Overview
0°) 4 Subroutines: "L"
"N" "O" "K"
1°) The Sun
2°) The Moon
3°) Mercury
4°) Venus
5°) Mars
6°) Jupiter
7°) Saturn
8°) Uranus
9°) Neptune
10°) Pluto
-The programs listed in "Astronomical Ephemeris for the HP-41" give
a good accuracy
( about 0.01° in the heliocentric longitudes ) over
the time span [1000,3000]
-In this page, the same accuracy is obtained over the interval [0,4000]
( except for Pluto whose coordinates are accurate between 1880
and 2110 only )
-The same method is used: we first solve Kepler's equation and then,
a few perturbations are added.
-But of course, more terms have been taken into account ( Fourier &
Poisson series )
-This precision of the order of 0.01° is probably achieved
over [-1000,5000] for the Sun, Mercury and Venus.
-But for Jupiter, Saturn and Uranus - even between 0 and 4000 - errors
may sometimes slightly exceed 0.01°
-The precision of the Moon's coordinates is more doubtful outside [1000-3000].
-The instructions are identical, except that the unit of time is 2000
Julian years ( from 2000/01/01 0h TT )
-The effects of nutation and aberration have been neglected and all
the coordinates are referred to the mean ecliptic and equinox of the date.
-For the Sun and the planets - except Pluto - these programs employ
the series VSOP87D
with improvements from the new theories VSOP09 & TOP2010
for Uranus and Neptune.
DATA REGISTERS:
-Registers R00 thru R15 are used by every program.
R00 = T = time since 2000/01/01 0h TT is to be initialized before
executing any program ( Unit = 2000 years = 730500
days )
R01 and R02 contain the Sun's rectangular ecliptic coordinates.
They are calculated and stored by the "SUN" program which must be executed
first.
R03 = geocentric longitude in decimal degrees
R04 = geocentric latitude ------------------
R05 = distance to the Earth in Astronomical Units ( except for
the Moon: R05 = the Moon's parallax in sexagesimal degrees )
R06 = Right Ascension in hh.mnss
R07 = Declination in ° ' ''
R08 = heliocentric longitude in decimal degrees (
except for the Sun and the Moon )
R09 = heliocentric latitude -------------------
---------------------------------
R10 = radius vector in Astronomical Units
---------------------------------
-Registers are also used for temporary data storage, for instance:
R05 thru R10 contain the mean elements of the planets: semi-major
axis, eccentricity, inclination,
mean longitude, longitude of perihelion, longitude of the ascending node.
R03 , R04 , R11 contain the perturbations in longitude, radius
vector and latitude respectively.
| STACK | INPUTS | OUTPUTS |
| T | / | elongation from the Sun* ( deg ) |
| Z | / | distance to the earth** ( AU ) |
| Y | / | declination ( ° ' '' ) |
| X | / | right ascension ( hh.mnss ) |
* except for the Sun
** or Moon's parallax ( ° ' " )
-The following routine may be used to store T in R00
-Line 06 may be replaced by XEQ "J1" or XEQ "J2"
( cf "Julian & Gregorian Calendar" )
| 01 LBL "TT"
02 HR 03 24 04 / 05 X<>Y 06 XEQ "J0" 07 + 08 730500 09 / 10 STO 00 11 END |
-For example: 5000/01/23 at 0h TT
5000.0123 ENTER^
0
XEQ "TT" >>>> T = R00 = 1.5
>>>> The HP-41 must be set in DEG mode.
0°) 4 Subroutines: "L" "N"
"O" "K"
-LBL 00 solves Kepler's Equation
-Line 97 is used for the Moon only
-LBL 01 = Spherical-Rectangular conversion
-LBL 02 = Rectangular-Spherical conversion
| 01 LBL "L"
02 + 03 E3 04 ST/ 03 05 ST/ 04 06 ST/ 07 07 ST/ 09 08 ST/ 11 09 / 10 STO 10 11 E5 12 ST/ 06 13 9 14 STO 15 15 RCL 08 16 360 17 MOD 18 27.942 19 RCL 00 20 * 21 + 22 RCL 09 23 - 24 ENTER^ 25 ENTER^ 26 LBL 00 27 SIN 28 RCL 06 29 R-D 30 * 31 + 32 DSE 15 33 GTO 00 34 2 35 / 36 1 37 RCL 06 38 + 39 1 40 LASTX 41 - 42 / 43 SQRT 44 P-R 45 LASTX |
46 /
47 R-P 48 RDN 49 ST+ X 50 1 51 R^ 52 ST+ X 53 COS 54 RCL 06 55 * 56 - 57 RCL 05 58 * 59 RCL 04 60 + 61 X<> 10 62 STO 04 63 - 64 RCL 09 65 + 66 COS 67 RCL 07 68 LASTX 69 SIN 70 P-R 71 X<>Y 72 ASIN 73 RCL 11 74 + 75 STO 09 76 X<> Z 77 R-P 78 CLX 79 RCL 04 80 + 81 RCL 03 82 + 83 STO 08 84 RCL 10 85 XEQ 01 86 RCL 02 87 ST+ Z 88 CLX 89 RCL 01 90 + |
91 XEQ 02
92 STO 05 93 RDN 94 STO 03 95 X<>Y 96 STO 04 97 LBL "N" 98 RCL 00 99 15 100 / 101 X^2 102 .2602 103 - 104 RCL 00 105 * 106 23.4393 107 + 108 CHS 109 RCL 04 110 RCL 03 111 RCL 05 112 XEQ 01 113 RDN 114 R-P 115 X<> Z 116 ST- Y 117 X<> Z 118 P-R 119 R^ 120 XEQ 02 121 CLX 122 15 123 / 124 24 125 MOD 126 RCL 02 127 RCL 01 128 R-P 129 CLX 130 RCL 03 131 - 132 COS 133 RCL 04 134 COS 135 * |
136 ACOS
137 RCL 05 138 R^ 139 HMS 140 STO 07 141 R^ 142 HMS 143 STO 06 144 RTN 145 LBL 01 146 X<>Y 147 RDN 148 P-R 149 R^ 150 X<>Y 151 P-R 152 RTN 153 LBL 02 154 R-P 155 X<>Y 156 RDN 157 R-P 158 R^ 159 X<>Y 160 RTN 161 LBL "O" 162 XEQ "K" 163 CLX 164 STO 04 165 STO 11 166 8905342.229 167 RCL 00 168 .708 169 * 170 - 171 RCL 00 172 * 173 68.245 174 - 175 STO 13 176 ST+ X 177 STO 14 178 1170356.317 179 RCL 00 180 * |
181 181.179
182 + 183 STO 07 184 719987.453 185 RCL 00 186 * 187 80.027 188 - 189 STO 08 190 - 191 STO 12 192 LASTX 193 382805.985 194 RCL 00 195 * 196 4.829 197 - 198 STO 09 199 ST+ X 200 - 201 4 202 * 203 RCL 05 204 3 205 * 206 + 207 STO 10 208 RTN 209 LBL "K" 210 60698.113 211 RCL 00 212 * 213 34.31 214 + 215 STO 05 216 24442.279 217 RCL 00 218 * 219 50.061 220 + 221 STO 06 222 - 223 STO 10 224 LASTX 225 - |
226 STO 11
227 RCL 10 228 + 229 STO 12 230 RCL 06 231 ST+ X 232 - 233 STO 09 234 ST+ X 235 STO 03 236 8569.345 237 RCL 00 238 * 239 45.955 240 - 241 STO 07 242 4369.712 243 RCL 00 244 * 245 55.654 246 - 247 STO 08 248 - 249 STO 14 250 LASTX 251 - 252 STO 15 253 RCL 06 254 RCL 07 255 3 256 * 257 - 258 STO 04 259 LASTX 260 RCL 09 261 RCL 06 262 - 263 + 264 STO 13 265 RCL 09 266 END |
( 446 bytes / SIZE 016 )
1°) The Sun
| 01 LBL "SUN"
02 XEQ "O" 03 COS 04 RCL 08 05 RCL 05 06 - 07 STO 03 08 SIN 09 + 10 RCL 13 11 SIN 12 + 13 ST+ X 14 RCL 12 15 SIN 16 LASTX 17 ST+ X 18 SIN 19 + 20 2 |
21 SQRT
22 * 23 - 24 RCL 03 25 ST+ X 26 SIN 27 RCL 05 28 SIN 29 - 30 2 31 SQRT 32 / 33 + 34 STO 03 35 RCL 13 36 COS 37 PI 38 % 39 RCL 08 40 RCL 05 |
41 -
42 COS 43 61 44 / 45 - 46 RCL 12 47 ST+ X 48 COS 49 63 50 / 51 + 52 STO 04 53 RCL 00 54 34389 55 RCL 00 56 183 57 * 58 + 59 * 60 77063 |
61 -
62 STO 09 63 CLX 64 5 65 * 66 84 67 + 68 * 69 CHS 70 1671 71 + 72 STO 06 73 SIGN 74 STO 05 75 RDN 76 X^2 77 CHS 78 121 79 + 80 * |
81 *
82 E3 83 / 84 ST+ 08 85 CLST 86 STO 01 87 STO 02 88 STO 07 89 XEQ "L" 90 RCL 03 91 RCL 05 92 P-R 93 STO 01 94 X<>Y 95 STO 02 96 RCL 05 97 RCL 07 98 RCL 06 99 END |
( 135 bytes / SIZE 016 )
| STACK | INPUTS | OUTPUTS |
| Z | / | distance to the earth ( AU ) |
| Y | / | declination ( ° ' '' ) |
| X | / | right ascension ( hh.mnss ) |
Example: T = 1.5 ( 5000/01/23
0h TT ) 1.5
STO 00
XEQ "SUN" >>>> R.A. = 20h18m22s
= R06
R03 = l = -57.604° = 302.396°
Ecliptic Longitude
RDN Decl = -19°18'60" = -19°19'00" = R07
and R04 = b = 0°
Ecliptic Latitude is always 0°
RDN r = 0.986964
= R05
and the rectangular ecliptic coordinates of the Sun:
R01 = X = 0.528784 UA
R02 = Y = -0.833359 UA
2°) The Moon
| 01 LBL "MO"
