TransNeptunian Objects(II) for the HP-41
Overview
-The programs hereunder calculate the heliocentric coordinates of 8 transneptunian objects:
>>> Pluto, Eris, Sedna, Hauméa, Makémaké, Quaoar, Orcus and Varuna over the time-span [2010-2030]
-More exactly, the interval is 2010/01/01 0h TT - 2030/10/22 0h TT
-A polynomial is used for each coordinate and the precision is about
0°00005 for the longitudes and the latitudes,
0.00004 AU for the radius vector ( the errors are often
much smaller ).
-So, the accuracy is much better than the results in "Transneptunian
objects(I)"
Program Listing
-Register R00 must contain T = ( DD - 7305 ) / 4000 where
DD = number of days since 2000/01/01 0h TT
-The short routine hereunder may be used to initialize R00
| 01 LBL "T"
02 HR 03 24 04 / 05 X<>Y 06 XEQ "J0" 07 + 08 7305 09 - 10 4000 11 / 12 STO 00 13 END |
where "J0" ( or "J1" or "J2" ) is listed in "Julian & Gregorian
Calendars for the HP-41"
-The inputs are the date YYYY.MNDD in register Y and the time HH.MNSS
in register X ( expressed in TT )
-If you have a TIME module, line 06 may be replaced by 1.012
X<>Y DDAYS
-In this case, key in the date in MDY or DMY format.
Data Registers: • R00 = T = ( DD - 7305 ) / 4000 where DD = number of days since 2000/01/01 0h TT
( Register R00 is to be initialized before executing these programs )
R06 = L = heliocentric longitude ( deg )
R07 = B = heliocentric latitude ( deg )
referred to the mean ecliptic and equinox of the date
R08 = R = radius vector ( AU )
Flags: /
Subroutines: /
| 01 LBL "PL"
02 RCL 00 03 3095 04 RCL 00 05 16661 06 * 07 - 08 * 09 53778 10 + 11 * 12 3465 13 - 14 * 15 68546 16 - 17 * 18 11028 19 - 20 * 21 44016 22 + 23 * 24 27254 25 + 26 * 27 15135 28 - 29 * 30 9966 31 - 32 * 33 148133 34 - 35 * 36 2012339 37 + 38 * 39 29275252 40 + 41 STO 06 42 CLX 43 57 44 * 45 - 46 624 47 + 48 * 49 229 50 + 51 * 52 2009 53 - 54 * 55 277 56 - 57 * 58 2662 59 + 60 * 61 3371 62 - 63 * 64 9559 65 + 66 * 67 51375 68 + 69 * 70 613855 71 - 72 * 73 67160 74 - 75 STO 07 76 CLX 77 1935 78 * 79 9252 80 - 81 * 82 4542 83 - 84 * 85 26158 86 + 87 * 88 8161 89 + 90 * 91 28756 92 - 93 * 94 15519 95 - 96 * 97 16022 98 + 99 * 100 17565 101 + 102 * 103 11665 104 - 105 * 106 11179 107 + 108 * 109 262697 110 + 111 * 112 3395056 113 XEQ 10 114 RTN 115 LBL "ER" 116 RCL 00 117 6442 118 RCL 00 119 1507 120 * 121 - 122 * 123 3927 124 + 125 * 126 17986 127 - 128 * 129 7587 130 - 131 * 132 19615 |
133 +
134 * 135 13182 136 + 137 * 138 10979 139 - 140 * 141 12958 142 - 143 * 144 3728 145 + 146 * 147 5404 148 + 149 * 150 252725 151 + 152 * 153 2381775 154 + 155 STO 06 156 CLX 157 639 158 * 159 311 160 + 161 * 162 1567 163 - 164 * 165 1474 166 - 167 * 168 1450 169 + 170 * 171 2460 172 + 173 * 174 705 175 - 176 * 177 1527 178 - 179 * 180 3037 181 + 182 * 183 215324 184 + 185 * 186 1174145 187 - 188 STO 07 189 CLX 190 13031 191 * 192 CHS 193 2369 194 + 195 * 196 40908 197 + 198 * 199 1878 200 - 201 * 202 51035 203 - 204 * 205 10007 206 - 207 * 208 32765 209 + 210 * 211 21157 212 + 213 * 214 12108 215 - 216 * 217 14934 218 - 219 * 220 8616 221 - 222 * 223 79690 224 - 225 * 226 9601143 227 XEQ 10 228 RTN 229 LBL "SE" 230 RCL 00 231 4993 232 RCL 00 233 3156 234 * 235 + 236 * 237 10965 238 - 239 * 240 15708 241 - 242 * 243 11873 244 + 245 * 246 21682 247 + 248 * 249 677 250 - 251 * 252 18089 253 - 254 * 255 7039 256 - 257 * 258 8469 259 + 260 * 261 27837 262 + 263 * 264 681782 |
