Overview
Registers
R01 = X Rectangular
R02 = Y coordinates of the Sun,
R03 = Geocentric longitude ( deg )
R04 = Geocentric latitude ( deg )
R05 = Distance Earth-Planet ( AU )
R06 = Right-ascension ( deg )
R07 = Declination ( deg )
R08 = Heliocentric longitude ( deg )
R09 = Heliocentric latitude ( deg )
R10 = Radius vector ( AU )
R11 = Azimuth ( deg ) ( reckoned clockwise from South )
R12 = local true sidereal time ( deg )
• R13 = Longitude of the observer ( deg ) positive East
• R14 = Latitude of the observer ( deg)
Flags: /
Subroutines: /
| 01 LBL "EPH" 02 19 03 10^X 04 SQRT 05 / 06 STO 00 07 RDN 08 HR 09 15 10 * 11 STO 12 12 360 13 / 14 + 15 36525 16 / 17 ST+ 00 18 3600077 19 STO 06 20 * 21 2 22 10^X 23 STO 04 24 STO 07 25 ST/ Y 26 + 27 31 28 1/X 29 - 30 RCL 13 31 + 32 ST+ 12 33 167 34 STO 03 35 8003 36 CHS 37 STO 09 38 297 39 + 40 STO 05 41 CLST 42 STO 01 43 STO 02 44 STO 11 45 XEQ 14 46 CLX 47 RCL 03 48 RCL 05 49 P-R 50 STO 01 51 RDN 52 STO 02 53 CLX 54 RCL 11 55 RTN 56 LBL 01 57 38.71 58 STO 04 59 2056 60 STO 03 61 700 62 STO 11 63 84 64 STO 07 65 7746 66 STO 05 67 25020 68 STO 09 69 14947407 70 STO 06 71 4833 72 119 73 XEQ 14 74 RTN 75 LBL 02 76 72.333 77 STO 04 78 68 79 STO 03 80 STO 07 81 339 82 STO 11 83 13156 84 STO 05 85 18118 86 STO 09 87 5851921 88 STO 06 89 7668 90 90 91 XEQ 14 92 RTN 93 LBL 03 94 RCL 00 95 3599905 96 % 97 3 98 - 99 STO 03 100 STO 11 101 RCL 00 102 89053422 103 % 104 43.48 105 + 106 STO 05 107 STO 06 108 STO 10 |
109 ST- 11 110 RCL 00 111 48320202 112 % 113 3.34 114 - 115 STO 09 116 SIN 117 LASTX 118 RCL 00 119 77.48 120 X^2 121 * 122 48.24 123 + 124 - 125 ST- 05 126 STO 07 127 ST+ 10 128 SIN 129 * 130 56 131 * 132 RCL 06 133 RCL 09 134 + 135 COS 136 PI 137 * 138 - 139 RCL 06 140 RCL 09 141 - 142 COS 143 17 144 * 145 + 146 RCL 07 147 ST+ X 148 STO 08 149 RCL 09 150 + 151 COS 152 3 153 SQRT 154 * 155 + 156 RCL 10 157 RCL 09 158 - 159 COS 160 - 161 RCL 08 162 RCL 09 163 - 164 COS 165 - 166 RCL 09 167 RCL 11 168 + 169 COS 170 + 171 RCL 09 172 COS 173 513 174 * 175 + 176 RCL 05 177 RCL 09 178 + 179 COS 180 ST+ Y 181 RCL 05 182 RCL 09 183 ST+ 09 184 - 185 COS 186 - 187 5 188 * 189 + 190 STO 04 191 RCL 06 192 RCL 08 193 - 194 SIN 195 RCL 05 196 RCL 03 197 - 198 SIN 199 - 200 ST+ X 201 RCL 08 202 SIN 203 7 204 * 205 - 206 RCL 03 207 RCL 07 208 + 209 SIN 210 - 211 RCL 06 212 SIN 213 22 214 * 215 + 216 RCL 03 |
217 RCL 07 218 - 219 SIN 220 RCL 10 221 SIN 222 RCL 11 223 SIN 224 + 225 ST+ T 226 + 227 - 228 4 229 * 230 - 231 RCL 06 232 ST+ X 233 RCL 07 234 ST+ 08 235 - 236 SIN 237 - 238 RCL 08 239 SIN 240 - 241 RCL 05 242 ST+ X 243 SIN 244 + 245 RCL 03 246 RCL 05 247 + 248 SIN 249 - 250 RCL 09 251 SIN 252 STO 10 253 RCL 07 254 COS 255 ST+ X 256 STO 08 257 * 258 - 259 RCL 05 260 SIN 261 85 262 * 263 RCL 09 264 RCL 06 265 - 266 SIN 267 - 268 3 269 * 270 RCL 07 271 SIN 272 34 273 * 274 RCL 03 275 SIN 276 + 277 37 278 * 279 - 280 RCL 10 281 23 282 * 283 + 284 RCL 06 285 2 286 / 287 COS 288 7 289 ST* 08 290 * 291 + 292 2 293 / 294 + 295 48126788 296 RCL 00 297 * 298 21173 299 + 300 + 301 2 302 10^X 303 ST/ 04 304 / 305 360 306 MOD 307 STO 03 308 257 309 RCL 08 310 + 311 5 312 10^X 313 / 314 STO 05 315 XEQ 00 316 RTN 317 LBL 04 318 112 319 STO 07 320 8730 321 D-R 322 STO 04 323 934 324 RCL 00 |
325 + 326 STO 03 327 185 328 STO 11 329 1914170 330 STO 06 331 2394 332 CHS 333 STO 05 334 13 335 - 336 5 337 / 338 STO 09 339 4956 340 77 341 XEQ 14 342 RTN 343 LBL 05 344 XEQ 12 345 RCL 04 346 75 347 - 348 SIN 349 R^ 350 24 351 - 352 STO 10 353 9 354 - 355 SIN 356 ST+ X 357 + 358 3 359 * 360 RCL 11 361 ST- 06 362 SIN 363 8 364 * 365 RCL 06 366 10 367 + 368 COS 369 + 370 4 371 * 372 - 373 RCL 10 374 2 375 / 376 SIN 377 RCL 00 378 2402 379 * 380 46 381 - 382 COS 383 + 384 ST+ X 385 - 386 3431 387 + 388 STO 09 389 520.3 390 STO 04 391 4 392 / 393 STO 11 394 303630 395 STO 06 396 485 397 RCL 00 398 ST+ X 399 + 400 STO 03 401 89 402 STO 07 403 1433 404 STO 05 405 8613 406 + 407 102 408 XEQ 14 409 RTN 410 LBL 06 411 XEQ 12 412 RCL 11 413 SIN 414 80 415 * 416 RCL 04 417 ST+ X 418 28 419 + 420 COS 421 9 422 * 423 RCL 04 424 20 425 + 426 COS 427 6 428 * 429 + 430 RCL 08 431 3 432 * |
433 4 434 + 435 SIN 436 + 437 ST+ X 438 + 439 5006 440 + 441 STO 09 442 122351 443 STO 06 444 954 445 STO 04 446 555 447 RCL 00 448 PI 449 * 450 - 451 STO 03 452 249 453 STO 11 454 2 455 / 456 STO 07 457 9306 458 STO 05 459 2061 460 + 461 88 462 XEQ 14 463 RTN 464 LBL 07 465 XEQ 12 466 65 467 - 468 SIN 469 89 470 * 471 RCL 08 472 ST+ X 473 19 474 + 475 SIN 476 23 477 * 478 - 479 RCL 00 480 325 481 * 482 SIN 483 + 484 RCL 00 485 787 486 * 487 COS 488 + 489 RCL 04 490 7 491 / 492 45 493 - 494 COS 495 - 496 RCL 00 497 2598 498 * 499 15 500 - 501 COS 502 ST+ X 503 + 504 4596 505 - 506 STO 09 507 42986 508 STO 06 509 1919 510 STO 04 511 463 512 STO 03 513 77 514 STO 07 515 STO 11 516 17299 517 STO 05 518 7400 519 52 520 XEQ 14 521 RTN 522 LBL 08 523 XEQ 12 524 27 525 ST+ 08 526 + 527 COS 528 59 529 * 530 RCL 08 531 SIN 532 8 533 * 534 + 535 5565 536 - 537 STO 09 538 21988 539 STO 06 540 3007 |
