 * 1165 14 1166 + 1167 STO 03 1168 CLX 1169 11605 1170 * 1171 CHS 1172 960 1173 - 1174 * 1175 8 1176 + 1177 STO 05 1178 CLX 1179 641.294 1180 * 1181 20.862 1182 + 1183 STO 12 1184 68.049 1185 STO 09 1186 43364 1187 STO 10 1188 43867 1189 STO 11 1190 RCL 00 1191 13970 1192 * 1193 187249 1194 + 1195 STO 13 1196 151210 1197 CHS 1198 GTO 14 1199 LBL 12 1200 30349.057 1201 RCL 00 1202 * 1203 STO 06 1204 12221.14 1205 LASTX 1206 * 1207 STO 07 1208 - 1209 STO 08 1210 LASTX 1211 - 1212 STO 09 1213 RCL 08 1214 + 1215 STO 10 1216 RCL 07 1217 ST+ X 1218 - 1219 STO 11 1220 4284.673 1221 RCL 00 1222 * 1223 STO 12 1224 2184.856 1225 LASTX 1226 * 1227 STO 13 1228 - 1229 STO 14 1230 ST+ X 1231 STO 15 1232 RCL 12 1233 - 1234 STO 05 1235 ST+ X 1236 STO 04 1237 RCL 07 1238 RCL 12 1239 3 1240 * 1241 - 1242 STO 03 1243 RTN 1244 LBL 13 1245 0 1246 STO 03 1247 STO 04 1248 STO 05 1249 RDN 1250 LBL 14 1251 + 1252 E3 1253 ST/ 03 1254 ST/ 04 1255 ST/ 05 1256 ST/ 11 1257 ST/ 13 1258 / 1259 STO 14 1260 E5 1261 ST/ 10 1262 12 1263 STO 08 1264 RCL 12 1265 RCL 13 1266 - 1267 RCL 00 1268 13.971 1269 * 1270 + 1271 360 1272 MOD 1273 ENTER 1274 ENTER 1275 LBL 11 1276 SIN 1277 RCL 10 1278 R-D 1279 * 1280 + 1281 DSE 08 1282 GTO 11 1283 2 1284 / 1285 1 1286 RCL 10 1287 + 1288 1 1289 LASTX 1290 - 1291 / 1292 SQRT 1293 P-R 1294 LASTX 1295 / 1296 R-P 1297 RDN 1298 ST+ X 1299 1 1300 R^ 1301 ST+ X 1302 COS 1303 RCL 10 1304 * 1305 - 1306 RCL 09 1307 * 1308 RCL 05 1309 + 1310 STO 08 1311 CLX 1312 RCL 14 1313 - 1314 RCL 13 1315 + 1316 COS 1317 RCL 11 1318 LASTX 1319 SIN 1320 P-R 1321 X<>Y 1322 ASIN 1323 RCL 04 1324 + 1325 STO 07 1326 X<> Z 1327 R-P 1328 CLX 1329 RCL 14 1330 + 1331 RCL 03 1332 + 1333 STO 06 1334 RCL 08 1335 X<>Y 1336 RDN 1337 P-R 1338 R^ 1339 X<>Y 1340 P-R 1341 RCL 02 1342 ST+ Z 1343 CLX 1344 RCL 01 1345 + 1346 R-P 1347 X<>Y 1348 RDN 1349 R-P 1350 R^ 1351 X<>Y 1352 STO 05 1353 X<> Z 1354 STO 04 1355 X<>Y 1356 STO 03 1357 END |
( 2041 bytes / SIZE 016 )
| STACK | INPUTS | OUTPUTS |
| Z | / | distance to the earth ( AU ) |
| Y | / | geocentric latitude ( deg ) |
| X | / | geocentric longitude ( deg ) |
Example: T = 0.1
i-e 2100/01/01 0h TT
• XEQ "SUN" >>>>
Long = -79°389
= R03
R01 = X = 0.181078
RDN Lat = 0
= R04 and
R02 = Y = -0.966557
RDN Dist = 0.983372 AU
= R05
• Mercury R/S or
XEQ 01 >>>> Long = -71°982
= R03
R06 = -54°797 = L
RDN Lat = -2°113
= R04 and
R07 = -6°791 = B
RDN Dist = 1.38605 AU
= R05
R08 = 0.43213 AU = R
• Venus
R/S or XEQ 02 >>>> Long
= -39°924
= R03
R06 = 19°729
RDN Lat = -1°852
= R04 and
R07 = -2°876
RDN Dist = 1.1257 AU
= R05
R08 = 0.7252 AU
• Mars
R/S or XEQ 04 >>>>
Long = 29°538
= R03
R06 = 67°572
RDN Lat = 0°950
= R04 and
R07 = 0°548
RDN Dist = 0.870 AU
= R05
R08 = 1.510 AU
• Jupiter R/S
or XEQ 05 >>>> Long =
-158°788
= R03
R06 = 190°998
RDN Lat = 1°275
= R04 and
R07 = 1°297
RDN Dist = 5.547 AU
= R05
R08 = 5.452 AU
• Saturn R/S
or XEQ 06 >>>> Long = -154°364
= R03
R06 = 199°992
RDN Lat = 2°424
= R04 and
R07 = 2°476
RDN Dist = 9.874 AU
= R05
R08 = 9.667 AU
• Uranus R/S or
XEQ 07 >>>> Long =
17°742
= R03
R06 = 20°541
RDN Lat = -0°630
= R04 and
R07 = -0°625
RDN Dist = 19.832 AU
= R05
R08 = 19.978 AU
• Neptune R/S or XEQ
08 >>>> Long = 167°291
= R03
R06 = 165°578
RDN Lat = 0°965
= R04 and
R07 = 0°952
RDN Dist = 29.805 AU
= R05
R08 = 30.207 AU
• Pluto R/S
or XEQ 09 >>>> Long
= 32°402
= R03
R06 = 33°518
RDN Lat = -16°921
= R04 and
R07 = -16°793
RDN Dist = 48.583 AU
= R05
R08 = 48.941 AU
• Xena R/S
or XEQ 10 >>>> Long
= 43°192
= R03
R06 = 43°761
RDN Lat = 6°180
= R04 and
R07 = 6°141
RDN Dist = 83.419 AU
= R05
R08 = 83.950 AU
Notes:
-If you don't want to calculate the position of the "tenth planet",
delete lines 1145 to 1197.
-Like the program listed in §1, a few lines may be added after
line 01 of this "SUN" program to allow execution from another program,
for example: GTO IND X LBL 00
-Then place 0 in X-register to compute the position of the Sun, 1 for
Mercury, ..... , 10 for Xena/Lilah/Eris.
-Or replace LBL 01 by LBL "ME" ............... LBL 10 by LBL "XE"
References:
[1] Jean Meeus - "Astronomical Algorithms" - Willmann-Bell
- ISBN 0-943396-61-1
[2] VSOP87D Series ftp://ftp.imcce.fr/pub/ephem/planets/vsop87/
[3] VSOP09 & TOP10 Series http://www.imcce.fr/~jlsimon
[4] A fantastic software, "SOLEX" which may be downloaded from
http://chemistry.unina.it/~alvitagl/solex/