Overview
-This program calculates the coordinates x and y of the first 7 satellites
of Saturn, namely:
1 = Mimas
3 = Tethys 5 = Rhea 7 = Hyperion
2 = Enceladus 4 = Dione
6 = Titan
-The x-axis coincides with the equator of the planet.
-The center of Saturn is the origin and x , y are measured in units
of Saturn's equatorial radius ( the polar radius of Saturn is 0.895
).
y ( North )
|
|
|
( East ) --------------Saturn------------------ x ( West
)
|
|
( South )
Data Registers: R00 thru R14 are used for temporay data storage and when the program stops:
Mimas - Enceladus - Tethys - Dione - Rhea - Titan - Hyperion
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
Flags: F01 F02
F03 F04 F05 F06 F07
-Flag nn is set when the distance Earth-Satellite n is shorter
than the distance Earth-Saturn ( 0 < nn < 8 )
Subroutine: none if you have a Time
Module
"J0" otherwise .( cf for instance "Phases of the Moon for the
HP-41" )
Program listing
-If you have a Time module, replace lines 07-08 by
the 3 lines 1.012 DDAYS
-
-If you don't have an HP-41 CX , replace lines 187-188 by CF
01 CF 02 CF 03 CF 04 CF 05 CF 06 CF
07
| 01 LBL "METDRTH"
02 DEG 03 HR 04 24 05 / 06 X<>Y 07 XEQ "J0" 08 + 09 E6 10 / 11 STO 00 12 985600 13 * 14 2.96 15 - 16 STO 01 17 SIN 18 1.92 19 * 20 RCL 01 21 ST+ X 22 SIN 23 50 24 / 25 + 26 STO 02 27 RCL 00 28 33444 29 * 30 43 31 - 32 STO 03 33 SIN 34 636 35 * 36 RCL 03 37 ST+ X 38 SIN 39 22 40 * 41 + 42 RCL 00 43 1116 44 * 45 7 46 - 47 SIN 48 81 49 * 50 + 51 RCL 00 52 32344 53 * 54 60 55 - 56 STO 06 57 SIN 58 23 59 * 60 - 61 RCL 00 62 34576 63 * 64 50 65 - 66 SIN 67 5 68 * 69 + 70 RCL 00 71 16172 72 * 73 76 74 - 75 SIN 76 12 77 * 78 - 79 E2 80 / 81 STO 04 82 - 83 RCL 00 84 952149 85 * 86 + 87 49.91 88 + 89 STO 05 90 1 91 RCL 01 92 ST+ 02 93 COS 94 60 95 / 96 - |
97 9.57
98 RCL 03 99 COS 100 .53 101 * 102 - 103 RCL 03 104 ST+ 04 105 ST+ X 106 COS 107 68 108 / 109 - 110 RCL 06 111 COS 112 53 113 / 114 + 115 STO 06 116 X^2 117 LASTX 118 R^ 119 * 120 ST+ X 121 RCL 05 122 COS 123 * 124 - 125 X<>Y 126 X^2 127 + 128 SQRT 129 STO 01 130 / 131 RCL 05 132 SIN 133 * 134 ASIN 135 RCL 05 136 + 137 RCL 02 138 - 139 23.41 140 - 141 RCL 00 142 9 143 * 144 - 145 STO 02 146 COS 147 28.05 148 STO 07 149 SIN 150 STO 05 151 * 152 RCL 04 153 30 154 RCL 00 155 * 156 + 157 20.61 158 - 159 SIN 160 23 161 / 162 RCL 06 163 * 164 RCL 01 165 / 166 ST* 05 167 RCL 07 168 COS 169 STO 03 170 * 171 + 172 X<> 02 173 1 174 P-R 175 CHS 176 RCL 03 177 * 178 RCL 05 179 + 180 X<>Y 181 R-P 182 X<>Y 183 X<> 01 184 173 E6 185 / 186 ST- 00 187 CLX 188 X<> F 189 16919949 190 RCL 00 191 * 192 240.7 |