02 XEQ "O" 03 RCL 00 04 6.451 05 RCL 00 06 .061 07 * 08 + 09 * 10 77.063 11 - 12 ST- 08 13 CLX 14 11 15 * 16 CHS 17 115 18 + 19 * 20 3542 21 + 22 * 23 9543977351 24 + 25 * 26 128341 27 + 28 E3 29 / 30 STO 07 31 ST+ X 32 STO 12 33 RDN 34 ST+X 35 1417 36 + 37 * 38 9664040349 39 - 40 * 41 86657 42 - 43 E3 44 / 45 STO 09 46 ST+ X 47 STO 06 48 6036 49 RCL 14 50 RCL 07 51 - 52 STO 03 53 COS 54 58 55 * 56 - 57 RCL 14 58 COS 59 46 60 * 61 - 62 RCL 12 63 COS 64 9 65 * 66 - 67 RCL 14 68 RCL 12 69 - 70 STO 15 71 COS 72 RCL 07 73 COS 74 82 75 * 76 - 77 4 78 * 79 + 80 RCL 14 81 RCL 08 82 - |
83 STO 11
84 COS 85 RCL 07 86 RCL 14 87 + 88 STO 10 89 COS 90 + 91 3 92 * 93 - 94 1 95 % 96 1/X 97 ASIN 98 HMS 99 STO 05 100 RCL 07 101 RCL 09 102 - 103 SIN 104 281 105 * 106 RCL07 107 RCL 09 108 + 109 SIN 110 278 111 * 112 + 113 RCL 09 114 RCL 14 115 + 116 STO 04 117 SIN 118 173 119 * 120 + 121 RCL 03 122 RCL 09 123 - 124 SIN 125 55 126 * 127 + 128 RCL 03 129 RCL 09 130 + 131 SIN 132 46 133 * 134 + 135 RCL 14 136 RCL 09 137 - 138 SIN 139 33 140 * 141 + 142 RCL 12 143 RCL 09 144 - 145 SIN 146 17 147 * 148 + 149 RCL 09 150 RCL 10 151 + 152 SIN 153 RCL 09 154 RCL 12 155 + 156 SIN 157 + 158 9 159 * 160 + 161 RCL 09 162 RCL 11 163 + 164 SIN |
165 RCL 09
166 SIN 167 641 168 * 169 - 170 8 171 * 172 + 173 RCL 09 174 RCL 15 175 + 176 SIN 177 RCL 10 178 RCL 09 179 - 180 SIN 181 + 182 4 183 * 184 + 185 RCL 04 186 RCL 08 187 + 188 SIN 189 3 190 * 191 - 192 RCL 11 193 RCL 09 194 - 195 STO 04 196 RCL 07 197 - 198 SIN 199 LASTX 200 RCL 06 201 + 202 SIN 203 + 204 RCL 04 205 SIN 206 + 207 RCL 09 208 RCL 07 209 - 210 STO 04 211 RCL 08 212 + 213 SIN 214 - 215 RCL 04 216 RCL 14 217 ST+ X 218 + 219 SIN 220 + 221 RCL 08 222 RCL 09 223 - 224 SIN 225 - 226 RCL 06 227 RCL 09 228 + 229 SIN 230 + 231 ST+ X 232 + 233 STO 04 234 RCL 03 235 RCL 08 236 - 237 SIN 238 57 239 * 240 RCL 08 241 SIN 242 185 243 * 244 - 245 RCL 11 246 SIN |
247 46
248 * 249 + 250 RCL 08 251 RCL 07 252 - 253 SIN 254 41 255 * 256 - 257 RCL 07 258 RCL 08 259 + 260 SIN 261 30 262 * 263 - 264 RCL 03 265 RCL 08 266 + 267 SIN 268 8 269 * 270 - 271 RCL 08 272 RCL 14 273 + 274 SIN 275 7 276 * 277 - 278 1 279 RCL 00 280 20 281 / 282 - 283 * 284 RCL 07 285 SIN 286 6289 287 * 288 + 289 RCL 14 290 SIN 291 658 292 * 293 + 294 RCL 12 295 SIN 296 214 297 * 298 + 299 RCL 06 300 SIN 301 114 302 * 303 + 304 RCL 15 305 SIN 306 59 307 * 308 + 309 RCL 10 310 SIN 311 53 312 * 313 + 314 RCL 03 315 SIN 316 98 317 * 318 RCL 07 319 RCL 06 320 - 321 SIN 322 - 323 13 324 * 325 + 326 RCL 06 327 RCL 07 328 + |
329 SIN
330 RCL 14 331 ST+ X 332 RCL 07 333 - 334 SIN 335 + 336 11 337 * 338 + 339 RCL 03 340 ST+ X 341 SIN 342 9 343 * 344 + 345 RCL 13 346 SIN 347 7 348 * 349 RCL 06 350 RCL 14 351 + 352 SIN 353 3 354 * 355 - 356 RCL 07 357 RCL 12 358 + 359 SIN 360 ST+ X 361 - 362 RCL 13 363 RCL 07 364 - 365 SIN 366 + 367 RCL 08 368 RCL 13 369 + 370 SIN 371 - 372 5 373 * 374 - 375 RCL 10 376 RCL 08 377 - 378 SIN 379 RCL 12 380 RCL 14 381 + 382 SIN 383 + 384 RCL 14 385 ST+ X 386 SIN 387 + 388 RCL 03 389 RCL 12 390 - 391 SIN 392 + 393 RCL 00 394 46 395 * 396 1 397 - 398 R-D 399 SIN 400 - 401 4 402 * 403 + 404 RCL 08 405 RCL 12 406 - 407 SIN 408 RCL 03 409 RCL 06 410 - |
411 SIN
412 + 413 3 414 * 415 - 416 RCL 11 417 RCL 08 418 - 419 SIN 420 LASTX 421 RCL 07 422 - 423 SIN 424 + 425 RCL 11 426 RCL 12 427 - 428 SIN 429 + 430 RCL 07 431 RCL 13 432 + 433 SIN 434 - 435 RCL 08 436 RCL 12 437 + 438 SIN 439 - 440 RCL 08 441 ST+ X 442 SIN 443 - 444 RCL 06 445 RCL 10 446 + 447 SIN 448 - 449 RCL 14 450 RCL 06 451 - 452 SIN 453 - 454 RCL 00 455 ENTER^ 456 + 457 CHS 458 15 459 + 460 RCL 00 461 * 462 631 463 - 464 RCL 00 465 * 466 9625357624 467 + 468 RCL 00 469 * 470 211728 471 + 472 E3 473 / 474 360 475 MOD 476 SIN 477 ST+ X 478 ST- 04 479 X<> L 480 STO 03 481 RCL 09 482 + 483 SIN 484 + 485 ST+ X 486 + 487 E3 488 ST/ 04 489 / 490 ST+ 03 491 XEQ "N" 492 END |
( 631 bytes / SIZE 016 )
| STACK | INPUTS | OUTPUTS |
| T | / | elongation from the Sun* ( deg ) |
| Z | / | Moon's parallax ( ° ' '' ) |
| Y | / | declination ( ° ' '' ) |
| X | / | right ascension ( hh.mnss ) |
Example: T = 1.5 ( 5000/01/23
0h TT )
( geocentric )
XEQ "MO" >>>> R.A. = 5h28m58s = R06
R03 = l = 82.940°
RDN Decl = 24°30'13" = R07
R04 = b = 1.627°
RDN Paral = 1°00'38" = R05
RDN Elong = 140.52°
3°) Mercury
| 01 LBL "ME"
02 RCL 00 03 127125 04 * 05 87 06 + 07 COS 08 ST+ X 09 STO 03 10 CLX 11 STO 04 |
12 STO 11
13 .3871 14 STO 05 15 RCL 00 16 36 17 RCL 00 18 7 19 * 20 - 21 * 22 7005 |
23 +
24 STO 07 25 RDN 26 X^2 27 CHS 28 121 29 + 30 * 31 2989453501 32 + 33 * |
34 250205
35 + 36 E3 37 / 38 STO 08 39 RDN 40 CHS 41 41 42 + 43 * 44 20563 |
45 +
46 STO 06 47 CLX 48 118 49 * 50 31128 51 + 52 * 53 77456 54 + 55 STO 09 |
56 RDN
57 ST+ X 58 70 59 + 60 * 61 23722 62 + 63 * 64 48331 65 XEQ "L" 66 END |
( 132 bytes / SIZE 016 )
| STACK | INPUTS | OUTPUTS |
| T | / | elongation from the Sun ( deg ) |
| Z | / | distance to the earth ( AU ) |
| Y | / | declination ( ° ' '' ) |
| X | / | right ascension ( hh.mnss ) |
Example: T = 1.5 ( 5000/01/23
0h TT )
( geocentric )
( heliocentric )
XEQ "ME" >>>> R.A. = 20h29m40s = R06
R03 = l = -55.257° = 304.743°
R08 = L = -50.267° = 309.733°
RDN Decl = -20°21'19" = R07
R04 = b = -1.623°
R09 = B = -5.049°
RDN r = 1.4495
UA = R05
R10 = R = 0.46636 UA
RDN Elong = 2.85°
4°) Venus
| 01 LBL "VE"
02 XEQ "O" 03 RCL 12 04 SIN 05 2 06 SQRT 07 * 08 RCL 12 09 3 10 * 11 SIN 12 ST+ X 13 - 14 RCL 12 15 ST+ X 16 SIN |
17 PI
18 * 19 - 20 STO 03 21 .72333 22 STO 05 23 RCL 00 24 96 25 CHS 26 RCL 00 27 4 28 * 29 + 30 * 31 677 32 + |
33 STO 06
34 CLX 35 4 36 * 37 CHS 38 45 39 - 40 * 41 430 42 - 43 * 44 28043 45 + 46 * 47 131564 48 + |
49 STO 09
50 RDN 51 X^2 52 CHS 53 124 54 + 55 * 56 * 57 E3 58 / 59 RCL 07 60 + 61 STO 08 62 CLX 63 20 64 * |
65 3395
66 + 67 STO 07 68 CLX 69 162 70 * 71 18021 72 + 73 * 74 76680 75 XEQ "L" 76 END |
( 126 bytes / SIZE 016 )
| STACK | INPUTS | OUTPUTS |
| T | / | elongation from the Sun* ( deg ) |
| Z | / | distance to the earth** ( AU ) |
| Y | / | declination ( ° ' '' ) |
| X | / | right ascension ( hh.mnss ) |
Example: T = 1.5 ( 5000/01/23
0h TT )
( geocentric )
( heliocentric )
XEQ "VE" >>>> R.A. = 22h50m30s =
R06
R03 = l = -19.568° = 340.432°
R08 = L = 37.443°
RDN Decl = -9°20'44" = R07
R04 = b = -1.946°
R09 = B = -3.145°
RDN r = 1.1728
UA = R05
R10 = R = 0.7261 UA
RDN Elong = 38.08°
5°) Mars
| 01 LBL "MA"
02 XEQ "O" 03 5 04 P-R 05 3 06 * 07 - 08 RCL 10 09 SIN 10 4 11 * 12 RCL 00 13 * 14 + 15 RCL 09 16 RCL 05 17 - 18 STO 13 19 SIN 20 7 21 * 22 - 23 RCL 13 24 RCL 05 25 - |
26 5
27 P-R 28 2 29 / 30 - 31 + 32 RCL 07 33 ST+ X 34 RCL 13 35 7 36 * 37 - 38 RCL 05 39 + 40 RCL 06 41 6 42 * 43 - 44 3.6 45 P-R 46 - 47 + 48 RCL 08 49 RCL 09 50 - |
51 STO 14
52 LASTX 53 - 54 STO 15 55 3 56 P-R 57 - 58 - 59 RCL 13 60 ST+ X 61 SIN 62 4 63 * 64 + 65 RCL 14 66 RCL 15 67 + 68 SIN 69 RCL 14 70 SIN 71 - 72 ST+ X 73 + 74 RCL 09 75 3 |
76 *
77 RCL 07 78 - 79 COS 80 RCL 03 81 2 82 / 83 RCL 10 84 ST+ X 85 - 86 COS 87 + 88 RCL 10 89 RCL 09 90 - 91 COS 92 + 93 2 94 SQRT 95 * 96 - 97 STO 03 98 1.5237 99 STO 05 100 RCL 00 |
101 RCL 09
102 RCL 00 103 X^2 104 .124 105 * 106 + 107 STO 08 108 CLX 109 PI 110 * 111 CHS 112 181 113 + 114 * 115 9340 116 + 117 STO 06 118 CLX 119 4 120 * 121 54 122 + 123 * 124 36819 125 + |
126 *
127 23940 128 - 129 STO 09 130 CLX 131 5 132 * 133 12 134 - 135 * 136 1850 137 + 138 STO 07 139 CLX 140 18 141 * 142 6 143 + 144 * 145 15440 146 + 147 * 148 49558 149 XEQ "L" 150 END |
( 202 bytes / SIZE 016 )
| STACK | INPUTS | OUTPUTS |
| T | / | elongation from the Sun* ( deg ) |
| Z | / | distance to the earth** ( AU ) |
| Y | / | declination ( ° ' '' ) |
| X | / | right ascension ( hh.mnss ) |
Example: T = 1.5 ( 5000/01/23
0h TT )
( geocentric )
( heliocentric )
XEQ "MA" >>>> R.A. = 0h33m15s =
R06
R03 = l = 8.729°
R08 = L = 49.535°
RDN Decl = 2°45'57"
= R07
R04 = b = -0.697°
R09 = B = -0.728°
RDN r = 1.4433
UA = R05
R10 = R = 1.3834 UA
RDN Elong = 66.34°
6°) Jupiter
| 01 LBL "JU"
02 XEQ "K" 03 4 04 P-R 05 + 06 CHS 07 RCL 00 08 * 09 RCL 09 10 16 11 P-R 12 6 13 SQRT 14 SQRT 15 * 16 - 17 - 18 RCL 00 19 * 20 RCL 09 21 99 22 P-R 23 5 24 SQRT 25 / 26 + 27 + 28 RCL 05 29 RCL 09 30 + 31 STO 08 32 PI 33 P-R 34 ST+ X 35 - 36 + 37 RCL 09 38 RCL 05 39 - 40 STO 07 41 6 42 P-R 43 2 44 / 45 + 46 + 47 RCL 03 48 3 49 P-R 50 4 51 LN 52 / |
53 +
54 - 55 RCL 00 56 * 57 RCL 09 58 74 59 P-R 60 3.4 61 * 62 - 63 + 64 RCL 08 65 23 66 P-R 67 6 68 / 69 + 70 - 71 RCL 11 72 5 73 P-R 74 + 75 + 76 RCL 12 77 5 78 P-R 79 .8 80 * 81 + 82 + 83 RCL 07 84 6 85 P-R 86 ST+ X 87 - 88 + 89 RCL 06 90 RCL 09 91 + 92 SIN 93 6 94 SQRT 95 * 96 - 97 RCL 03 98 2 99 P-R 100 ST+ X 101 - 102 - 103 RCL 00 104 * |
105 RCL 09
106 325 107 P-R 108 9 109 D-R 110 * 111 + 112 - 113 RCL 10 114 ST+ X 115 STO 14 116 SIN 117 56 118 * 119 + 120 RCL 08 121 3 122 P-R 123 14 124 * 125 + 126 + 127 RCL 11 128 36 129 P-R 130 6 131 / 132 - 133 + 134 RCL 12 135 12 136 P-R 137 5 138 LN 139 * 140 - 141 + 142 RCL 10 143 SIN 144 22 145 * 146 - 147 RCL 07 148 15 149 P-R 150 5 151 SQRT 152 / 153 + 154 - 155 RCL 11 156 ST+ X |
157 2
158 P-R 159 ST+ X 160 + 161 + 162 RCL 10 163 RCL 14 164 + 165 SIN 166 5 167 * 168 + 169 RCL 10 170 RCL 12 171 + 172 2 173 P-R 174 ST+ X 175 - 176 - 177 RCL 06 178 7 179 SQRT 180 P-R 181 + 182 + 183 RCL 05 184 RCL 14 185 + 186 SIN 187 RCL 12 188 RCL 14 189 + 190 COS 191 + 192 RCL 13 193 SIN 194 + 195 RCL 03 196 SIN 197 + 198 3 199 * 200 + 201 RCL 11 202 RCL 06 203 - 204 2 205 P-R 206 - 207 - 208 STO 03 |
209 RCL 08
210 2 211 P-R 212 LASTX 213 / 214 RCL 00 215 * 216 + 217 RCL 14 218 COS 219 3 220 * 221 - 222 RCL 12 223 SIN 224 - 225 RCL 07 226 COS 227 - 228 RCL 10 229 COS 230 + 231 STO 04 232 RCL 08 233 COS 234 5 235 * 236 RCL 08 237 RCL 00 238 PI 239 * 240 P-R 241 RCL 00 242 * 243 2 244 / 245 + 246 - 247 RCL 07 248 COS 249 PI 250 * 251 - 252 STO 11 253 RCL 00 254 110 255 CHS 256 RCL 00 257 2 258 * 259 + 260 * |
261 1303
262 + 263 STO 07 264 CLX 265 .089 266 * 267 * 268 RCL 05 269 + 270 STO 08 271 CLX 272 5.203 273 STO 05 274 RDN 275 ST+ X 276 19 277 + 278 * 279 CHS 280 326 281 + 282 * 283 4849 284 + 285 STO 06 286 CLX 287 36 288 * 289 CHS 290 412 291 + 292 * 293 32253 294 + 295 * 296 14331 297 + 298 STO 09 299 CLX 300 3 301 * 302 161 303 + 304 * 305 20420 306 + 307 * 308 100464 309 XEQ "L" 310 END |
( 384 bytes / SIZE 016 )
| STACK | INPUTS | OUTPUTS |
| T | / | elongation from the Sun* ( deg ) |
| Z | / | distance to the earth** ( AU ) |
| Y | / | declination ( ° ' '' ) |
| X | / | right ascension ( hh.mnss ) |
Example: T = 1.5 ( 5000/01/23
0h TT )
( geocentric )
( heliocentric )
XEQ "JU" >>>> R.A. = 1h52m13s
= R06
R03 = l = 29.655°
R08 = L = 41.156°
RDN Decl = 10°05'22" = R07
R04 = b = -1.159°
R09 = B = -1.147°
RDN r = 4.893
UA = R05
R10 = R = 4.945 UA
RDN Elong = 87.26°
7°) Saturn
| 01 LBL "SA"
02 XEQ "K" 03 3 04 SQRT 05 P-R 06 + 07 CHS 08 RCL 00 09 * 10 RCL 09 11 11 12 P-R 13 + 14 + 15 RCL 00 16 * 17 RCL 09 18 40 19 P-R 20 1.54 21 * 22 - 23 + 24 RCL 11 25 ST+ X 26 STO 08 27 6 28 P-R 29 3 30 / 31 + 32 - 33 RCL 09 34 RCL 06 35 - 36 STO 14 37 6 38 P-R 39 + 40 + 41 RCL 03 42 3 43 P-R 44 + 45 - 46 RCL 00 47 * 48 RCL 09 49 244 50 P-R 51 5 52 SQRT 53 / 54 + 55 - 56 RCL 08 57 3 58 P-R 59 11.6 60 * 61 - 62 - 63 RCL 11 64 2 65 P-R 66 - 67 + 68 RCL 14 69 15 70 P-R 71 1.3 72 * 73 - 74 + 75 RCL 03 76 8 77 P-R 78 1.5 79 / 80 + 81 + 82 RCL 00 83 * |
84 RCL 09
85 182 86 P-R 87 3.41 88 * 89 - 90 - 91 RCL 08 92 122 93 P-R 94 .14 95 * 96 - 97 + 98 RCL 11 99 15 100 P-R 101 .87 102 / 103 + 104 - 105 RCL 14 106 42 107 P-R 108 5 109 SQRT 110 / 111 + 112 - 113 RCL 11 114 RCL 06 115 - 116 STO 15 117 PI 118 P-R 119 + 120 + 121 RCL 12 122 4 123 P-R 124 - 125 + 126 RCL 13 127 PI 128 P-R 129 - 130 + 131 RCL 03 132 28 133 SQRT 134 P-R 135 ST+ X 136 - 137 + 138 RCL 03 139 RCL 04 140 - 141 SIN 142 RCL 14 143 RCL 06 144 - 145 COS 146 + 147 PI 148 * 149 - 150 RCL 03 151 RCL 06 152 + 153 4 154 P-R 155 2 156 / 157 RCL 00 158 * 159 + 160 - 161 RCL 00 162 * 163 RCL 09 164 800 165 P-R 166 9 |
167 D-R
168 * 169 + 170 + 171 RCL 08 172 72 173 P-R 174 3 175 * 176 + 177 - 178 RCL 11 179 117 180 P-R 181 32 182 SQRT 183 / 184 - 185 - 186 RCL 14 187 9 188 P-R 189 5 190 * 191 - 192 - 193 RCL 15 194 6 195 P-R 196 ST+ X 197 - 198 + 199 RCL 12 200 9 201 P-R 202 PI 203 / 204 + 205 - 206 RCL 10 207 2 208 P-R 209 4 210 * 211 + 212 + 213 RCL 10 214 ST+ X 215 SIN 216 9 217 * 218 - 219 RCL 13 220 SIN 221 8 222 * 223 - 224 RCL 03 225 7 226 P-R 227 3 228 / 229 + 230 - 231 RCL 04 232 COS 233 7 234 * 235 - 236 RCL 04 237 RCL 06 238 + 239 5 240 P-R 241 .6 242 * 243 + 244 + 245 RCL 06 246 RCL 07 247 - 248 ST+ X 249 SIN |
250 4
251 * 252 + 253 RCL 05 254 COS 255 RCL 14 256 RCL 06 257 - 258 SIN 259 - 260 RCL 08 261 RCL 09 262 + 263 COS 264 + 265 3 266 * 267 + 268 RCL 03 269 RCL 04 270 - 271 2 272 P-R 273 + 274 + 275 RCL 04 276 RCL 07 277 + 278 COS 279 RCL 06 280 RCL 07 281 - 282 SIN 283 - 284 RCL 05 285 RCL 12 286 + 287 SIN 288 - 289 ST+ X 290 + 291 STO 03 292 RCL 08 293 SIN 294 3 295 * 296 RCL 00 297 * 298 RCL 08 299 1 300 P-R 301 10 302 * 303 + 304 - 305 RCL 14 306 3 307 SQRT 308 P-R 309 ST+ X 310 - 311 + 312 RCL 09 313 SIN 314 3 315 * 316 - 317 RCL 00 318 * 319 RCL 08 320 18 321 P-R 322 3 323 / 324 - 325 - 326 RCL 10 327 COS 328 8 329 * 330 + 331 RCL 11 332 1 |
333 P-R
334 5 335 * 336 + 337 + 338 RCL 14 339 4 340 P-R 341 6 342 / 343 + 344 - 345 RCL 09 346 COS 347 4 348 * 349 + 350 RCL 10 351 ST+ X 352 COS 353 + 354 RCL 15 355 SIN 356 + 357 STO 04 358 RCL 08 359 SIN 360 3 361 * 362 CHS 363 RCL 00 364 * 365 RCL 14 366 3 367 P-R 368 2 369 SQRT 370 / 371 - 372 + 373 RCL 08 374 COS 375 8 376 * 377 + 378 RCL 12 379 SIN 380 3 381 SQRT 382 * 383 + 384 RCL 00 385 * 386 RCL 08 387 17 388 P-R 389 9 390 / 391 - 392 + 393 RCL 14 394 8 395 P-R 396 + 397 - 398 RCL 12 399 2 400 P-R 401 ST+ X 402 + 403 - 404 RCL 00 405 * 406 RCL 14 407 9 408 P-R 409 .6 410 / 411 - 412 - 413 RCL 08 414 5 415 P-R |
416 3.8
417 * 418 + 419 - 420 RCL 12 421 5 422 P-R 423 .7 424 * 425 - 426 - 427 RCL 09 428 SIN 429 4 430 * 431 + 432 RCL 10 433 COS 434 ST+ X 435 + 436 RCL 15 437 COS 438 3 439 * 440 - 441 STO 11 442 9.543 443 STO 05 444 RCL 00 445 335 446 RCL 00 447 39 448 * 449 + 450 * 451 39275 452 + 453 * 454 93057 455 + 456 STO 09 457 CLX 458 .208 459 * 460 * 461 RCL 06 462 + 463 STO 08 464 CLX 465 3 466 * 467 26 468 - 469 * 470 694 471 - 472 * 473 5553 474 + 475 STO 06 476 CLX 477 6 478 * 479 CHS 480 75 481 - 482 * 483 2489 484 + 485 STO 07 486 CLX 487 18 488 * 489 49 490 + 491 * 492 CHS 493 17542 494 + 495 * 496 113666 497 XEQ "L" 498 END |
( 601 bytes / SIZE 016 )
| STACK | INPUTS | OUTPUTS |
| T | / | elongation from the Sun* ( deg ) |
| Z | / | distance to the earth** ( AU ) |
| Y | / | declination ( ° ' '' ) |
| X | / | right ascension ( hh.mnss ) |
Example: T = 1.5 ( 5000/01/23
0h TT )
( geocentric )
( heliocentric )
XEQ "SA" >>>> R.A. = 1h40m09s
= R06
R03 = l = 26.063°
R08 = L = 31.844°
RDN Decl = 7°49'05"
= R07
R04 = b = -2.240°
R09 = B = -2.254°
RDN r = 9.806
UA = R05
R10 = R = 9.747 UA
RDN Elong = 83.67°
8°) Uranus
| 01 LBL "UR"
02 XEQ "K" 03 RCL 04 04 SIN 05 ST+ X 06 RCL 00 07 * 08 RCL 15 09 8 10 P-R 11 .3 12 / 13 - 14 + 15 RCL 04 16 RCL 07 17 + 18 STO 11 19 8 20 P-R 21 .7 22 * 23 + 24 + 25 RCL 08 26 ST+ X 27 STO 08 28 COS 29 7 30 SQRT 31 * 32 + 33 RCL 04 34 6 35 P-R 36 1.5 37 * 38 + 39 - 40 RCL 15 41 ST+ X 42 COS 43 ST+ X 44 - 45 RCL 13 46 7 47 SQRT 48 P-R 49 2 50 SQRT 51 * 52 - |
53 -
54 RCL 00 55 * 56 RCL 15 57 856 58 P-R 59 18 60 / 61 - 62 - 63 RCL 14 64 ST+ X 65 STO 10 66 209 67 P-R 68 E2 69 / 70 - 71 - 72 RCL 11 73 9 74 P-R 75 .23 76 / 77 + 78 - 79 RCL 08 80 39 81 P-R 82 5.5 83 / 84 + 85 - 86 RCL 04 87 5 88 P-R 89 7 90 * 91 - 92 - 93 RCL 15 94 ST+ X 95 35 96 P-R 97 6 98 / 99 + 100 - 101 RCL 13 102 6 103 P-R 104 3 |
105 /
106 + 107 + 108 RCL 05 109 RCL 07 110 - 111 SIN 112 RCL 10 113 RCL 15 114 + 115 STO 09 116 SIN 117 - 118 3 119 * 120 RCL 14 121 RCL 15 122 + 123 SIN 124 - 125 5 126 * 127 + 128 RCL 10 129 RCL 14 130 + 131 STO 06 132 SIN 133 4 134 * 135 + 136 RCL 07 137 RCL 10 138 + 139 STO 12 140 SIN 141 6 142 * 143 RCL 14 144 SIN 145 5 146 * 147 - 148 RCL 07 149 RCL 08 150 + 151 SIN 152 + 153 RCL 10 154 ST+ X 155 SIN 156 + |
157 RCL 09
158 RCL 08 159 - 160 SIN 161 - 162 RCL 15 163 RCL 08 164 - 165 SIN 166 + 167 RCL 07 168 21 169 + 170 SIN 171 - 172 ST+ X 173 + 174 RCL 13 175 RCL 07 176 - 177 3 178 SQRT 179 P-R 180 + 181 - 182 RCL 07 183 RCL 11 184 + 185 STO 13 186 6 187 P-R 188 3 189 / 190 + 191 + 192 STO 03 193 RCL 10 194 COS 195 34 196 * 197 RCL 08 198 1 199 P-R 200 6 201 * 202 - 203 - 204 RCL 11 205 6 206 P-R 207 LASTX 208 / |
209 -
210 - 211 RCL 05 212 RCL 07 213 - 214 COS 215 5 216 * 217 + 218 RCL 13 219 COS 220 PI 221 * 222 + 223 RCL 09 224 COS 225 RCL 15 226 COS 227 - 228 RCL 12 229 COS 230 - 231 ST+ X 232 + 233 RCL 04 234 SIN 235 - 236 RCL 14 237 COS 238 + 239 RCL 06 240 COS 241 - 242 STO 04 243 RCL 08 244 2 245 P-R 246 .4 247 / 248 - 249 RCL 10 250 COS 251 6 252 * 253 + 254 STO 11 255 19.192 256 STO 05 257 RCL 00 258 86 259 RCL 00 260 3 |
261 *
262 + 263 * 264 29726 265 + 266 * 267 172993 268 + 269 STO 09 270 CLX 271 .122 272 * 273 * 274 RCL 07 275 + 276 STO 08 277 CLX 278 PI 279 * 280 55 281 - 282 * 283 4630 284 + 285 STO 06 286 SIGN 287 + 288 15 289 * 290 * 291 773 292 + 293 STO 07 294 CLX 295 16 296 * 297 CHS 298 148 299 + 300 * 301 536 302 + 303 * 304 10423 305 + 306 * 307 74005 308 XEQ "L" 309 END |
( 386 bytes / SIZE 016 )
| STACK | INPUTS | OUTPUTS |
| T | / | elongation from the Sun* ( deg ) |
| Z | / | distance to the earth** ( AU ) |
| Y | / | declination ( ° ' '' ) |
| X | / | right ascension ( hh.mnss ) |
Example: T = 1.5 ( 5000/01/23