265 +
266 * 267 5753938 268 + 269 STO 06 270 CLX 271 953 272 * 273 184 274 - 275 * 276 2749 277 - 278 * 279 229 280 - 281 * 282 3561 283 + 284 * 285 1208 286 + 287 * 288 2624 289 - 290 * 291 535 292 - 293 * 294 9024 295 + 296 * 297 7168 298 + 299 * 300 1191229 301 - 302 STO 07 303 CLX 304 11189 305 * 306 CHS 307 7451 308 + 309 * 310 34603 311 + 312 * 313 17283 314 - 315 * 316 45569 317 - 318 * 319 9577 320 + 321 * 322 36343 323 + 324 * 325 6958 326 + 327 * 328 20445 329 - 330 * 331 7733 332 - 333 * 334 28457 335 + 336 * 337 304187 338 - 339 * 340 8463439 341 XEQ 10 342 RTN 343 LBL "HA" 344 RCL 00 345 10616 346 RCL 00 347 3185 348 * 349 + 350 * 351 CHS 352 9363 353 + 354 * 355 31309 356 + 357 * 358 4084 359 - 360 * 361 36419 362 - 363 * 364 14928 365 - 366 * 367 22244 368 + 369 * 370 22113 371 + 372 * 373 8018 374 - 375 * 376 14745 377 + 378 * 379 1150310 380 + 381 * 382 20653114 383 + 384 STO 06 385 CLX 386 3431 387 * 388 835 389 + 390 * 391 9037 392 - 393 * 394 5066 395 - 396 * |
397 9467
398 + 399 * 400 9517 401 + 402 * 403 5254 404 - 405 * 406 8920 407 - 408 * 409 44414 410 - 411 * 412 48575 413 + 414 * 415 2808514 416 + 417 STO 07 418 CLX 419 9192 420 * 421 2009 422 - 423 * 424 29797 425 - 426 * 427 2411 428 + 429 * 430 38576 431 + 432 * 433 6379 434 + 435 * 436 26021 437 - 438 * 439 16119 440 - 441 * 442 10456 443 + 444 * 445 12479 446 + 447 * 448 18886 449 - 450 * 451 91076 452 - 453 * 454 5036284 455 XEQ 10 456 RTN 457 LBL "MK" 458 RCL 00 459 12857 460 CHS 461 RCL 00 462 6487 463 * 464 + 465 * 466 18778 467 - 468 * 469 34303 470 + 471 * 472 27722 473 + 474 * 475 33073 476 - 477 * 478 32106 479 - 480 * 481 12664 482 + 483 * 484 26703 485 + 486 * 487 1173 488 - 489 * 490 29920 491 - 492 * 493 1082184 494 + 495 * 496 18564120 497 + 498 STO 06 499 CLX 500 2325 501 * 502 1736 503 + 504 * 505 5487 506 - 507 * 508 6819 509 - 510 * 511 3972 512 + 513 * 514 10602 515 + 516 * 517 539 518 - 519 * 520 5786 521 - 522 * 523 40817 524 - 525 * 526 124789 527 - 528 * |
529 2806426
530 + 531 STO 07 532 CLX 533 9067 534 * 535 780 536 + 537 * 538 29365 539 - 540 * 541 5561 542 - 543 * 544 36424 545 + 546 * 547 15054 548 + 549 * 550 20603 551 - 552 * 553 20635 554 - 555 * 556 4440 557 + 558 * 559 13275 560 + 561 * 562 13244 563 - 564 * 565 31693 566 + 567 * 568 5256935 569 XEQ 10 570 RTN 571 LBL "QU" 572 RCL 00 573 650 574 RCL 00 575 14700 576 * 577 - 578 * 579 46073 580 + 581 * 582 3959 583 + 584 * 585 55482 586 - 587 * 588 18196 589 - 590 * 591 30106 592 + 593 * 594 28436 595 + 596 * 597 5600 598 - 599 * 600 20012 601 - 602 * 603 12294 604 + 605 * 606 1447922 607 + 608 * 609 27306173 610 + 611 STO 06 612 CLX 613 801 614 * 615 871 616 - 617 * 618 2574 619 - 620 * 621 1823 622 + 623 * 624 4138 625 + 626 * 627 1326 628 - 629 * 630 3627 631 - 632 * 633 255 634 - 635 * 636 22674 637 - 638 * 639 20868 640 + 641 * 642 794162 643 + 644 STO 07 645 CLX 646 4706 647 * 648 9249 649 - 650 * 651 14106 652 - 653 * 654 24944 655 + 656 * 657 21329 658 + 659 * 660 24078 |
661 -