541 STO 04 542 90 543 STO 03 544 71 545 STO 07 546 177 547 RCL 00 548 - 549 STO 11 550 4812 551 STO 05 552 8366 553 + 554 110 555 XEQ 14 556 RTN 557 LBL 09 558 3949 559 STO 04 560 2490 561 STO 03 562 9 563 * 564 2 565 - 566 STO 05 567 68 568 STO 07 569 1714 570 STO 11 571 23893 572 STO 09 573 14657 574 STO 06 575 3626 576 - 577 140 578 LBL 14 579 72 580 ST+ 07 581 CLX 582 RCL 00 583 ST* 06 584 ST* 07 585 * 586 + 587 STO 08 588 X<> 09 589 9 590 X<> 06 591 + 592 RCL 05 593 RCL 07 594 + 595 ST- 09 596 - 597 4 598 10^X 599 ST/ 03 600 SQRT 601 ST/ 04 602 ST/ 08 603 ST/ 09 604 ST/ 11 605 / 606 ENTER 607 ENTER 608 LBL 11 609 SIN 610 RCL 03 611 R-D 612 * 613 + 614 DSE 06 615 GTO 11 616 STO 10 617 2 618 / 619 TAN 620 RCL 03 621 1 622 ST+ Y 623 RCL 03 624 - 625 / 626 SQRT 627 * 628 ATAN 629 ST+ X 630 RCL 09 631 - 632 COS 633 RCL 11 634 LASTX 635 SIN 636 P-R 637 RCL Z 638 R-P 639 RDN 640 ST+ 08 641 X<>Y 642 ASIN 643 STO 09 644 RCL 04 645 ST* 03 646 RCL 10 647 COS 648 RCL 03 |
649 * 650 - 651 STO 10 652 P-R 653 RCL 08 654 X<>Y 655 P-R 656 RCL 02 657 ST+ Z 658 CLX 659 RCL 01 660 + 661 R-P 662 X<>Y 663 STO 03 664 RDN 665 R-P 666 STO 05 667 X<>Y 668 STO 04 669 LBL 00 670 RCL 00 671 77 672 / 673 549.4 674 SQRT 675 - 676 RCL 03 677 RCL 04 678 XEQ 10 679 STO 06 680 RCL 12 681 - 682 RCL 14 683 90 684 STO 11 685 ST+ Z 686 - 687 X<> Z 688 STO 07 689 XEQ 10 690 ST- 11 691 X<>Y 692 ENTER 693 COS 694 RCL 05 695 409 696 * 697 / 698 - 699 10 700 RCL Y 701 5 702 + 703 / 704 + 705 TAN 706 1/X 707 59 708 / 709 + 710 X<>Y 711 RCL 11 712 RTN 713 LBL 10 714 SIN 715 X<>Y 716 LASTX 717 COS 718 P-R 719 RDN 720 R-P 721 X<> Z 722 - 723 X<>Y 724 P-R 725 R^ 726 R-P 727 X<>Y 728 RDN 729 R-P 730 * 731 R^ 732 RTN 733 LBL 12 734 210 735 RCL 00 736 * 737 STO 08 738 39 739 LASTX 740 * 741 7 742 - 743 STO 11 744 3035 745 RCL 00 746 * 747 STO 06 748 591 749 LASTX 750 * 751 STO 04 752 + 753 8 754 RCL 00 755 * 756 END |
( 1161 bytes / SIZE 015 )
-Nutation, aberration and time-light are not computed
-Maximum errors with heliocentric longitudes:
Mars: 0°023
Jupiter: 0°021
Saturn: 0°026
Uranus: 0°016
Neptune: 0°019
Pluto: 0°016
-Maximum errors with geocentric longitudes, the Moon: ~ 0°041
-Maximum errors with geocentric latitudes: 0°028
| STACK | INPUTS | OUTPUTS |
| Z | N | h0 = apparent altitude ( deg ) |
| Y | HH.MNSS (UT) | h = true altitude ( deg ) |
| X | DT = TT - UT ( sec) | Az = Azimuth ( deg ) |
N = number of days since 2000/01/01
N ENTER^
HH.MNSS ENTER^
TT - UT XEQ "EPH" returns the azimuthal coordinates of the Sun.
-Then R/S or XEQ 01 gives the coordinates of Mercury
-Then R/S or XEQ 02 ------------------------ Venus
-Then R/S or XEQ 03 ------------------------ the Moon
............................................................................
-Then R/S or XEQ 09 ------------------------- Pluto.