0h TT )
( geocentric )
( heliocentric )
XEQ "UR" >>>> R.A. = 16h55m56s
= R06
R03 = l = -104.822° = 255.178°
R08 = L = 252.934°
RDN Decl = -22°00'17" = R07
R04 = b = 0.251°
R09 = B = 0.260°
RDN r = 19.158
UA = R05
R10 = R = 18.502 UA
RDN Elong = 47.22°
9°) Neptune
| 01 LBL "NE"
02 XEQ "K" 03 RCL 15 04 583 05 P-R 06 18 07 / 08 - 09 RCL 15 10 5 11 RCL 00 12 * 13 P-R 14 13 15 SQRT 16 * 17 - 18 - 19 RCL 14 20 3 21 - 22 SIN 23 71 24 * 25 + 26 RCL 15 27 ST+ X 28 24 29 P-R 30 6 31 / 32 + 33 + 34 RCL 14 |
35 RCL 15
36 + 37 STO 13 38 SIN 39 22 40 * 41 + 42 RCL 05 43 RCL 08 44 - 45 STO 10 46 SIN 47 9 48 * 49 + 50 RCL 15 51 RCL 08 52 - 53 STO 12 54 4 55 P-R 56 + 57 + 58 RCL 06 59 RCL 08 60 - 61 STO 09 62 SIN 63 5 64 * 65 + 66 RCL 14 67 ST+ X 68 STO 11 |
69 SIN
70 RCL 13 71 RCL 15 72 + 73 SIN 74 - 75 ST+ X 76 - 77 STO 03 78 RCL 15 79 COS 80 8 81 * 82 RCL 14 83 1 84 P-R 85 17 86 * 87 + 88 - 89 RCL 10 90 COS 91 RCL 13 92 COS 93 - 94 5 95 * 96 + 97 RCL 09 98 COS 99 3 100 * 101 + 102 RCL 12 |
103 1
104 P-R 105 - 106 - 107 RCL 11 108 COS 109 + 110 STO 04 111 RCL 14 112 6 113 P-R 114 + 115 CHS 116 RCL 12 117 5 118 P-R 119 .7 120 / 121 - 122 - 123 STO 11 124 30.07 125 STO 05 126 RCL 00 127 899 128 RCL 00 129 13 130 * 131 + 132 STO 06 133 CLX 134 3 135 * 136 186 |
137 +
138 * 139 CHS 140 1770 141 + 142 STO 07 143 CLX 144 .124 145 * 146 * 147 ST+ 08 148 CLX 149 152 150 * 151 28525 152 + 153 * 154 48124 155 + 156 STO 09 157 CLX 158 5 159 * 160 CHS 161 104 162 + 163 * 164 22044 165 + 166 * 167 131784 168 XEQ "L" 169 END |
( 229 bytes / SIZE 016 )
| STACK | INPUTS | OUTPUTS |
| T | / | elongation from the Sun* ( deg ) |
| Z | / | distance to the earth** ( AU ) |
| Y | / | declination ( ° ' '' ) |
| X | / | right ascension ( hh.mnss ) |
Example: T = 1.5 ( 5000/01/23
0h TT )
( geocentric )
( heliocentric )
XEQ "NE" >>>> R.A. = 3h48m33s
= R06
R03 = l = 58.956°
R08 = L = 60.652°
RDN Decl = 18°11'05" = R07
R04 = b = -1.461°
R09 = B = -1.439°
RDN r = 29.389
UA = R05
R10 = R = 29.843 UA
RDN Elong = 116.55°
10°) Pluto
| 01 LBL "PL"
02 XEQ "K" 03 RCL 05 04 2903.4 05 RCL 00 06 * 07 238.925 08 + 09 STO 08 10 - 11 STO 10 12 SIN 13 7 14 * 15 RCL 08 16 COS |
17 4
18 * 19 - 20 RCL 08 21 ST+ X 22 STO 09 23 SIN 24 ST+ X 25 - 26 RCL 06 27 RCL 08 28 - 29 STO 11 30 SIN 31 4 32 * |
33 +
34 STO 03 35 RCL 09 36 1 37 P-R 38 RCL 08 39 SIN 40 - 41 ST+ X 42 + 43 RCL 10 44 COS 45 5 46 * 47 + 48 RCL 11 |
49 COS
50 ST+ X 51 + 52 STO 04 53 RCL 00 54 234 55 * 56 3 57 - 58 RCL 08 59 COS 60 5 61 * 62 - 63 STO 11 64 39.489 |
65 STO 05
66 24900 67 STO 06 68 17140 69 STO 07 70 27942 71 RCL 00 72 * 73 135925 74 - 75 STO 09 76 246232 77 XEQ "L" 78 END |
( 133 bytes / SIZE 016 )
| STACK | INPUTS | OUTPUTS |
| T | / | elongation from the Sun* ( deg ) |
| Z | / | distance to the earth** ( AU ) |
| Y | / | declination ( ° ' '' ) |
| X | / | right ascension ( hh.mnss ) |
Example: T = 0.05 ( 2100/01/01
0h TT )
( geocentric )
( heliocentric )
XEQ "PL" >>>> R.A. = 2h23m50s
= R06
R03 = l = 32.395°
R08 = L = 33.511°
RDN Decl = -3°37'43" =
R07
R04 = b = -16.921°
R09 = B = -16.794°
RDN r = 48.576
UA = R05
R10 = R = 48.934 UA
RDN Elong = 110.80°
( First execute "SUN" with T = 0.05 to get the correct
geocentric coordinates )
References:
[1] Jean Meeus - "Astronomical Algorithms" - Willmann-Bell
- ISBN 0-943396-35-2
[2] VSOP87D Series ftp://ftp.imcce.fr/pub/ephem/planets/vsop87/
[3] VSOP09 & TOP2010 Series http://www.imcce.fr/~jlsimon
[4] A fantastic software, "SOLEX" which may be downloaded from
http://chemistry.unina.it/~alvitagl/solex/