193 +
194 562103 195 RCL 00 196 * 197 76.9 198 - 199 STO 10 200 SIN 201 9.12 202 * 203 - 204 29.9 205 RCL 00 206 52548 207 * 208 - 209 STO 12 210 RCL 10 211 + 212 SIN 213 .23 214 * 215 - 216 RCL 10 217 RCL 12 218 - 219 SIN 220 .21 221 * 222 + 223 RCL 00 224 5657028 225 * 226 76.2 227 + 228 STO 09 229 SIN 230 9 231 / 232 + 233 RCL 10 234 RCL 09 235 - 236 SIN 237 RCL 12 238 SIN 239 + 240 11 241 / 242 - 243 RCL 09 244 ST+ X 245 SIN 246 7 247 / 248 + 249 RCL 09 250 3 251 * 252 SIN 253 RCL 09 254 RCL 10 255 + 256 SIN 257 - 258 15 259 / 260 + 261 RCL 09 262 4 263 * 264 SIN 265 25 266 / 267 + 268 STO 08 269 13.84 270 RCL 00 271 51135 272 * 273 - 274 STO 07 275 206 276 P-R 277 RCL 07 278 RCL 12 279 - 280 STO 06 281 49 282 P-R 283 X<>Y 284 ST+ T 285 RDN 286 + 287 RCL 07 288 RCL 10 |
289 +
290 5 291 P-R 292 X<>Y 293 ST+ T 294 RDN 295 + 296 RCL 07 297 RCL 10 298 - 299 3 300 P-R 301 X<>Y 302 ST+ T 303 RDN 304 + 305 RCL 07 306 RCL 09 307 + 308 2 309 P-R 310 X<>Y 311 ST- T 312 RDN 313 - 314 RCL 07 315 RCL 09 316 - 317 2 318 SQRT 319 P-R 320 X<>Y 321 ST+ T 322 RDN 323 + 324 R-P 325 2 E3 326 / 327 STO 13 328 RCL 08 329 ENTER^ 330 R^ 331 - 332 STO 11 333 SIN 334 ST+ X 335 R^ 336 ST* Y 337 X^2 338 5 339 * 340 4 341 / 342 RCL 11 343 ST+ X 344 SIN 345 * 346 - 347 R-D 348 - 349 RCL 01 350 + 351 RCL 13 352 X^2 353 2 354 / 355 1 356 RCL 11 357 ST+ X 358 COS 359 - 360 * 361 RCL 11 362 COS 363 RCL 13 364 * 365 + 366 24.57 367 ST* Y 368 + 369 P-R 370 X>0? 371 SF 07 372 RCL 02 373 * 374 STO 14 375 X<>Y 376 STO 13 377 RCL 00 378 22576976 379 * 380 43.62 381 - 382 79 383 RCL 00 384 302 |
385 *
386 + 387 SIN 388 12 389 / 390 - 391 STO Y 392 RCL 06 393 - 394 STO 10 395 SIN 396 3.31 397 * 398 - 399 RCL 10 400 ST+ X 401 SIN 402 17 403 / 404 + 405 RCL 01 406 + 407 20.29 408 RCL 10 409 COS 410 .59 411 * 412 + 413 P-R 414 X>0? 415 SF 06 416 RCL 02 417 * 418 STO 12 419 X<>Y 420 STO 11 421 79690048 422 RCL 00 423 * 424 27.59 425 - 426 RCL 01 427 + 428 8.75 429 P-R 430 X>0? 431 SF 05 432 RCL 02 433 * 434 STO 10 435 X<>Y 436 STO 09 437 131534932 438 RCL 00 439 * 440 71.19 441 + 442 5 443 RCL 00 444 84305 445 * 446 - 447 + 448 SIN 449 4 450 / 451 - 452 RCL 01 453 + 454 6.27 455 P-R 456 X>0? 457 SF 04 458 RCL 02 459 * 460 STO 08 461 X<>Y 462 STO 07 463 190697912 464 RCL 00 465 * 466 53.08 467 + 468 38.6 469 RCL 00 470 13968 471 * 472 - 473 STO 03 474 SIN 475 43.4 476 * 477 RCL 03 478 3 479 * 480 SIN |
481 .71
482 * 483 + 484 STO 03 485 21 486 / 487 - 488 RCL 01 489 + 490 4.89 491 P-R 492 X>0? 493 SF 03 494 RCL 02 495 * 496 STO 06 497 X<>Y 498 STO 05 499 262731903 500 RCL 00 501 * 502 11 503 + 504 RCL 00 505 88773 506 * 507 63 508 + 509 SIN 510 4 511 / 512 + 513 RCL 00 514 253657 515 * 516 44 517 - 518 SIN 519 5 520 / 521 + 522 49 523 RCL 00 524 337962 525 * 526 - 527 + 528 SIN 529 .55 530 * 531 - 532 RCL 01 533 + 534 3.95 535 P-R 536 X>0? 537 SF 02 538 RCL 02 539 * 540 STO 04 541 X<>Y 542 X<> 03 543 70.74 544 - 545 RCL 00 546 381994499 547 * 548 + 549 78.4 550 RCL 00 551 1000772 552 * 553 - 554 + 555 STO 00 556 SIN 557 2.31 558 * 559 - 560 RCL 01 561 + 562 3.08 563 RCL 00 564 COS 565 16 566 / 567 + 568 P-R 569 X>0? 570 SF 01 571 RCL 02 572 * 573 STO 02 574 X<>Y 575 STO 01 576 END |
( 909 bytes / SIZE 015 )
| STACK | INPUTS | OUTPUTS |
| Y | YYYY.MNDD | y1 |
| X | HH.MNSS(TT) | x1 |
| L | / | -sin LE |
where LE is the saturnicentric latitude of the Earth. ---Execution time = 67s---
Example1: On 2005 July 1st at 0h12m34s TT
2005.0701 ENTER^
0.1234
XEQ "METDRTH" >>>> x1 = 1.58
X<>Y y1 = 1.01
and in registers R01 thru R14:
Mimas - Enceladus - Tethys - Dione - Rhea - Titan - Hyperion
x1 = 1.58 x2
= 2.10 x3
= 2.25 x4
= 0.59 x5 = 2.12
x6 = 6.91
x7 = -20.00
y1 = 1.01 y2
= 1.24 y3
= -1.62 y4 = -2.32
y5 = 3.16 y6
= -7.23 y7
= -5.32
-Flags F01 F02 F05 are set, whence Mimas; Enceladus and Rhea are closer to the Earth than Saturn.
Example2: Every 15 years, the Earth is approximately in the plane of the rings. For instance on 1995/09/18 at 0h20m TT we find:
x4 = 0.00 with
flag F04 set: Dione is
in transit over the planet's disk
y4 = -0.14
Notes:
-This program uses a simplified method where the inclinations of the
orbits of the satellites on the equatorial plane of Saturn have been neglected.
( 1.5° - 0° - 1.9° - 0° - 0.4°
- 0.3° - 0.4° from Mimas to Hyperion respectively
)
-Therefore, the satellite phenomena ( occultations, transits ... etc
... ) can't always be determined with certainty.
-However, the most important perturbations have been taken into account
and the satellites may usually be identified.
-y-values are less accurate than x-values.
-The coordinates of Hyperion are less accurate than the other ones.
-If you don't want to compute the position of Hyperion, replace lines
391-392-393 ( STO Y RCL 06 - ) by
16.1 RCL 00 1412
* - + and delete lines 189 thru
376
References: More complete series may be found in
[1] A. Vienne and L. Duriez 1995 "TASS1.6:
Ephemerides of the major Saturnian Satellites" Astronomy & Astrophysics
297 , 588-605
[2] L. Duriez and A. Vienne 1997 "Theory of motion and
Ephemerides of Hyperion" Astronomy & Astrophysics 324 ,
366-380