Example: Seattle Longitude = -122°333 Latitude = 47°600
-122.333 STO 13
47.6 STO 14
Date = 2025/12/05 = 9470 since 2000/01/01
Time = 12h41m UT
TT - UT = 69.2 seconds
THE SUN
9470 ENTER^
12.41 ENTER^
69.2 XEQ "EPH"
Az = -88°25 = R11
RDN h = -29°51
RDN h0 = -29°54 ( often meaningless when < 0 )
and R01 = X = -0.27769 AU
R02 = Y = -0.94550
AU
R03 = -106°37 = Geocentric longitude
R06 = -107.75 = right-ascension
R04 = 0 =
Geocentric latitude
R07
= -22.43 = declination
R05 = 0.98543
AU = distance Earth-Sun
-And R12 = local true sidereal time = 9502°486 = 142.486 = 9h499 = 9h29m57s
MERCURY
R/S or XEQ 01 >>>> Az = -78.26
RDN h = -11.24
RDN h0 = -11.31 ( often meaningless when < 0 )
R03 = -126.73 = Geocentric longitude R06 = -128.47 = right-ascension R08 = 148.19 = heliocentric longitude
R04 = 2.50 = Geocentric latitude R07 = -16.16 = declination R09 = 6.90 = heliocentric latitude
R05 = 0.954 AU = distance Earth-Mercury R10 = 0.347 AU = radius vector
VENUS
R/S or XEQ 02 >>>> Az = -83.78
RDN h = -22.88
RDN h0 = -22.92 ( often meaningless when < 0 )
R03 = -114.10 = Geocentric longitude R06 = -115.89 = right-ascension R08 = 235.36 = heliocentric longitude
R04 = 0.53 = Geocentric latitude R07 = -20.76 = declination R09 = 1.25 = heliocentric latitude
R05 = 1.689 AU = distance Earth-Venus R10 = 0.724 AU = radius vector
THE MOON
R/S or XEQ 03 >>>>
Az = 90.85
RDN h
= 38.07
RDN h0
= 38.09
R04 = 4.94 = Geocentric latitude R07 = 28.10 = declination
R05 = 0.002439 AU = distance Earth-Moon
MARS
R/S or XEQ 04 >>>> Az = 265.78
RDN h = -37.08
RDN h0 = -37.11 ( often meaningless when < 0 )
R03 = -97.33 = Geocentric longitude R06 = -98.02 = right-ascension R08 = -91.24 = heliocentric longitude
R04 = -0.70 = Geocentric latitude R07 = -23.93 = declination R09 = -1.16 = heliocentric latitude
R05 = 2.424 AU = distance Earth-Mars R10 = 1.459 AU = radius vector
JUPITER
R/S or XEQ 05 >>>> Az = 48.17
RDN h = 56.35
RDN h0 = 56.36
R03 = 114.22 = Geocentric longitude R06 = 116.15 = right-ascension R08 = 107.14 = heliocentric longitude
R04 = 0.17 = Geocentric latitude R07 = 21.44 = declination R09 = 0.15 = heliocentric latitude
R05 = 4.413 AU = distance Earth-Jupiter R10 = 5.201 AU = radius vector
SATURN
R/S or XEQ 06 >>>> Az = 135.20
RDN h = -37.57
RDN h0 = -37.59 ( often meaningless when < 0 )
R03 = -4.79 = Geocentric longitude R06 = -3.46 = right-ascension R08 = 1.02 = heliocentric longitude
R04 = -2.36 = Geocentric latitude R07 = -4.07 = declination R09 = -2.29 = heliocentric latitude
R05 = 9.287 AU = distance Earth-Saturn R10 = 9.534 AU = radius vector
URANUS
R/S or XEQ 07 >>>> Az = 100.64
RDN h = 17.19
RDN h0 = 17.24
R03 = 58.87 = Geocentric longitude R06 = 56.69 = right-ascension R08 = 59.60 = heliocentric longitude
R04 = -0.20 = Geocentric latitude R07 = 19.71 = declination R09 = -0.19 = heliocentric latitude
R05 = 18.559 AU = distance Earth-Uranus R10 = 19.513 AU = radius vector
NEPTUNE
R/S or XEQ 08 >>>> Az = 133.06
RDN h = -33.65
RDN h0 = -33.68 ( often meaningless when < 0 )
R03 = -0.63 = Geocentric longitude R06 = -0.04 = right-ascension R08 = 1.19 = heliocentric longitude
R04 = -1.35 = Geocentric latitude R07 = -1.49 = declination R09 = -1.34 = heliocentric latitude
R05 = 29.603 AU = distance Earth-Neptune R10 = 29.885 AU = radius vector
PLUTO
R/S or XEQ 09 >>>> Az = 215.73
RDN h = -62.11
RDN h0 = -62.12 ( often meaningless when < 0 )
R03 = -57.99 = Geocentric longitude R06 = -54.82 = right-ascension R08 = -56.80 = heliocentric longitude
R04 = -3.76 = Geocentric latitude R07 = -23.37 = declination R09 = -3.83 = heliocentric latitude
R05 = 36.053 AU = distance Earth-Pluto R10 = 35.408 AU = radius vector