662 * 663 24749 664 - 665 * 666 8762 667 + 668 * 669 20473 670 + 671 * 672 363 673 + 674 * 675 6727 676 - 677 * 678 37642 679 - 680 * 681 4283773 682 XEQ 10 683 RTN 684 LBL "OR" 685 RCL 00 686 9916 687 CHS 688 RCL 00 689 9953 690 * 691 + 692 * 693 31521 694 - 695 * 696 25167 697 + 698 * 699 44475 700 + 701 * 702 19378 703 - 704 * 705 40876 706 - 707 * 708 889 709 - 710 * 711 26977 712 + 713 * 714 9224 715 + 716 * 717 1560 718 - 719 * 720 1113886 721 + 722 * 723 16103287 724 + 725 STO 06 726 CLX 727 1143 728 * 729 CHS 730 2125 731 - 732 * 733 2237 734 + 735 * 736 6911 737 + 738 * 739 89 740 + 741 * 742 9358 743 - 744 * 745 2451 746 - 747 * 748 6334 749 + 750 * 751 34973 752 + 753 * 754 113455 755 - 756 * 757 1965827 758 - 759 STO 07 760 CLX 761 6738 762 * 763 4618 764 + 765 * 766 22275 767 - 768 * 769 15676 770 - 771 * 772 25878 773 + 774 * 775 24308 776 + 777 * 778 9120 779 - 780 * 781 23356 782 - 783 * 784 4426 785 - 786 * 787 12876 788 + 789 * 790 19421 791 - 792 * |
793 3548
794 - 795 * 796 4806649 797 XEQ 10 798 RTN 799 LBL "VA" 800 RCL 00 801 4551 802 CHS 803 RCL 00 804 12624 805 * 806 + 807 * 808 41119 809 - 810 * 811 8235 812 + 813 * 814 54404 815 + 816 * 817 3773 818 + 819 * 820 38966 821 - 822 * 823 20074 824 - 825 * 826 17443 827 + 828 * 829 18588 830 + 831 * 832 8560 833 - 834 * 835 1309082 836 + 837 * 838 12289079 839 + 840 STO 06 841 CLX 842 399 843 * 844 CHS 845 1088 846 + 847 * 848 1412 849 + 850 * 851 2803 852 - 853 * 854 2675 855 - 856 * 857 2783 858 + 859 * 860 2905 861 + 862 * 863 3698 864 - 865 * 866 24369 867 - 868 * 869 356590 870 + 871 * 872 753108 873 + 874 STO 07 875 CLX 876 264 877 * 878 8822 879 + 880 * 881 2116 882 - 883 * 884 25524 885 - 886 * 887 643 888 - 889 * 890 29688 891 + 892 * 893 11831 894 + 895 * 896 18905 897 - 898 * 899 16258 900 - 901 * 902 6847 903 + 904 * 905 4182 906 + 907 * 908 48495 909 + 910 * 911 4396618 912 LBL 10 913 + 914 E5 915 ST/ 06 916 ST/ 07 917 / 918 STO 08 919 RCL 07 920 RCL 06 921 END |
( 2076 bytes / SIZE 009 )
| STACK | INPUTS | OUTPUTS |
| Z | / | R |
| Y | / | B |
| X | / | L |
L = heliocentric longitude ( deg )
where B = heliocentric
latitude ( deg )
referred to the mean ecliptic and equinox of the date
R = radius vector ( AU )
Example: T = 0.9372 ( i-e 2030/04/06 19h12m TT )
>>> 0.9372 STO 00
• PLUTO
XEQ "PL" >>>> L = 310°33002
RDN B = -5°91156
RDN R = 36.51259 AU
• ERIS
XEQ "ER" ( or R/S ) >>>>
L = 26°19867
RDN B = -9°70077
RDN R = 95.13540 AU
• SEDNA
XEQ "SE" >>>> L =
64°15595
RDN B = -11°77149
RDN R = 81.96791 AU
• HAUMEA
XEQ "HA" ( or R/S ) >>>>
L = 217°50699
RDN B = 28°10591
RDN R = 49.39406 AU
• MAKEMAKE
XEQ "MK" ( or R/S ) >>>> L = 195°60592
RDN B = 26°53388
RDN R = 52.77809 AU
• QUAOAR
XEQ "QU" ( or R/S ) >>>>
L = 286°69416
RDN B = 7°92200
RDN R = 42.49817 AU
• ORCUS
XEQ "OR" ( or R/S ) >>>> L = 171°57351
RDN B = -20°40884
RDN R = 47.86190 AU
• VARUNA
XEQ "VA" ( or R/S ) >>>> L = 135°17713
RDN B = 10°64755
RDN R = 44.40753 AU
Notes:
-The polynomials are fitted to the French ephemerides INPOP13c ( cf reference [1] ), except for Pluto whose coordinates are fitted to JPL DE421.
-Registers R01 & R02 are unused, in case you want to use them to
store the rectangular coordinates of the Sun.
-A subroutine may also be added after line 920 to calculate the geocentric
coordinates in registers R03-R04-R05
Reference: