Overview
0°) 2 Subroutines: "M" & "K"
1°) Sun+Moon
2°) Planets (
Mercury, Venus, ..... , Pluto , Xena )
3°) Sidereal Time
+ Sun + Moon + Subroutines
4°) Single Programs [ 1900 , 2100
]
a) Program#1
b) Program#2
Latest Update: §4°)
-The following programs calculate 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) )
-The subroutine "K" listed in §0°) leads to coordinates which
are referred to the mean equinox of the date.
-In paragraph 3°) "K" is improved to compute
the apparent coordinates:
-The nutation, aberration, time-light and parallax
are taken into account to get the topocentric azimuthal coordinates.
-A small correction has been made to take the new precession formulas into account.
-For the Sun, Mercury & Venus, truncated series from the VSOP87/VSOP09
theories are used.
-For Jupiter, Saturn, Uranus & Neptune, the perturbations
come from the new theory TOP2010.
-They are expressed as functions of a unique variable
µ with µ = 20°599908944 T
-The perturbations of Mars are expressed with µ
too.
-For Jupiter and Saturn, these series converge more rapidly than the usual
perturbations expressed with the mean mean longitudes.
-The smallest retained terms are of order of 0°002
( sometimes even smaller )
-However, a comparison between DE406 and DE422 also suggests another correction in longitudes of Uranus & Neptune:
dL = -0°0007 T for Uranus and dL = 0°0024T for Neptune. These corrections have been added to the mean longitude.
-The coordinates of Pluto & Xena are obtained by a least-squares fit
of DE406, thanks to my HP48.
-For the Moon, the series are those given by Jean
Meeus in his "Astronomical Algorithms".
-The results are valid at least between 1000 and 3000 for the Sun, the
Moon and the major planets.
-And over more limited time-spans: [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°007 Cos ( 28897 T + 65 ) + 0°004 Cos ( 10769 T +76
)
max error ~ 0°009
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
-Other orbital elements ( valid over larger time-spans ) may also be used
for Pluto & Xena, cf paragraph 2°)
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 in decimal degrees
R05 = distance to the Earth in Astronomical
Units ( parallax in sexagesimal degrees for the Moon )
R06 = heliocentric longitude in decimal degrees
= L
R07 = heliocentric latitude in decimal degrees
= B
R08 = radius vector in Astronomical Units
= R
R09 = semi-major axis
R10 = eccentricity
R11 = inclination over the ecliptic.
R12 = mean longitude
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.
0°) 2 Subroutines: "M" & "K"
-After executing "M" with T in register R00, we get:
R03 = 31 µ R06 = 1473
µ R09 = 287 µ
R12 = 208 µ R15 = µ
( R00-R01-R02 are unchanged )
R04 = 8 µ
R07 = 593 µ R10
= 1760 µ R13 = 106 µ
R05 = 4 µ
R08 = 880 µ R11
= 19 µ
R14 = 102 µ
-"K" solves Kepler's equation, calculates the heliocentric ecliptic coordinates and finally the geocentric ecliptic longitude, latitude and distance to the Earth.
-Line 59 ( 12 ) is the number of iterations to solve the equation of Kepler.
-It's only useful for the 10th planet.
-Otherwise, 12 may be replaced by 9.
-Lines 151-152 & 126-127 are not essential and
may be deleted.
-Of course, you can add program lines before the END to compute the right-ascension,
declination ...
| 01 LBL "M" 02 102 03 RCL 00 04 20.599909 05 * 06 STO 15 07 * 08 STO 14 09 106 10 LASTX 11 * 12 STO 13 13 + 14 STO 12 15 19 16 RCL 15 17 * 18 STO 11 19 593 20 LASTX 21 * 22 STO 07 23 LASTX 24 880 25 * 26 STO 08 27 + 28 STO 06 29 LASTX 30 RCL 07 31 - |
32 STO 09 33 + 34 STO 10 35 4 36 RCL 15 37 * 38 STO 05 39 ST+ X 40 STO 04 41 LASTX 42 31 43 * 44 STO 03 45 RTN 46 LBL "K" 47 + 48 E3 49 ST/ 03 50 ST/ 04 51 ST/ 05 52 ST/ 11 53 ST/ 12 54 ST/ 13 55 / 56 STO 14 57 E5 58 ST/ 10 59 12 60 STO 08 61 RCL 12 62 RCL 13 |
63 - 64 360 65 MOD 66 ENTER 67 ENTER 68 LBL 10 69 SIN 70 RCL 10 71 R-D 72 * 73 + 74 DSE 08 75 GTO 10 76 2 77 / 78 1 79 RCL 10 80 + 81 1 82 LASTX 83 - 84 / 85 SQRT 86 P-R 87 LASTX 88 / 89 R-P 90 RDN 91 ST+ X 92 1 93 R^ |
94 ST+ X 95 COS 96 RCL 10 97 * 98 - 99 RCL 09 100 * 101 RCL 05 102 + 103 STO 08 104 CLX 105 RCL 14 106 - 107 RCL 13 108 + 109 COS 110 RCL 11 111 LASTX 112 SIN 113 P-R 114 X<>Y 115 ASIN 116 RCL 04 117 + 118 STO 07 119 X<> Z 120 R-P 121 CLX 122 RCL 14 123 + 124 RCL 03 |
125 + 126 360 127 MOD 128 STO 06 129 RCL 08 130 X<>Y 131 RDN 132 P-R 133 R^ 134 X<>Y 135 P-R 136 RCL 02 137 ST+ Z 138 CLX 139 RCL 01 140 + 141 R-P 142 X<>Y 143 RDN 144 R-P 145 R^ 146 X<>Y 147 STO 05 148 X<> Z 149 STO 04 150 X<>Y 151 360 152 MOD 153 STO 03 154 END |
( 206 bytes / SIZE 016 )
1°) Sun + Moon
-To get a better precision and faster results, "SUN" calls "SUN3" listed
in "Astronomical Ephemeris(I).
-Simply replace line 106 in the "SUN3" listing
( 30010 ) by 30009 to take into account the new precession
formulae.
| 01 LBL "SUN" 02 XEQ "SUN3" 03 STO 05 04 X<>Y 05 STO 03 06 X<>Y 07 P-R 08 STO 01 09 X<>Y 10 STO 02 11 RCL 05 12 0 13 STO 04 14 RCL 03 15 RTN 16 LBL "MO" 17 RCL 00 18 359990.503 19 RCL 00 20 65 21 / 22 - 23 * 24 2.964 25 - 26 STO 08 27 CLX 28 .188 29 * 30 CHS 31 4452671.114 32 + 33 * 34 68.245 35 - 36 STO 13 37 ST+ X 38 STO 14 39 CLX 40 70 41 / 42 .874 43 + 44 * 45 4771988.675 46 + 47 * 48 128.431 49 + 50 STO 07 51 ST+ X 52 STO 12 53 CLX 54 .365 55 * 56 4832020.175 57 - 58 * 59 86.657 60 - 61 STO 09 62 ST+ X 63 STO 06 64 6036 65 RCL 14 66 RCL 07 67 - 68 STO 03 69 COS 70 58 71 * 72 - 73 RCL 14 74 COS 75 46 76 * 77 - 78 RCL 12 79 COS 80 9 81 * 82 - 83 RCL 14 84 RCL 12 |
85 - 86 STO 15 87 COS 88 RCL 07 89 COS 90 82 91 * 92 - 93 4 94 * 95 + 96 RCL 14 97 RCL 08 98 - 99 STO 11 100 COS 101 RCL 14 102 RCL 07 103 + 104 STO 10 105 COS 106 + 107 3 108 * 109 - 110 1 111 % 112 1/X 113 ASIN 114 HMS 115 STO 05 116 RCL 07 117 RCL 09 118 - 119 SIN 120 281 121 * 122 RCL 07 123 RCL 09 124 + 125 SIN 126 278 127 * 128 + 129 RCL 14 130 RCL 09 131 + 132 SIN 133 173 134 * 135 + 136 RCL 03 137 RCL 09 138 - 139 SIN 140 55 141 * 142 + 143 RCL 03 144 RCL 09 145 + 146 SIN 147 46 148 * 149 + 150 RCL 14 151 RCL 09 152 - 153 SIN 154 33 155 * 156 + 157 RCL 12 158 RCL 09 159 - 160 SIN 161 17 162 * 163 + 164 RCL 10 165 RCL 09 166 + 167 SIN 168 RCL 12 |
169 RCL 09 170 + 171 SIN 172 + 173 9 174 * 175 + 176 RCL 11 177 RCL 09 178 + 179 SIN 180 RCL 09 181 SIN 182 641 183 * 184 - 185 8 186 * 187 + 188 RCL 15 189 RCL 09 190 + 191 SIN 192 RCL 10 193 RCL 09 194 - 195 SIN 196 + 197 4 198 * 199 + 200 RCL 14 201 RCL 08 202 + 203 RCL 09 204 + 205 SIN 206 PI 207 * 208 - 209 RCL 11 210 RCL 09 211 - 212 STO 04 213 RCL 07 214 - 215 SIN 216 LASTX 217 RCL 06 218 + 219 SIN 220 + 221 RCL 04 222 SIN 223 + 224 RCL 09 225 RCL 07 226 - 227 STO 04 228 RCL 08 229 + 230 SIN 231 - 232 RCL 04 233 RCL 14 234 ST+ X 235 + 236 SIN 237 + 238 RCL 08 239 RCL 09 240 - 241 SIN 242 - 243 RCL 06 244 RCL 09 245 + 246 SIN 247 + 248 ST+ X 249 + 250 STO 04 251 RCL 07 252 SIN |
253 6289 254 * 255 RCL 14 256 SIN 257 658 258 * 259 + 260 RCL 12 261 SIN 262 214 263 * 264 + 265 RCL 06 266 SIN 267 114 268 * 269 + 270 RCL 15 271 SIN 272 59 273 * 274 + 275 RCL 03 276 RCL 08 277 - 278 SIN 279 57 280 * 281 + 282 RCL 10 283 SIN 284 53 285 * 286 + 287 RCL 11 288 SIN 289 46 290 * 291 + 292 RCL 08 293 RCL 07 294 - 295 SIN 296 41 297 * 298 - 299 RCL 03 300 SIN 301 98 302 * 303 RCL 07 304 RCL 06 305 - 306 SIN 307 - 308 13 309 * 310 + 311 RCL 07 312 RCL 06 313 + 314 SIN 315 RCL 14 316 ST+ X 317 RCL 07 318 - 319 SIN 320 + 321 11 322 * 323 + 324 RCL 03 325 ST+ X 326 SIN 327 9 328 * 329 + 330 RCL 03 331 RCL 08 332 + 333 SIN 334 8 335 * 336 - |
337 RCL 14 338 RCL 08 339 + 340 SIN 341 7 342 * 343 - 344 RCL 08 345 SIN 346 RCL 00 347 37 348 - 349 * 350 RCL 13 351 SIN 352 7 353 * 354 - 355 RCL 07 356 RCL 08 357 + 358 SIN 359 6 360 * 361 - 362 RCL 14 363 RCL 06 364 + 365 SIN 366 3 367 * 368 + 369 RCL 07 370 RCL 12 371 + 372 SIN 373 ST+ X 374 + 375 RCL 13 376 RCL 07 377 - 378 SIN 379 - 380 RCL 13 381 RCL 08 382 + 383 SIN 384 + 385 5 386 * 387 + 388 RCL 10 389 RCL 08 390 - 391 SIN 392 RCL 14 393 RCL 12 394 + 395 SIN 396 + 397 RCL 14 398 ST+ X 399 SIN 400 + 401 RCL 03 402 RCL 12 403 - 404 SIN 405 + 406 RCL 00 407 23 408 * 409 1 410 - 411 R-D 412 SIN 413 - 414 4 415 * 416 + 417 RCL 08 418 RCL 12 419 - 420 SIN |
421 RCL 03 422 RCL 06 423 - 424 SIN 425 + 426 3 427 * 428 - 429 RCL 11 430 RCL 08 431 - 432 SIN 433 LASTX 434 RCL 07 435 - 436 SIN 437 + 438 RCL 11 439 RCL 12 440 - 441 SIN 442 + 443 RCL 13 444 RCL 07 445 + 446 SIN 447 - 448 RCL 12 449 RCL 08 450 + 451 SIN 452 - 453 RCL 08 454 ST+ X 455 SIN 456 - 457 RCL 06 458 RCL 10 459 + 460 SIN 461 - 462 RCL 14 463 RCL 06 464 - 465 SIN 466 - 467 RCL 00 468 ST+ X 469 158 470 - 471 RCL 00 472 * 473 4812678812 474 + 475 RCL 00 476 * 477 211728 478 + 479 E3 480 / 481 360 482 MOD 483 SIN 484 ST+ X 485 ST- 04 486 X<> L 487 STO 03 488 RCL 09 489 + 490 SIN 491 + 492 ST+ X 493 + 494 E3 495 ST/ 04 496 / 497 ST+ 03 498 RCL 05 499 RCL 04 500 RCL 03 501 END |
( 663 bytes / SIZE 016 )
| STACK | INPUTS | OUTPUTS |
| Z | / | distance to the earth ( AU )* |
| Y | / | geocentric latitude ( deg ) |
| X | / | geocentric longitude ( deg ) |
* or parallax for the Moon in ° ' "
Example: T = 1.2
i-e 3200/01/10 0h TT
• XEQ "SUN" >>>>
Long = 288°786
= R03
R01 = X = 0.316992
RDN Lat =
0
= R04 and
R02 = Y = -0.931927
RDN Dist = 0.984364
AU = R05
• XEQ "MO" or R/S >>>>
Long = 307°037
= R03
RDN Lat = -0°686
= R04
RDN parallax = 1°01'14"
= R05
-The Sun position may also be calculated without calling "SUN3":
-For example, replace lines 01 to 16 by
| 01 LBL "SUN" 02 RCL 00 03 4452671 04 * 05 68 06 - 07 STO 03 08 SIN 09 329645 10 RCL 00 11 * 12 23 13 - 14 COS 15 - 16 202 17 RCL 00 18 * |
19 18 20 - 21 COS 22 - 23 ST+ X 24 RCL 00 25 225184 26 * 27 81 28 + 29 SIN 30 LASTX 31 ST+ X 32 SIN 33 - 34 2 35 SQRT 36 * |
37 + 38 X<> 03 39 COS 40 PI 41 % 42 STO 05 43 RCL 00 44 360007697 45 RCL 00 46 30 47 * 48 + 49 * 50 80026 51 - 52 STO 12 53 CLX 54 42 |
55 + 56 * 57 CHS 58 1671 59 + 60 STO 10 61 SIGN 62 STO 09 63 CLX 64 46 65 * 66 17194 67 + 68 * 69 77063 70 - 71 STO 13 72 CLST |
73 STO 01 74 STO 02 75 STO 04 76 STO 11 77 XEQ "K" 78 RCL 03 79 RCL 05 80 P-R 81 STO 01 82 X<>Y 83 STO 02 84 RCL 05 85 RCL 04 86 RCL 03 87 RTN 88 LBL "MO" 89 . . . |
Same example:
T = 1.2 i-e 3200/01/10
0h TT
• XEQ "SUN" >>>>
Long = 288°786
= R03
R01 = X = 0.316992
RDN Lat =
0
= R04 and
R02 = Y = -0.931926
RDN Dist = 0.984362
AU = R05
Notes:
-The results are slightly less accurate and the routine runs slower, but
it saves bytes !
-Since several arguments also appear to calculate
the positions of Venus and Mars,
one can write another subroutine that would
be called by "SUN" , "VE" , "MA"
-These arguments are: 225184 T + 81 and 202 T - 18
-Another argument ( rounded to 4452671 T - 68 for
the Sun ) is also used by "MO" ...
2°) The Planets
-Of course, this huge program may be split in several parts...
| 01 LBL "ME" 02 RCL 00 03 63563 04 * 05 SIN 06 ST+ X 07 CHS 08 STO 03 09 CLX 10 STO 04 11 STO 05 12 .3871 13 STO 09 14 RCL 00 15 18 16 RCL 00 17 2 18 * 19 - 20 * 21 7005 22 + 23 STO 11 24 CLX 25 30 26 * 27 1494740721 28 + 29 * 30 250205 31 + 32 STO 12 33 CLX 34 20 35 * 36 20563 37 + 38 STO 10 39 CLX 40 30 41 * 42 15563 43 + 44 * 45 77456 46 + 47 STO 13 48 CLX 49 18 50 * 51 11860 52 + 53 * 54 48331 55 XEQ "K" 56 RTN 57 LBL "VE" 58 RCL 00 59 225184 60 * 61 81 62 + 63 STO 03 64 3 65 * 66 SIN 67 ST+ X 68 RCL 03 69 ST+ X 70 SIN 71 PI 72 * 73 - 74 RCL 03 75 SIN 76 2 77 SQRT 78 * 79 - 80 STO 03 81 CLX 82 STO 04 83 STO 05 84 .72333 85 STO 09 86 RCL 00 87 585192129 88 RCL 00 89 31 90 * 91 + 92 * 93 181178 94 + 95 STO 12 96 CLX 97 48 98 - 99 * 100 677 101 + 102 STO 10 103 CLX 104 10 105 * 106 3395 107 + 108 STO 11 109 CLX 110 18 111 + 112 * 113 CHS 114 6 115 * 116 14021 117 + 118 * 119 131564 120 + 121 STO 13 122 CLX 123 41 124 * 125 9010 126 + 127 * 128 76680 129 XEQ "K" 130 RTN 131 LBL "MA" 132 XEQ "M" 133 RCL 15 134 2215 135 * 136 71 137 - 138 COS 139 RCL 15 140 9301 141 * 142 STO 05 143 COS 144 + 145 RCL 05 146 RCL 11 147 - 148 37 149 + 150 COS 151 + 152 2 153 SQRT 154 * 155 RCL 11 156 28 157 * 158 49 159 + 160 COS 161 RCL 03 162 264 163 * 164 STO 05 165 13 166 + 167 COS 168 + 169 RCL 15 170 7077 171 * 172 ST- 05 173 SIN 174 - 175 RCL 15 176 10 177 * 178 STO 04 179 SIN 180 RCL 00 181 * 182 + 183 ST+ X 184 + 185 RCL 09 186 22 187 * 188 RCL 03 189 + 190 ST+ 06 191 12 192 - 193 COS 194 6 195 * 196 - 197 RCL 05 198 21 199 + 200 COS 201 RCL 06 202 ST+ X 203 11 204 + 205 COS 206 - 207 4 208 * 209 + 210 RCL 06 211 48 212 + 213 COS 214 7 215 * 216 + 217 RCL 04 218 18 219 - 220 COS 221 15 222 * 223 + 224 STO 03 225 CLX 226 STO 04 227 STO 05 228 1.5237 229 STO 09 230 RCL 00 231 191416964 232 RCL 00 233 31 234 * 235 + 236 * 237 4830 238 - 239 STO 12 240 RDN 241 CHS 242 90 243 + 244 * 245 9340 246 + |
247 STO 10 248 CLX 249 6 250 - 251 * 252 1850 253 + 254 STO 11 255 CLX 256 13 257 * 258 18409 259 + 260 * 261 23940 262 - 263 STO 13 264 CLX 265 SIGN 266 + 267 * 268 ST+ X 269 7719 270 + 271 * 272 49558 273 XEQ "K" 274 RTN 275 LBL "JU" 276 XEQ "M" 277 RCL 11 278 49 279 - 280 SIN 281 PI 282 * 283 RCL 00 284 * 285 RCL 09 286 COS 287 ST+ X 288 - 289 RCL 06 290 RCL 11 291 - 292 STO 15 293 23 294 - 295 COS 296 5 297 * 298 + 299 RCL 11 300 32 301 - 302 COS 303 41 304 * 305 + 306 RCL 00 307 * 308 RCL 06 309 39 310 - 311 COS 312 2 313 SQRT 314 * 315 + 316 RCL 07 317 ST+ X 318 67 319 + 320 COS 321 ST+ X 322 - 323 RCL 04 324 RCL 05 325 + 326 SIN 327 RCL 14 328 3 329 * 330 76 331 + 332 COS 333 + 334 RCL 11 335 ST+ X 336 75 337 + 338 COS 339 + 340 RCL 06 341 RCL 15 342 + 343 30 344 - 345 SIN 346 + 347 RCL 06 348 RCL 10 349 + 350 11 351 - 352 SIN 353 + 354 3 355 * 356 + 357 RCL 07 358 COS 359 RCL 09 360 RCL 10 361 + 362 69 363 - 364 COS 365 + 366 4 367 * 368 + 369 RCL 09 370 ST+ X 371 65 372 - 373 SIN 374 RCL 08 375 RCL 10 376 + 377 62 378 - 379 SIN 380 + 381 5 382 * 383 + 384 RCL 06 385 RCL 11 386 + 387 STO 04 388 12 389 + 390 SIN 391 16 392 * 393 - 394 RCL 08 395 73 396 + 397 COS 398 22 399 * 400 + 401 RCL 10 402 RCL 07 403 - 404 41 405 + 406 SIN 407 23 408 * 409 - 410 RCL 09 411 75 412 - 413 SIN 414 37 415 * 416 + 417 RCL 15 418 61 419 - 420 SIN 421 42 422 * 423 + 424 RCL 10 425 33 426 - 427 SIN 428 56 429 * 430 + 431 RCL 11 432 7.3 433 - 434 SIN 435 329 436 * 437 - 438 STO 03 439 RCL 04 440 18 441 + 442 COS 443 4 444 * 445 RCL 15 446 63 447 - 448 SIN 449 5 450 * 451 + 452 STO 04 453 RCL 15 454 29 455 + 456 SIN 457 ST+ X 458 RCL 10 459 57 460 + 461 SIN 462 3 463 * 464 + 465 CHS 466 STO 05 467 RCL 00 468 1303 469 RCL 00 470 55 471 * 472 - 473 STO 11 474 CLX 475 22 476 * 477 30363027 478 + 479 * 480 34310 481 + 482 STO 12 483 CLX 484 5.203 485 STO 09 486 INT 487 CHS 488 * 489 163 490 + 491 * 492 4849 |
493 + 494 STO 10 495 CLX 496 4 497 * 498 CHS 499 103 500 + 501 * 502 16126 503 + 504 * 505 14331 506 + 507 STO 13 508 CLX 509 40 510 * 511 10209 512 + 513 * 514 100464 515 XEQ "K" 516 RTN 517 LBL "SA" 518 XEQ "M" 519 RCL 03 520 48 521 - 522 SIN 523 RCL 11 524 ST+ X 525 STO 13 526 39 527 - 528 COS 529 - 530 RCL 10 531 RCL 07 532 - 533 STO 05 534 30 535 - 536 COS 537 - 538 ST+ X 539 RCL 09 540 COS 541 6 542 * 543 + 544 RCL 11 545 41 546 + 547 COS 548 RCL 00 549 * 550 RCL 07 551 RCL 11 552 + 553 4 554 - 555 SIN 556 - 557 8 558 * 559 + 560 RCL 09 561 ST+ X 562 27 563 - 564 COS 565 21 566 * 567 - 568 RCL 11 569 32 570 - 571 COS 572 101 573 * 574 - 575 RCL 00 576 * 577 RCL 09 578 RCL 11 579 - 580 56 581 + 582 COS 583 RCL 08 584 RCL 10 585 + 586 44 587 + 588 COS 589 + 590 RCL 07 591 RCL 12 592 - 593 STO 14 594 ST+ 14 595 COS 596 - 597 RCL 14 598 RCL 15 599 + 600 78 601 - 602 COS 603 + 604 RCL 12 605 RCL 03 606 - 607 39 608 + 609 SIN 610 - 611 ST+ X 612 + 613 RCL 07 614 RCL 13 615 - 616 36 617 + 618 COS 619 RCL 05 620 RCL 13 621 + 622 STO 04 623 COS 624 - 625 RCL 15 626 7 627 * 628 28 629 - 630 SIN 631 + 632 RCL 07 633 59 634 + 635 COS 636 - 637 RCL 06 638 14 639 + 640 COS 641 + 642 PI 643 * 644 + 645 RCL 14 646 11 647 + 648 SIN 649 RCL 07 650 RCL 03 651 - 652 COS 653 + 654 6 655 * 656 - 657 RCL 03 658 21 659 - 660 COS 661 RCL 13 662 15 663 - 664 SIN 665 + 666 RCL 03 667 RCL 11 668 - 669 SIN 670 - 671 RCL 08 672 30 673 - 674 COS 675 + 676 8 677 * 678 + 679 RCL 10 680 54 681 + 682 COS 683 RCL 05 684 25 685 + 686 COS 687 + 688 9 689 * 690 + 691 RCL 09 692 RCL 11 693 + 694 STO 06 695 2 696 - 697 SIN 698 14 699 * 700 + 701 RCL 07 702 RCL 11 703 + 704 STO 14 705 50 706 - 707 SIN 708 45 709 * 710 + 711 RCL 09 712 14 713 + 714 COS 715 118 716 * 717 + 718 RCL 07 719 RCL 11 720 - 721 30 722 + 723 COS 724 228 725 * 726 + 727 RCL 11 728 7.3 729 - 730 SIN 731 810 732 * 733 + 734 STO 03 735 RCL 06 736 76 737 - 738 COS |
739 RCL 08 740 48 741 - 742 COS 743 + 744 3 745 * 746 RCL 04 747 67 748 + 749 SIN 750 ST+ X 751 - 752 RCL 11 753 SIN 754 RCL 09 755 ST+ X 756 STO 13 757 46 758 + 759 SIN 760 RCL 00 761 * 762 - 763 4 764 * 765 + 766 RCL 05 767 28 768 - 769 COS 770 6 771 * 772 + 773 RCL 14 774 20 775 + 776 COS 777 18 778 * 779 - 780 RCL 13 781 33 782 + 783 COS 784 20 785 * 786 + 787 STO 04 788 RCL 09 789 73 790 - 791 COS 792 6 793 * 794 RCL 11 795 COS 796 RCL 14 797 50 798 - 799 COS 800 + 801 4 802 * 803 - 804 RCL 08 805 20 806 - 807 COS 808 8 809 * 810 + 811 RCL 13 812 60 813 - 814 COS 815 19 816 * 817 + 818 12 819 - 820 STO 05 821 9.555 822 STO 09 823 RCL 00 824 347 825 RCL 00 826 6 827 * 828 + 829 * 830 CHS 831 5551 832 + 833 STO 10 834 CLX 835 52 836 * 837 12235109 838 + 839 * 840 50061 841 + 842 STO 12 843 RDN 844 ST+ X 845 CHS 846 37 847 - 848 * 849 2489 850 + 851 STO 11 852 CLX 853 5 854 * 855 84 856 + 857 * 858 19637 859 + 860 * 861 93057 862 + 863 STO 13 864 CLX 865 6 866 + 867 * 868 ST+ X 869 CHS 870 8770 871 + 872 * 873 113665 874 XEQ "K" 875 RTN 876 LBL "UR" 877 XEQ "M" 878 RCL 04 879 41 880 - 881 SIN 882 RCL 04 883 RCL 05 884 + 885 54 886 + 887 SIN 888 - 889 ST+ X 890 RCL 12 891 RCL 03 892 - 893 65 894 + 895 COS 896 RCL 03 897 44 898 + 899 COS 900 + 901 8 902 * 903 + 904 RCL 12 905 RCL 05 906 - 907 21 908 + 909 COS 910 10 911 * 912 + 913 RCL 05 914 52 915 - 916 COS 917 27 918 * 919 + 920 RCL 00 921 * 922 RCL 03 923 RCL 05 924 - 925 SIN 926 RCL 03 927 RCL 12 928 + 929 59 930 - 931 COS 932 + 933 RCL 04 934 RCL 12 935 + 936 SIN 937 + 938 RCL 14 939 ST+ X 940 STO 11 941 ST+ X 942 STO 15 943 46 944 - 945 COS 946 + 947 RCL 15 948 RCL 04 949 - 950 50 951 - 952 COS 953 - 954 RCL 12 955 65 956 + 957 COS 958 + 959 ST+ X 960 + 961 RCL 11 962 RCL 04 963 - 964 63 965 - 966 SIN 967 PI 968 * 969 + 970 RCL 11 971 RCL 14 972 + 973 60 974 - 975 COS 976 4 977 * 978 + 979 RCL 14 980 RCL 05 981 - 982 78 983 + 984 SIN |
985 5 986 * 987 - 988 RCL 09 989 RCL 14 990 + 991 RCL 05 992 - 993 STO 10 994 28 995 + 996 COS 997 6 998 * 999 + 1000 RCL 04 1001 RCL 05 1002 + 1003 80 1004 - 1005 COS 1006 7 1007 * 1008 + 1009 RCL 14 1010 10 1011 + 1012 SIN 1013 10 1014 * 1015 - 1016 RCL 11 1017 RCL 12 1018 + 1019 20 1020 - 1021 SIN 1022 12 1023 * 1024 + 1025 RCL 06 1026 RCL 12 1027 - 1028 10 1029 - 1030 COS 1031 RCL 12 1032 RCL 04 1033 - 1034 COS 1035 - 1036 15 1037 * 1038 + 1039 RCL 03 1040 73 1041 + 1042 SIN 1043 RCL 04 1044 39 1045 + 1046 SIN 1047 + 1048 35 1049 * 1050 - 1051 RCL 05 1052 RCL 12 1053 + 1054 STO 07 1055 11 1056 - 1057 COS 1058 39 1059 * 1060 + 1061 RCL 12 1062 RCL 03 1063 - 1064 STO 15 1065 51 1066 - 1067 COS 1068 40 1069 * 1070 + 1071 RCL 11 1072 19 1073 + 1074 SIN 1075 209 1076 * 1077 - 1078 RCL 05 1079 62.2 1080 - 1081 SIN 1082 858 1083 * 1084 + 1085 STO 03 1086 RCL 11 1087 33 1088 + 1089 COS 1090 RCL 07 1091 SIN 1092 - 1093 6 1094 * 1095 RCL 05 1096 39 1097 + 1098 SIN 1099 ST+ X 1100 - 1101 STO 04 1102 RCL 06 1103 RCL 12 1104 - 1105 80 1106 + 1107 COS 1108 5 1109 * 1110 RCL 10 1111 SIN 1112 PI 1113 * 1114 - 1115 RCL 11 1116 RCL 05 1117 - 1118 SIN 1119 ST+ X 1120 - 1121 RCL 07 1122 11 1123 - 1124 SIN 1125 RCL 15 1126 49 1127 - 1128 SIN 1129 + 1130 6 1131 * 1132 + 1133 RCL 11 1134 19 1135 + 1136 COS 1137 34 1138 * 1139 + 1140 26 1141 - 1142 STO 05 1143 19.218 1144 STO 09 1145 RCL 00 1146 8 1147 RCL 00 1148 4 1149 * 1150 + 1151 * 1152 773 1153 + 1154 STO 11 1155 CLX 1156 27 1157 - 1158 * 1159 4630 1160 + 1161 STO 10 1162 CLX 1163 30 1164 * 1165 4298642 1166 + 1167 * 1168 45955 1169 - 1170 STO 12 1171 CLX 1172 21 1173 * 1174 14862 1175 + 1176 * 1177 172993 1178 + 1179 STO 13 1180 RDN 1181 CHS 1182 18 1183 + 1184 * 1185 134 1186 + 1187 * 1188 5210 1189 + 1190 * 1191 74005 1192 XEQ "K" 1193 RTN 1194 LBL "NE" 1195 XEQ "M" 1196 RCL 14 1197 RCL 04 1198 - 1199 61 1200 + 1201 COS 1202 RCL 14 1203 ST+ X 1204 24 1205 + 1206 SIN 1207 - 1208 RCL 14 1209 COS 1210 RCL 05 1211 38 1212 + 1213 SIN 1214 9 1215 * 1216 + 1217 RCL 00 1218 * 1219 - 1220 ST+ X 1221 RCL 07 1222 RCL 13 1223 - 1224 STO 10 1225 16 1226 + 1227 COS 1228 RCL 05 1229 RCL 13 1230 + |
1231 77 1232 - 1233 COS 1234 + 1235 5 1236 * 1237 + 1238 RCL 06 1239 RCL 13 1240 - 1241 STO 08 1242 COS 1243 9 1244 * 1245 + 1246 RCL 14 1247 RCL 05 1248 - 1249 STO 09 1250 11 1251 - 1252 COS 1253 22 1254 * 1255 + 1256 RCL 04 1257 50 1258 - 1259 COS 1260 24 1261 * 1262 + 1263 RCL 14 1264 7 1265 + 1266 SIN 1267 71 1268 * 1269 + 1270 RCL 05 1271 27.8 1272 + 1273 COS 1274 584 1275 * 1276 + 1277 STO 03 1278 RCL 04 1279 RCL 14 1280 + 1281 69 1282 - 1283 SIN 1284 RCL 14 1285 54 1286 + 1287 SIN 1288 - 1289 9 1290 * 1291 STO 04 1292 RCL 09 1293 11 1294 - 1295 SIN 1296 RCL 08 1297 SIN 1298 - 1299 5 1300 * 1301 RCL 10 1302 16 1303 + 1304 SIN 1305 3 1306 * 1307 - 1308 RCL 05 1309 63 1310 - 1311 COS 1312 8 1313 * 1314 + 1315 RCL 14 1316 6 1317 + 1318 COS 1319 17 1320 * 1321 - 1322 41 1323 - 1324 STO 05 1325 30.11 1326 STO 09 1327 RCL 00 1328 899 1329 RCL 00 1330 6 1331 * 1332 + 1333 STO 10 1334 CLX 1335 93 1336 + 1337 * 1338 CHS 1339 1770 1340 + 1341 STO 11 1342 CLX 1343 31 1344 * 1345 2198828 1346 + 1347 * 1348 55654 1349 - 1350 STO 12 1351 CLX 1352 38 1353 * 1354 14260 1355 + 1356 * 1357 48124 1358 + 1359 STO 13 1360 CLX 1361 26 1362 * 1363 11021 1364 + 1365 * 1366 131784 1367 XEQ "K" 1368 RTN 1369 LBL "PL" 1370 RCL 00 1371 28897 1372 * 1373 65 1374 + 1375 COS 1376 7 1377 * 1378 RCL 00 1379 10769 1380 * 1381 76 1382 + 1383 COS 1384 4 1385 * 1386 + 1387 STO 03 1388 RCL 00 1389 86 1390 * 1391 4 1392 - 1393 STO 04 1394 RCL 00 1395 21 1396 * 1397 STO 05 1398 39.489 1399 STO 09 1400 24900 1401 STO 10 1402 17140 1403 STO 11 1404 1465671 1405 RCL 00 1406 * 1407 238927 1408 + 1409 STO 12 1410 RCL 00 1411 13971 1412 * 1413 135925 1414 - 1415 STO 13 1416 246232 1417 XEQ "K" 1418 RTN 1419 LBL "XE" 1420 RCL 00 1421 1358 1422 RCL 00 1423 26587 1424 * 1425 + 1426 * 1427 124 1428 - 1429 * 1430 STO 04 1431 CLX 1432 3080 1433 * 1434 1175 1435 - 1436 * 1437 14 1438 + 1439 STO 03 1440 CLX 1441 11605 1442 * 1443 960 1444 + 1445 * 1446 CHS 1447 8 1448 + 1449 STO 05 1450 CLX 1451 655265 1452 * 1453 20862 1454 + 1455 STO 12 1456 68.049 1457 STO 09 1458 43364 1459 STO 10 1460 503 1461 + 1462 STO 11 1463 RCL 00 1464 13970 1465 * 1466 187249 1467 + 1468 STO 13 1469 208790 1470 XEQ "K" 1471 END |
( 2168 bytes / SIZE 016
)
| STACK | INPUTS | OUTPUTS |
| Z | / | distance to the earth ( AU ) |
| Y | / | geocentric latitude ( deg ) |
| X | / | geocentric longitude ( deg ) |
Example1: If you
are using the subroutine "K" listed in paragraph 0°)
T = 1.2 = R00
i-e 3200/01/10 0h TT
• Mercury
XEQ "ME" >>>>
Long = 308°394
= R03
R06 = 41°700 = L
RDN Lat = -0°917
= R04 and
R07 = -2°516 = B
RDN Dist = 0.908313
AU = R05
R08 = 0.331214 AU = R
• Venus R/S
or XEQ "VE" >>>>
Long = 334°440
= R03
R06 = 51°123
RDN Lat = -1°714
= R04 and
R07 = -2°025
RDN Dist = 0.85506
AU = R05
R08 = 0.72386 AU
• Mars
R/S or XEQ "MA" >>>>
Long = 343°729
= R03
R06 = 19°233
RDN Lat = -0°963
= R04 and
R07 = -1°176
RDN Dist = 1.6951 AU
= R05
R08 = 1.3878 AU
• Jupiter R/S
or XEQ "JU" >>>>
Long = 116°734
= R03
R06 = 115°221
RDN Lat =
0°066
= R04 and
R07 = 0°054
RDN Dist = 4.177
AU = R05
R08 = 5.154 AU
• Saturn R/S
or XEQ "SA" >>>>
Long = 326°093
= R03
R06 = 329°536
RDN Lat = -0°975
= R04 and
R07 = -1°050
RDN Dist = 10.702 AU
= R05
R08 = 9.937 AU
• Uranus R/S or
XEQ "UR" >>>>
Long = 66°500
= R03
R06 = 68°428
RDN Lat = -0°172
= R04 and
R07 = -0°165
RDN Dist = 18.940 AU
= R05
R08 = 19.679 AU
• Neptune R/S or XEQ "NE"
>>>> Long = 61°159
= R03
R06 = 62°558
RDN Lat = -1°680
= R04 and
R07 = -1°642
RDN Dist = 29.113 AU
= R05
R08 = 29.785 AU
-For the 2 following planets, store T = 0.1 in R00
( 2100/01/01 0h TT ) and execute "SUN" first
• Pluto R/S
or XEQ "PL" >>>>
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 "XE" >>>>
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
Example2: If you are using the subroutine
"K" listed in paragraph 3°) below, see the example at the
bottom of this paragraph.
Notes:
-The following elements may also be used for Pluto & Xena:
• PLUTO
L = 238°927 + 1465°744 T - 0°957 T^2 + 3°457 T^3
i = 17°141
- 0°056 T
a = 39.487 + T/22
omegabar = -135°925 + 13°889 T + 0°030 T^2
e = 0.24885 + 0.00060 T
OMEGA = omegabar + 246°232 -0°383 T
-After solving Kepler's equation with these orbital elements, add the following corrections:
dL = 0°007 Cos ( 28881 T + 64 ) + 0°007 Cos ( 1452 T -
79 )
max error ~ 0°015
dB = 0
max error ~ 0°007
between 1700 and 2300
dR = 0
max error ~ 0.018
• XENA
L = 21°030 + 659°569 T + 2°408 T^2 - 24°460 T^3
- 55°036 T^4
i = 43°993
+ 0°099 T
a = 67.842
omegabar = 187°200 + 13°429 T
e = 0.43846 + 0.00169 T
OMEGA = 35°978 + 13°878 T
-After solving Kepler's equation with these orbital elements, add the following corrections:
dL = 0
max error ~ 0°010
dB = 0
max error ~ 0°006
between 1793 and 2177
dR = 0.025 + 0.036 Cos ( 966 T +177
)
max error ~ 0.010
-The accuracy is lesser but the domain of validity is larger.
>>>> These formulas are used in the listing hereunder,
which can replace lines 1369 to 1471 in the listing above.
| 01 LBL "PL" 02 RCL 00 03 28881 04 * 05 64 06 + 07 COS 08 RCL 00 09 1452 10 * 11 79 12 - 13 COS 14 + 15 7 16 * 17 STO 03 18 CLX 19 STO 04 20 STO 05 21 RCL 00 22 39.487 23 RCL 00 24 22 25 / 26 + |
27 STO 09 28 CLX 29 60 30 * 31 24885 32 + 33 STO 10 34 CLX 35 56 36 * 37 17141 38 X<>Y 39 - 40 STO 11 41 CLX 42 3457 43 * 44 957 45 - 46 * 47 1465744 48 + 49 * 50 238927 51 + 52 STO 12 |
53 CLX 54 30 55 * 56 13889 57 + 58 * 59 135925 60 - 61 STO 13 62 X<>Y 63 383 64 * 65 - 66 246232 67 XEQ "K" 68 RTN 69 LBL "XE" 70 67.842 71 STO 09 72 CLX 73 STO 03 74 STO 04 75 25 76 RCL 00 77 966 78 * |
79 PI 80 - 81 COS 82 36 83 * 84 - 85 STO 05 86 RCL 00 87 24460 88 RCL 00 89 55036 90 * 91 + 92 * 93 CHS 94 2408 95 + 96 * 97 659569 98 + 99 * 100 21030 101 + 102 STO 12 103 CLX 104 169 |
105 * 106 43846 107 + 108 STO 10 109 CLX 110 99 111 * 112 43993 113 + 114 STO 11 115 CLX 116 13429 117 * 118 187200 119 + 120 STO 13 121 CLX 122 13878 123 * 124 35978 125 XEQ "K" 126 END |
( 257 bytes )
Example:
-With T = 0.176 ( i-e 2176/01/02 0h TT ) this variant gives the following ecliptic heliocentric coordinates:
• Pluto L = 109°531
B = -0°969
R = 41.791 AU
• Xena L = 76°411
B = 30°737
R = 61.237 AU
3°) Sidereal Time + Sun + Moon + Subroutines
-The nutation, aberration & time-light and parallax are taken into
account to get the topocentric azimuthal coordinates.
-The geocentric apparent coordinates are referred
to the true equinox of the date.
-For the nutation, however, only the largest term
is used.
Data Registers: ( Registers R16 thru R18 are to be initialized before executing these programs )
R00 = T = time since 2000/01/01 0h TT is initialized by executing
"ST"
( Unit = 1000 years = 365250 days )
R01, R02 contain the Sun's rectangular
ecliptic coordinates.
R03 = geocentric longitude in decimal degrees
R04 = geocentric latitude in decimal
degrees
R05 = distance to the Earth in Astronomical
Units ( for the Moon too )
R06 = heliocentric longitude in decimal
degrees = L
R07 = heliocentric latitude in decimal
degrees = B
R08 = radius vector in Astronomical
Units = R
R09 = right-ascension ( hh.mnss )
R10 = declination ( ° ' " )
R11 = Azimuth ( ° ' " ) reckoned
clockwise from South.
R12 = height ( ° ' " )
R13 = height ( ° ' " ) corrected
for refraction
R14 = elongation from the Sun ( deg
)
R15: temp
• R16 = Longitude ( ° ' " )
• R17 = Latitude ( °
' " )
• R18 = Delta T = TT - UT
( in seconds )
R19 = local true sidereal time ( hh.mnss )
R20 = true obliquity of the ecliptic
( deg )
R21 = nutation in longitude ( deg )
R22 = apparent longitude of the Sun
( deg )
R23 = distance Sun-Earth ( AU )
Flags: F01 F02 F03
SF 01 = the programs return the heliocentric coordinates L
, B , R in registers X , Y , Z respectively
CF 01 & SF 02 = the true geocentric
coordinates l , b , r are in X , Y , Z and the elongation
from the Sun is in T-register.
CF 01 & CF 02 = the topocentric
coordinates Az , h , h0 , and the elongation from the
Sun are returned in X , Y , Z , T respectively
CF 03 = the aberration & light-time are taken into account
SF 03 = no aberration & no light-time
correction
Subroutines:
"SUN3" ( cf "Astronomical Ephemeris (I)" ) Replace line
106 in the "SUN3" listing ( 30010 ) by 30009 to take into
account the new precession formulae.
"J0" or "J1" or "J2" ( cf "Julian &
Gregorian Calendars" )
| 01 LBL "ST" 02 DEG 03 HR 04 STO Z 05 X<>Y 06 XEQ "J0" 07 24 08 * 09 + 10 8766 E3 11 / 12 STO 00 13 .259 14 % 15 24000.51337 16 + 17 * 18 6.66452 19 + 20 + 21 RCL 18 22 315576 E5 23 / 24 RCL 00 25 + 26 STO 00 27 X^2 28 6 29 * 30 1301 31 - 32 RCL 00 33 * 34 E4 35 / 36 23.4393 37 + 38 19341 39 RCL 00 40 * 41 125 42 - 43 STO 20 44 COS 45 391 46 / 47 + 48 COS 49 LASTX 50 X<> 20 51 SIN 52 209 53 / 54 STO 21 55 * 56 RCL 16 57 HR 58 + 59 15 60 / 61 + 62 24 63 MOD 64 HMS 65 STO 19 66 RTN 67 LBL "SUN" 68 XEQ "SUN3" 69 STO 05 70 STO 23 71 X<>Y 72 STO 03 73 X<>Y 74 P-R 75 STO 01 76 X<>Y 77 STO 02 78 CLX 79 STO 04 80 RCL 03 81 176 82 1/X 83 - 84 RCL 21 85 + 86 STO 03 87 STO 22 88 XEQ 08 89 RTN 90 LBL "MO" 91 RCL 00 92 359990.503 93 RCL 00 94 65 95 / 96 - 97 * 98 2.964 99 - 100 STO 08 101 CLX 102 .188 103 * 104 CHS 105 4452671.114 106 + 107 * 108 68.245 109 - 110 STO 13 111 ST+ X 112 STO 14 113 CLX 114 70 115 / 116 .874 117 + 118 * 119 4771988.675 120 + 121 * 122 128.431 123 + 124 STO 07 125 ST+ X 126 STO 12 127 CLX 128 .365 129 * 130 4832020.175 131 - 132 * 133 86.657 134 - 135 STO 09 136 ST+ X 137 STO 06 138 2574 139 RCL 07 140 COS 141 28 142 * 143 RCL 14 144 RCL 07 145 - 146 STO 03 147 COS 148 5 149 * 150 + 151 RCL 14 152 COS 153 4 154 * 155 + |
156 5 157 * 158 - 159 RCL 12 160 COS 161 4 162 * 163 - 164 RCL 14 165 RCL 12 166 - 167 STO 15 168 COS 169 RCL 14 170 RCL 08 171 - 172 STO 11 173 COS 174 - 175 2 176 SQRT 177 * 178 + 179 RCL 07 180 RCL 14 181 + 182 STO 10 183 COS 184 - 185 RCL 03 186 RCL 08 187 - 188 COS 189 - 190 E6 191 / 192 STO 05 193 RCL 07 194 RCL 09 195 - 196 SIN 197 281 198 * 199 RCL 07 200 RCL 09 201 + 202 SIN 203 278 204 * 205 + 206 RCL 14 207 RCL 09 208 + 209 SIN 210 173 211 * 212 + 213 RCL 03 214 RCL 09 215 - 216 SIN 217 55 218 * 219 + 220 RCL 03 221 RCL 09 222 + 223 SIN 224 46 225 * 226 + 227 RCL 14 228 RCL 09 229 - 230 SIN 231 33 232 * 233 + 234 RCL 12 235 RCL 09 236 - 237 SIN 238 17 239 * 240 + 241 RCL 10 242 RCL 09 243 + 244 SIN 245 RCL 12 246 RCL 09 247 + 248 SIN 249 + 250 9 251 * 252 + 253 RCL 11 254 RCL 09 255 + 256 SIN 257 RCL 09 258 SIN 259 641 260 * 261 - 262 8 263 * 264 + 265 RCL 15 266 RCL 09 267 + 268 SIN 269 RCL 10 270 RCL 09 271 - 272 SIN 273 + 274 4 275 * 276 + 277 RCL 14 278 RCL 08 279 + 280 RCL 09 281 + 282 SIN 283 PI 284 * 285 - 286 RCL 11 287 RCL 09 288 - 289 STO 04 290 RCL 07 291 - 292 SIN 293 LASTX 294 RCL 06 295 + 296 SIN 297 + 298 RCL 04 299 SIN 300 + 301 RCL 09 302 RCL 07 303 - 304 STO 04 305 RCL 08 306 + 307 SIN 308 - 309 RCL 04 310 RCL 14 |
311 ST+ X 312 + 313 SIN 314 + 315 RCL 08 316 RCL 09 317 - 318 SIN 319 - 320 RCL 06 321 RCL 09 322 + 323 SIN 324 + 325 ST+ X 326 + 327 STO 04 328 RCL 07 329 SIN 330 6289 331 * 332 RCL 14 333 SIN 334 658 335 * 336 + 337 RCL 12 338 SIN 339 214 340 * 341 + 342 RCL 06 343 SIN 344 114 345 * 346 + 347 RCL 15 348 SIN 349 59 350 * 351 + 352 RCL 03 353 RCL 08 354 - 355 SIN 356 57 357 * 358 + 359 RCL 10 360 SIN 361 53 362 * 363 + 364 RCL 11 365 SIN 366 46 367 * 368 + 369 RCL 08 370 RCL 07 371 - 372 SIN 373 41 374 * 375 - 376 RCL 03 377 SIN 378 98 379 * 380 RCL 07 381 RCL 06 382 - 383 SIN 384 - 385 13 386 * 387 + 388 RCL 07 389 RCL 06 390 + 391 SIN 392 RCL 14 393 ST+ X 394 RCL 07 395 - 396 SIN 397 + 398 11 399 * 400 + 401 RCL 03 402 ST+ X 403 SIN 404 9 405 * 406 + 407 RCL 03 408 RCL 08 409 + 410 SIN 411 8 412 * 413 - 414 RCL 14 415 RCL 08 416 + 417 SIN 418 7 419 * 420 - 421 RCL 08 422 SIN 423 RCL 00 424 37 425 - 426 * 427 RCL 13 428 SIN 429 7 430 * 431 - 432 RCL 07 433 RCL 08 434 + 435 SIN 436 6 437 * 438 - 439 RCL 14 440 RCL 06 441 + 442 SIN 443 3 444 * 445 + 446 RCL 07 447 RCL 12 448 + 449 SIN 450 ST+ X 451 + 452 RCL 13 453 RCL 07 454 - 455 SIN 456 - 457 RCL 13 458 RCL 08 459 + 460 SIN 461 + 462 5 463 * 464 + 465 RCL 10 |
466 RCL 08 467 - 468 SIN 469 RCL 14 470 RCL 12 471 + 472 SIN 473 + 474 RCL 14 475 ST+ X 476 SIN 477 + 478 RCL 03 479 RCL 12 480 - 481 SIN 482 + 483 RCL 00 484 23 485 * 486 1 487 - 488 R-D 489 SIN 490 - 491 4 492 * 493 + 494 RCL 08 495 RCL 12 496 - 497 SIN 498 RCL 03 499 RCL 06 500 - 501 SIN 502 + 503 3 504 * 505 - 506 RCL 11 507 RCL 08 508 - 509 SIN 510 LASTX 511 RCL 07 512 - 513 SIN 514 + 515 RCL 11 516 RCL 12 517 - 518 SIN 519 + 520 RCL 13 521 RCL 07 522 + 523 SIN 524 - 525 RCL 12 526 RCL 08 527 + 528 SIN 529 - 530 RCL 08 531 ST+ X 532 SIN 533 - 534 RCL 06 535 RCL 10 536 + 537 SIN 538 - 539 RCL 14 540 RCL 06 541 - 542 SIN 543 - 544 RCL 00 545 ST+ X 546 158 547 - 548 RCL 00 549 * 550 4812678812 551 + 552 RCL 00 553 * 554 211728 555 + 556 E3 557 / 558 360 559 MOD 560 SIN 561 ST+ X 562 ST- 04 563 X<> L 564 STO 03 565 RCL 09 566 + 567 SIN 568 + 569 ST+ X 570 + 571 E3 572 ST/ 04 573 / 574 RCL 21 575 + 576 ST+ 03 577 XEQ 08 578 RTN 579 GTO "ME" 580 LBL "M" 581 102 582 RCL 00 583 20.599909 584 * 585 STO 15 586 * 587 STO 14 588 106 589 LASTX 590 * 591 STO 13 592 + 593 STO 12 594 19 595 RCL 15 596 * 597 STO 11 598 593 599 LASTX 600 * 601 STO 07 602 LASTX 603 880 604 * 605 STO 08 606 + 607 STO 06 608 LASTX 609 RCL 07 610 - 611 STO 09 612 + 613 STO 10 614 4 615 RCL 15 616 * 617 STO 05 618 ST+ X 619 STO 04 620 LASTX |
621 31 622 * 623 STO 03 624 RTN 625 LBL "K" 626 + 627 E3 628 ST/ 03 629 ST/ 04 630 ST/ 05 631 ST/ 11 632 ST/ 12 633 ST/ 13 634 / 635 STO 14 636 E5 637 ST/ 10 638 12 639 STO 08 640 RCL 12 641 RCL 13 642 - 643 360 644 MOD 645 ENTER 646 ENTER 647 LBL 10 648 SIN 649 RCL 10 650 R-D 651 * 652 + 653 DSE 08 654 GTO 10 655 2 656 / 657 1 658 RCL 10 659 + 660 1 661 LASTX 662 - 663 / 664 SQRT 665 P-R 666 LASTX 667 / 668 R-P 669 RDN 670 ST+ X 671 1 672 R^ 673 ST+ X 674 COS 675 RCL 10 676 * 677 - 678 RCL 09 679 * 680 RCL 05 681 + 682 STO 08 683 CLX 684 RCL 14 685 - 686 RCL 13 687 + 688 COS 689 RCL 11 690 LASTX 691 SIN 692 P-R 693 X<>Y 694 ASIN 695 RCL 04 696 + 697 STO 07 698 X<> Z 699 R-P 700 CLX 701 RCL 14 702 + 703 RCL 03 704 + 705 360 706 MOD 707 STO 06 708 RCL 08 709 RCL 07 710 RCL 06 711 FS? 01 712 RTN 713 RCL 08 714 XEQ 07 715 RCL 02 716 ST+ Z 717 CLX 718 RCL 01 719 + 720 XEQ 06 721 STO 05 722 CLX 723 RCL 21 724 + 725 STO 03 726 X<>Y 727 STO 04 728 FS? 03 729 GTO 08 730 RCL 05 731 X^2 732 RCL 23 733 X^2 734 STO 11 735 - 736 RCL 08 737 X^2 738 + 739 RCL 05 740 ST+ X 741 / 742 RCL 09 743 1 744 RCL 10 745 X^2 746 - 747 * 748 SQRT 749 RCL 08 750 X^2 751 / 752 RCL 11 753 1/X 754 - 755 * 756 RCL 05 757 RCL 11 758 / 759 + 760 176 761 / 762 ST- 03 763 LBL 08 764 RCL 03 765 RCL 22 766 - 767 COS 768 RCL 04 769 COS 770 * 771 ACOS 772 STO 14 773 RCL 05 774 RCL 04 775 RCL 03 |
776 FS? 02 777 RTN 778 RCL 20 779 CHS 780 RCL 04 781 RCL 03 782 XEQ 05 783 X<>Y 784 HMS 785 X<>Y 786 15 787 / 788 24 789 MOD 790 HMS 791 STO 09 792 STO 11 793 X<>Y 794 STO 10 795 STO 12 796 RCL 19 797 HR 798 RCL 11 799 HR 800 - 801 15 802 * 803 RCL 17 804 HR 805 90 806 - 807 RCL 12 808 HR 809 90 810 R^ 811 - 812 XEQ 05 813 90 814 X<>Y 815 - 816 360 817 MOD 818 STO 11 819 X<>Y 820 1 821 P-R 822 STO 13 823 CLX 824 23455 825 RCL 05 826 * 827 1/X 828 RCL 17 829 HR 830 STO 12 831 SIN 832 X^2 833 298.257 834 STO 15 835 / 836 CHS 837 1 838 + 839 * 840 ST- Y 841 RCL 12 842 ST+ X 843 SIN 844 RCL 15 845 / 846 * 847 STO 15 848 RCL 11 849 COS 850 RCL 13 851 * 852 ST+ X 853 - 854 RCL 15 855 * 856 RCL 13 857 X^2 858 + 859 SQRT 860 R-P 861 X<>Y 862 HMS 863 STO 12 864 RCL 11 865 RCL 13 866 P-R 867 RCL 15 868 - 869 R-P 870 RDN 871 HMS 872 STO 11 873 X<>Y 874 HR 875 19.272 876 RCL Y 877 6.942 878 + 879 / 880 + 881 5.459 882 X<>Y 883 / 884 + 885 TAN 886 1/X 887 62.6 888 / 889 X<0? 890 CLX 891 + 892 HMS 893 STO 13 894 RCL 14 895 X<>Y 896 RCL 12 897 RCL 11 898 RTN 899 LBL 05 900 1 901 XEQ 07 902 RDN 903 R-P 904 X<> Z 905 ST- Y 906 X<> Z 907 P-R 908 R^ 909 XEQ 06 910 RDN 911 RTN 912 LBL 06 913 R-P 914 X<>Y 915 RDN 916 R-P 917 R^ 918 X<>Y 919 RTN 920 LBL 07 921 X<>Y 922 RDN 923 P-R 924 R^ 925 X<>Y 926 P-R 927 END |
( 1286 bytes / SIZE 024
)
| STACK | INPUTS | OUTPUTS |
| T | / | Elg = elongation from the Sun ( deg ) |
| Z | / | h0 = apparent altitude ( ° ' '' ) |
| Y | / | h = true altitude ( ° ' '' ) |
| X | / | Az = Azimuth ( ° ' '' ) |
Example: Suppose we are
at the US Naval Observatory at Washington ( D.C. ) on 2100/01/01
7h41m UT , assuming TT-UT = 203 seconds
• Longitude = 77°03'56"
W = -77°03'56" STO 16
• Latitude
= 38°55'17" N = +38°55'17" STO 17
•
DELTA T = TT - UT = 203s
STO 18
CF 01 CF 02 CF 03
• True local sidereal time
2100.0101 ENTER^
7.41 XEQ "ST" >>>>
TLST = 9h16m57s3 = R19
-We also have
true obliquity of the ecliptic = 23°4288 = R20
nutation in longitude
= 0°0008 = R21
• The Sun
R/S or XEQ "SUN" >>>>
Az = -105°36'34" = R11
RDN h = -54°33'15" = R12
RDN h0 = -54°33'15" = R13
( when h0 < 0 , h0 is meaningless )
RDN Elg = 0
R03 = l = 280°932
R09 = R.A. = 18h47m33s
R04 = b = 0
R10 = Decl = 22°58'44"
R05 = r = 0.983349 AU
the rectangular coordinates of the Sun: R01 = X = 0.186563
& R02 = Y = -0.965489
apparent longitude of Sun = R22 = 280°932
distance Earth-Sun = R23 = 0.983349
AU
• The Moon:
R/S or XEQ "MO"
>>>> Az = -41°28'13" = R11
RDN h = 51°16'54"
= R12
RDN h0 = 51°17'40"
= R13
RDN Elg = 119°01 = R14
R03 = l = 161°921
R09 = R.A. = 10h54m23s
R04 = b = 0°699
R10 = Decl = 7°44'04"
R05 = r = 0.002483 AU
• Mercury:
R/S or XEQ "ME"
>>>> Az = -112°29'21" = R11
RDN h = -61°33'32" = R12
RDN h0 = -61°33'32" = R13
RDN Elg = 7°88 = R14
R03 = l = -71°472
R06 = L = 306°251
R09 = R.A. = 19h21m32s
R04 = b = -2°120
R07 = B = -6°822
R10 = Decl = -24°14'53"
R05 = r = 1.38310 AU
R08 = R = 0.43077 AU
• Venus:
R/S or XEQ "VE"
>>>> Az = 169°29'37" =
R11
RDN h = -67°11'25" = R12
RDN h0 = -67°11'25" = R13
RDN Elg = 39°56 = R14
R03 = l = -39°542
R06 = L = 20°246
R09 = R.A. = 21h33m52s
R04 = b = -1°845
R07 = B = -2°860
R10 = Decl = -16°24'46"
R05 = r = 1.1236 AU
R08 = R = 0.7252 AU
• Mars:
R/S or XEQ "MA"
>>>> Az = 113°32'57" =
R11
RDN h = -8°43'04" = R12
RDN h0 = -8°43'04" = R13
RDN Elg = 108°73 = R14
R03 = l = 29°662
R06 = L = 67°745
R09 = R.A. = 1h48m59s
R04 = b = 0°957
R07 = B = 0°553
R10 = Decl = 12°14'35"
R05 = r = 0.8729 AU
R08 = R = 1.5100 AU
• Jupiter:
R/S or XEQ "JU"
>>>> Az = -65°15'06" =
R11
RDN h = 17°20'45" = R12
RDN h0 = 17°23'46" = R13
RDN Elg = 79°69 = R14
R03 = l = -158°757
R06 = L = 191°020
R09 = R.A. = 13h20m27s
R04 = b = 1°277
R07 = B = 1°298
R10 = Decl = -7°05'55"
R05 = r = 5.540 AU
R08 = R = 5.451 AU
• Saturn:
R/S or XEQ "SA"
>>>> Az = -68°05'24" =
R11
RDN h = 13°42'40" = R12
RDN h0 = 13°46'29" = R13
RDN Elg = 75°30 = R14
R03 = l = -154°353
R06 = L = 199°997
R09 = R.A. = 13h38m40s
R04 = b = 2°424
R07 = B = 2°475
R10 = Decl = -7°39'01"
R05 = r = 9.868 AU
R08 = R = 9.665 AU
• Uranus:
R/S or XEQ "UR"
>>>> Az = 116°49'08" =
R11
RDN h = -20°18'51" = R12
RDN h0 = -20°18'51" = R13
RDN Elg = 96°81 = R14
R03 = l = 17°745
R06 = L = 20°547
R09 = R.A. = 1h06m25s
R04 = b = -0°631
R07 = B = -0°626
R10 = Decl = 6°22'39"
R05 = r = 19.834 AU
R08 = R = 19.974 AU
• Neptune:
R/S or XEQ "NE"
>>>> Az = -46°29'42" =
R11
RDN h = 47°36'39"
= R12
RDN h0 =
47°37'32" = R13
RDN Elg = 113°64 = R14
R03 = l = 167°288
R06 = L = 165°577
R09 = R.A. = 11h14m44s
R04 = b = 0°966
R07 = B = 0°953
R10 = Decl = 5°54'31"
R05 = r = 29.801 AU
R08 = R = 30.209 AU
• Pluto:
R/S or XEQ "PL"
>>>> Az = 95°34'30"
= R11
RDN h = -12°35'27"
= R12
RDN h0 = -12°35'27"
= R13
RDN Elg = 110°50 = R14
R03 = l = 32°402
R06 = L = 33°519
R09 = R.A. = 2h23m51s
R04 = b = -16°919
R07 = B = -16°793
R10 = Decl = -3°37'21"
R05 = r = 48.588 AU
R08 = R = 48.941 AU
• Xena:
R/S or XEQ "XE"
>>>> Az = 113°18'36"
= R11
RDN h = 5°45'32"
= R12
RDN h0 =
5°53'56" = R13
RDN Elg = 122°05 = R14
R03 = l = 43°193
R06 = L = 43°761
R09 = R.A. = 2h34m58s
R04 = b = 6°180
R07 = B = 6°141
R10 = Decl = 21°40'31"
R05 = r = 83.424 AU
R08 = R = 83.950 AU
Notes:
-For Pluto & Xena, the 1st formulas at the top of this page have been used.
-The formulae for the aberration and light-time are only approximate (
lines 730 to 762 ).
-A better method is to compute the true positions
of the Sun and the planet at the instant ( t minus light-time ),
but it would be much slower.
-Lines 820 to 873 calculate the correction for parallax ( cf "Parallax
for the HP-41" )
-Lines 874 to 892 may be replaced by XEQ "H-H0"
where "H-H0" is listed in "Astronomical Refraction"
-The LBL 05 LBL 06 LBL 07 ( lines 899 to 927 )
are actually the routines "EE" "R-S" "S-R"
listed in "Transformation of Coordinates for the HP-41"
4°) Single Program [ 1900 , 2100 ]
a) Program#1
-Here is a smaller program - but less accurate.
-Xena coordinates are not computed.
-Nutation, aberration and time-light are not taken into account
Registers
R01 = X Rectangular
R02 = Y coordinates of the Sun,
R03 = Geocentric longitude ( deg )
R04 = Geocentric latitude ( deg )
R05 = Distance Earth-Planet ( AU )
R06 = Heliocentric longitude ( deg )
R07 = Heliocentric latitude ( deg )
R08 = Radius vector ( AU )
R09 = Right-ascension ( deg )
R10 = Declination ( deg )
R11 = Azimuth ( deg ) ( reckoned clockwise from South )
R12 = height ( deg )
R13 = height corrected for refraction ( deg )
R14 & R15: temp
• R16 = Longitude of the observer ( ° ' " ) positive East
• R17 = Latitude of the observer ( ° ' " )
• R18 = DeltaT = TT - UT ( seconds )
R19 = local true sidereal time ( deg )
Flags: /
Subroutine: "J" or "J1" ( cf "Julian & Gregorian Calendars for the HP-41" )
-With an HP41CX or a TIME module, lines 08-09 may be replaced by 1.012 DDAYS -
| 01 LBL "EPH" 02 DEG 03 HR 04 STO 15 05 24 06 / 07 X<>Y 08 XEQ "J" 09 + 10 36525 11 / 12 STO 00 13 36000770 14 STO 06 15 * 16 E3 17 STO 09 18 / 19 99.9678 20 + 21 RCL 15 22 15 23 * 24 + 25 RCL 16 26 HR 27 + 28 STO 19 29 RCL 18 30 315576 E4 31 / 32 ST+ 00 33 1671 34 STO 10 35 48 36 + 37 STO 15 38 4 39 CHS 40 STO 14 41 80026 42 CHS 43 STO 12 44 2963 45 + 46 STO 13 47 RCL 00 48 445267 49 * 50 68 51 - 52 STO 03 53 SIN 54 RCL 00 55 20 56 * 57 18 58 - 59 COS 60 - 61 RCL 00 62 32964 63 * 64 23 65 - 66 COS 67 - 68 ST+ X 69 X<> 03 70 COS 71 PI 72 % 73 STO 05 74 CLST 75 STO 01 76 STO 02 77 STO 04 78 STO 11 79 XEQ 14 80 RCL 03 81 RCL 05 82 P-R 83 STO 01 84 X<>Y 85 STO 02 86 RCL 13 87 RCL 12 88 RCL 11 89 RTN 90 LBL 03 91 RCL 00 92 RCL 00 93 3599905 94 % 95 2.96 96 - 97 STO 11 98 STO 12 99 CLX 100 44526711 101 % 102 68.25 103 - 104 STO 13 105 ST+ X 106 STO 03 107 STO 10 108 ST- 11 109 STO 14 110 CLX 111 47719887 112 + 113 % 114 128.43 115 + 116 ST- 03 117 STO 07 118 ST+ 10 119 ST+ X 120 STO 08 121 STO 15 122 CLX 123 48320202 124 % 125 86.66 126 + 127 STO 09 128 ST+ 15 129 ST+ X 130 STO 06 131 2574 132 RCL 07 133 COS 134 28 135 * 136 RCL 03 137 COS 138 5 139 * 140 + 141 RCL 14 142 COS 143 4 144 * 145 + 146 5 147 * 148 - 149 E6 150 / 151 STO 05 152 RCL 07 153 RCL 09 154 + 155 SIN 156 281 157 * 158 RCL 07 159 RCL 09 160 - 161 SIN 162 278 163 * 164 + 165 RCL 14 166 RCL 09 167 - 168 SIN 169 173 170 * 171 + 172 RCL 03 173 RCL 09 174 + 175 SIN 176 55 177 * 178 + 179 RCL 03 180 RCL 09 181 - 182 SIN 183 46 184 * 185 + 186 RCL 09 187 RCL 14 188 + 189 SIN 190 33 191 * 192 + 193 RCL 15 194 SIN 195 17 196 * 197 + 198 RCL 10 199 RCL 09 200 - 201 SIN 202 RCL 08 203 RCL 09 204 - 205 SIN 206 + 207 9 208 * 209 + |
210 RCL 09 211 RCL 11 212 + 213 SIN 214 RCL 09 215 SIN 216 641 217 * 218 - 219 8 220 * 221 - 222 RCL 14 223 RCL 15 224 - 225 SIN 226 RCL 09 227 RCL 10 228 + 229 SIN 230 + 231 4 232 * 233 + 234 RCL 12 235 RCL 14 236 + 237 RCL 09 238 - 239 SIN 240 3 241 * 242 - 243 STO 04 244 RCL 07 245 SIN 246 6289 247 * 248 RCL 14 249 SIN 250 658 251 * 252 + 253 RCL 08 254 SIN 255 214 256 * 257 + 258 RCL 06 259 SIN 260 114 261 * 262 - 263 RCL 14 264 RCL 08 265 - 266 SIN 267 59 268 * 269 + 270 RCL 03 271 RCL 12 272 - 273 SIN 274 57 275 * 276 + 277 RCL 10 278 SIN 279 53 280 * 281 + 282 RCL 11 283 SIN 284 46 285 * 286 - 287 RCL 12 288 RCL 07 289 - 290 SIN 291 41 292 * 293 - 294 RCL 03 295 SIN 296 98 297 * 298 RCL 06 299 RCL 07 300 + 301 SIN 302 - 303 13 304 * 305 + 306 RCL 07 307 RCL 06 308 - 309 SIN 310 RCL 14 311 ST+ X 312 STO 15 313 RCL 07 314 - 315 SIN 316 + 317 11 318 * 319 + 320 RCL 03 321 ST+ X 322 SIN 323 9 324 * 325 + 326 RCL 03 327 RCL 12 328 + 329 SIN 330 8 331 * 332 - 333 RCL 12 334 RCL 14 335 + 336 SIN 337 7 338 * 339 - 340 RCL 12 341 SIN 342 37 343 * 344 RCL 13 345 SIN 346 7 347 * 348 + 349 RCL 07 350 RCL 12 351 + 352 SIN 353 6 354 * 355 + 356 RCL 14 357 RCL 06 358 - 359 SIN 360 3 361 * 362 - 363 RCL 07 364 RCL 08 365 + 366 SIN 367 ST+ X 368 - 369 RCL 13 370 RCL 07 371 - 372 SIN 373 + 374 RCL 12 375 RCL 13 376 + 377 SIN 378 - 379 5 380 * 381 - 382 RCL 10 383 RCL 12 384 - 385 SIN 386 RCL 08 387 ST- 12 388 RCL 14 389 + 390 SIN 391 + 392 RCL 15 393 SIN 394 + 395 RCL 03 396 RCL 08 397 - 398 SIN 399 + 400 RCL 00 401 132 402 * 403 60 404 - 405 SIN 406 - 407 4 408 * 409 + 410 RCL 12 411 SIN 412 RCL 03 413 RCL 06 414 + 415 SIN 416 + 417 3 418 * |
419 - 420 481267881 421 RCL 00 422 ST+ X 423 - 424 RCL 00 425 * 426 211728 427 + 428 + 429 E3 430 ST/ 04 431 / 432 360 433 MOD 434 STO 03 435 XEQ 00 436 RTN 437 LBL 01 438 387.1 439 STO 09 440 20563 441 STO 10 442 7005 443 RCL 00 444 2 445 STO 14 446 * 447 + 448 STO 11 449 1556 450 STO 15 451 77456 452 STO 13 453 250205 454 STO 12 455 149474072 456 STO 06 457 48331 458 1186 459 XEQ 13 460 RTN 461 LBL 02 462 723.33 463 STO 09 464 677 465 STO 10 466 5 467 CHS 468 STO 14 469 3395 470 RCL 00 471 + 472 STO 11 473 1402 474 STO 15 475 131564 476 STO 13 477 181179 478 STO 12 479 58519213 480 STO 06 481 76680 482 901 483 XEQ 13 484 RTN 485 LBL 04 486 XEQ 12 487 RCL 15 488 10 489 * 490 18 491 - 492 COS 493 16 494 * 495 RCL 09 496 22 497 * 498 RCL 03 499 + 500 ST+ 06 501 12 502 - 503 COS 504 6 505 * 506 - 507 RCL 06 508 49 509 + 510 COS 511 7 512 * 513 + 514 RCL 08 515 RCL 11 516 + 517 RCL 12 518 + 519 21 520 + 521 COS 522 RCL 06 523 ST+ X 524 11 525 + 526 COS 527 - 528 4 529 * 530 + 531 STO 03 532 CLX 533 STO 04 534 STO 05 535 1523.7 536 STO 09 537 9340 538 STO 10 539 1850 540 STO 11 541 9 542 STO 14 543 - 544 STO 15 545 4829 546 CHS 547 STO 12 548 19141696 549 STO 06 550 23940 551 CHS 552 STO 13 553 49558 554 772 555 XEQ 14 556 RTN 557 LBL 05 558 XEQ 12 559 RCL 11 560 32 561 - 562 COS 563 4 564 * 565 RCL 00 566 * 567 RCL 08 568 73 569 + 570 COS 571 RCL 10 572 RCL 07 573 - 574 41 575 + 576 SIN 577 - 578 509 579 SQRT 580 * 581 + 582 RCL 06 583 RCL 11 584 + 585 STO 04 586 12 587 + 588 SIN 589 16 590 * 591 - 592 RCL 08 593 3 594 * 595 28 596 + 597 COS 598 RCL 09 599 ST+ X 600 STO 13 601 25 602 + 603 COS 604 + 605 5 606 * 607 - 608 RCL 13 609 RCL 06 610 + 611 69 612 - 613 COS 614 RCL 07 615 COS 616 + 617 RCL 06 618 ST+ X 619 STO 13 620 RCL 09 621 + 622 79 623 + 624 COS 625 - 626 4 627 * |
628 + 629 RCL 11 630 ST- 06 631 ST- 13 632 ST+ X 633 75 634 ST- 09 635 + 636 COS 637 RCL 13 638 60 639 + 640 COS 641 - 642 3 643 * 644 + 645 RCL 09 646 SIN 647 37 648 * 649 + 650 RCL 06 651 61 652 - 653 SIN 654 42 655 * 656 + 657 RCL 10 658 33 659 - 660 STO 10 661 SIN 662 56 663 * 664 + 665 RCL 11 666 7.3 667 - 668 SIN 669 329 670 * 671 - 672 STO 03 673 RCL 04 674 18 675 + 676 COS 677 4 678 * 679 RCL 06 680 63 681 - 682 SIN 683 5 684 * 685 + 686 STO 04 687 RCL 10 688 COS 689 3 690 * 691 CHS 692 STO 05 693 5203 694 STO 09 695 1303 696 RCL 00 697 5 698 * 699 - 700 STO 11 701 4849 702 STO 10 703 16 704 STO 14 705 1613 706 STO 15 707 34310 708 STO 12 709 3036303 710 STO 06 711 14331 712 STO 13 713 86133 714 + 715 1021 716 XEQ 14 717 RTN 718 LBL 06 719 XEQ 12 720 21 721 - 722 COS 723 RCL 11 724 ST+ X 725 75 726 + 727 COS 728 - 729 RCL 04 730 ST+ 14 731 RCL 05 732 + 733 SIN 734 - 735 8 736 * 737 RCL 06 738 RCL 09 739 RCL 11 740 + 741 STO 13 742 - 743 25 744 + 745 COS 746 RCL 08 747 30 748 - 749 COS 750 + 751 RCL 10 752 54 753 + 754 COS 755 + 756 9 757 * 758 + 759 RCL 07 760 RCL 03 761 - 762 COS 763 RCL 08 764 RCL 14 765 - 766 79 767 - 768 COS 769 + 770 6 771 * 772 - 773 RCL 06 774 14 775 + 776 COS 777 RCL 15 778 7 779 * 780 62 781 + 782 COS 783 - 784 3 785 * 786 + 787 RCL 13 788 SIN 789 14 790 * 791 + 792 RCL 11 793 32 794 - 795 COS 796 10 797 * 798 RCL 00 799 * 800 - 801 RCL 07 802 RCL 11 803 + 804 STO 04 805 50 806 - 807 SIN 808 45 809 * 810 + 811 RCL 09 812 14 813 + 814 COS 815 118 816 * 817 + 818 RCL 09 819 ST+ X 820 STO 13 821 ST+ 07 822 30 823 + 824 COS 825 228 826 * 827 + 828 RCL 11 829 7.3 830 - 831 SIN 832 810 833 * 834 + 835 STO 03 836 RCL 13 |
837 33 838 + 839 COS 840 20 841 ST+ 04 842 ST- 08 843 * 844 RCL 04 845 COS 846 18 847 * 848 - 849 RCL 07 850 28 851 - 852 COS 853 6 854 * 855 + 856 RCL 11 857 SIN 858 4 859 * 860 + 861 STO 04 862 RCL 13 863 60 864 - 865 COS 866 19 867 * 868 RCL 08 869 COS 870 8 871 * 872 + 873 RCL 09 874 73 875 - 876 COS 877 6 878 * 879 + 880 STO 05 881 9543 882 STO 09 883 5553 884 STO 10 885 35 886 CHS 887 STO 14 888 2489 889 RCL 00 890 4 891 * 892 - 893 STO 11 894 1964 895 STO 15 896 50061 897 STO 12 898 1223511 899 STO 06 900 93057 901 STO 13 902 20609 903 + 904 877 905 XEQ 14 906 RTN 907 LBL 07 908 XEQ 12 909 RCL 12 910 ST- 07 911 RCL 14 912 ST+ X 913 STO 11 914 + 915 20 916 - 917 SIN 918 RCL 13 919 12 920 ST* Z 921 - 922 COS 923 5 924 * 925 - 926 RCL 04 927 RCL 05 928 + 929 STO 13 930 80 931 - 932 COS 933 7 934 * 935 + 936 RCL 07 937 28 938 + 939 COS 940 6 941 * 942 + 943 RCL 11 944 RCL 14 945 + 946 60 947 - 948 COS 949 4 950 * 951 + 952 RCL 12 953 ST- 06 954 RCL 13 955 - 956 27 957 + 958 COS 959 PI 960 * 961 - 962 RCL 14 963 10 964 STO 10 965 + 966 SIN 967 RCL 10 968 ST- 06 969 * 970 - 971 RCL 06 972 COS 973 RCL 12 974 RCL 04 975 - 976 COS 977 - 978 15 979 * 980 + 981 RCL 05 982 RCL 12 983 + 984 STO 13 985 11 986 - 987 COS 988 39 989 * 990 + 991 RCL 12 992 RCL 03 993 - 994 51 995 - 996 COS 997 40 998 * 999 + 1000 RCL 03 1001 73 1002 + 1003 SIN 1004 RCL 04 1005 39 1006 + 1007 SIN 1008 + 1009 35 1010 * 1011 - 1012 RCL 11 1013 19 1014 + 1015 STO 11 1016 SIN 1017 209 1018 * 1019 - 1020 RCL 05 1021 62.2 1022 - 1023 SIN 1024 858 1025 * 1026 + 1027 STO 03 1028 RCL 11 1029 14 1030 + 1031 COS 1032 RCL 13 1033 SIN 1034 - 1035 6 1036 * 1037 STO 04 1038 RCL 11 1039 COS 1040 34 1041 * 1042 RCL 13 1043 79 1044 + 1045 COS |
1046 7 1047 * 1048 - 1049 STO 05 1050 19192 1051 STO 09 1052 45955 1053 CHS 1054 STO 12 1055 429864 1056 STO 06 1057 4630 1058 STO 10 1059 3 1060 CHS 1061 STO 14 1062 773 1063 RCL 00 1064 + 1065 STO 11 1066 1486 1067 STO 15 1068 172993 1069 STO 13 1070 74005 1071 521 1072 XEQ 14 1073 RTN 1074 LBL 08 1075 XEQ 12 1076 RCL 04 1077 50 1078 - 1079 COS 1080 24 1081 * 1082 RCL 13 1083 11 1084 - 1085 COS 1086 22 1087 * 1088 + 1089 RCL 06 1090 RCL 14 1091 ST+ 04 1092 RCL 05 1093 + 1094 ST- 07 1095 - 1096 COS 1097 9 1098 * 1099 + 1100 RCL 04 1101 77 1102 - 1103 COS 1104 RCL 07 1105 16 1106 + 1107 COS 1108 + 1109 5 1110 * 1111 + 1112 RCL 14 1113 7 1114 + 1115 SIN 1116 71 1117 * 1118 + 1119 RCL 05 1120 27.8 1121 + 1122 COS 1123 584 1124 * 1125 + 1126 STO 03 1127 RCL 04 1128 69 1129 - 1130 SIN 1131 RCL 14 1132 36 1133 - 1134 COS 1135 - 1136 9 1137 * 1138 STO 04 1139 RCL 05 1140 63 1141 - 1142 COS 1143 8 1144 * 1145 RCL 14 1146 6 1147 + 1148 COS 1149 17 1150 * 1151 - 1152 STO 05 1153 30070 1154 STO 09 1155 899 1156 STO 10 1157 CLX 1158 STO 14 1159 1770 1160 RCL 00 1161 9 1162 * 1163 - 1164 STO 11 1165 1426 1166 STO 15 1167 55654 1168 CHS 1169 STO 12 1170 219883 1171 STO 06 1172 48124 1173 STO 13 1174 83660 1175 + 1176 1102 1177 XEQ 14 1178 RTN 1179 LBL 09 1180 RCL 00 1181 2890 1182 * 1183 65 1184 + 1185 COS 1186 7 1187 * 1188 RCL 00 1189 1077 1190 * 1191 76 1192 + 1193 COS 1194 4 1195 * 1196 + 1197 STO 03 1198 RCL 00 1199 9 1200 * 1201 4 1202 - 1203 STO 04 1204 RCL 00 1205 ST+ X 1206 STO 05 1207 39489 1208 STO 09 1209 24900 1210 STO 10 1211 CLX 1212 STO 14 1213 17140 1214 STO 11 1215 224075 1216 STO 13 1217 238927 1218 STO 12 1219 146567 1220 STO 06 1221 36260 1222 - 1223 1397 1224 STO 15 1225 GTO 14 1226 LBL 12 1227 98 1228 RCL 00 1229 2.06 1230 * 1231 STO 15 1232 * 1233 STO 13 1234 4 1235 LASTX 1236 * 1237 STO 04 1238 ST+ 04 1239 STO 05 1240 + 1241 STO 14 1242 208 1243 RCL 15 1244 * 1245 STO 12 1246 19 1247 LASTX 1248 * 1249 STO 11 1250 593 1251 LASTX 1252 * 1253 STO 07 |
1254 LASTX 1255 880 1256 * 1257 STO 08 1258 + 1259 STO 06 1260 LASTX 1261 RCL 07 1262 - 1263 STO 09 1264 + 1265 STO 10 1266 RCL 15 1267 31 1268 * 1269 STO 03 1270 RTN 1271 LBL 13 1272 0 1273 STO 03 1274 STO 04 1275 STO 05 1276 RDN 1277 LBL 14 1278 RCL 00 1279 ST* 06 1280 ST* 14 1281 ST* 15 1282 * 1283 + 1284 X<> 14 1285 ST+ 10 1286 E5 1287 ST/ 10 1288 9 1289 STO 08 1290 RCL 06 1291 RCL 12 1292 + 1293 RCL 13 1294 RCL 15 1295 + 1296 E3 1297 ST/ 03 1298 ST/ 04 1299 ST/ 05 1300 ST/ 09 1301 ST/ 11 1302 ST/ 14 1303 ST/ Z 1304 / 1305 STO 13 1306 - 1307 ENTER 1308 ENTER 1309 LBL 11 1310 SIN 1311 RCL 10 1312 R-D 1313 * 1314 + 1315 DSE 08 1316 GTO 11 1317 STO 15 1318 2 1319 / 1320 RCL 10 1321 1 1322 ST+ Y 1323 RCL 10 1324 - 1325 / 1326 SQRT 1327 P-R 1328 LASTX 1329 / 1330 R-P 1331 X<>Y 1332 ST+ X 1333 1 1334 RCL 15 1335 COS 1336 RCL 10 1337 * 1338 - 1339 RCL 09 1340 * 1341 RCL 05 1342 + 1343 STO 08 1344 CLX 1345 RCL 13 1346 + 1347 RCL 14 1348 ST+ 03 1349 - 1350 COS 1351 RCL 11 1352 LASTX 1353 SIN 1354 P-R 1355 X<>Y 1356 ASIN 1357 RCL 04 1358 + 1359 STO 07 1360 X<> Z 1361 R-P 1362 CLX 1363 RCL 03 1364 + 1365 STO 06 1366 RCL 08 1367 XEQ 10 1368 RCL 02 1369 ST+ Z 1370 CLX 1371 RCL 01 1372 + 1373 XEQ 12 1374 STO 05 1375 RDN 1376 STO 03 1377 X<>Y 1378 STO 04 1379 LBL 00 1380 RCL 00 1381 77 1382 / 1383 549.4 1384 SQRT 1385 - 1386 RCL 04 1387 RCL 03 1388 XEQ 13 1389 STO 09 1390 X<>Y 1391 STO 10 1392 RCL 17 1393 HR 1394 90 1395 STO 11 1396 - 1397 RCL 10 1398 LASTX 1399 RCL 09 1400 + 1401 RCL 19 1402 - 1403 XEQ 13 1404 ST- 11 1405 X<>Y 1406 ENTER 1407 COS 1408 RCL 05 1409 409 1410 * 1411 / 1412 - 1413 STO 12 1414 19.272 1415 RCL 12 1416 6.942 1417 + 1418 / 1419 + 1420 5.459 1421 X<>Y 1422 / 1423 + 1424 TAN 1425 1/X 1426 62.6 1427 / 1428 + 1429 STO 13 1430 X<>Y 1431 RCL 11 1432 RTN 1433 LBL 13 1434 1 1435 XEQ 10 1436 RDN 1437 R-P 1438 X<> Z 1439 ST- Y 1440 X<> Z 1441 P-R 1442 R^ 1443 XEQ 12 1444 RDN 1445 RTN 1446 LBL 10 1447 X<>Y 1448 RDN 1449 P-R 1450 R^ 1451 X<>Y 1452 P-R 1453 RTN 1454 LBL 12 1455 R-P 1456 X<>Y 1457 RDN 1458 R-P 1459 R^ 1460 X<>Y 1461 END |
( 2152 bytes / SIZE 020 )
| STACK | INPUTS | OUTPUTS |
| Z | / | h0 = apparent altitude ( deg ) |
| Y | YYYY.MNDD | h = true altitude ( deg ) |
| X | hh.mnss (UT) | Az = Azimuth ( deg ) |
YYYY.MNDD ENTER^
hh.mnss XEQ "EPH" returns the azimuthal coordinates of the Sun.
-Then R/S or XEQ 03 gives the coordinates of the Moon
-Then R/S or XEQ 01 ------------------------ Mercury
............................................................................
-Then R/S or XEQ 09 ------------------------- Pluto.
Note:
-There are also smaller programs ( even less accurate ) listed in "Astronomical Ephemeris(IV)"
b) Program#2
-Nutation, aberration and time-light are approximately computed ( not for the heliocentric coordinates )
Registers
R01 = X Rectangular
R02 = Y coordinates of the Sun,
R03 = Geocentric longitude ( deg )
R04 = Geocentric latitude ( deg )
R05 = Distance Earth-Planet ( AU )
R06 = Heliocentric longitude ( deg )
R07 = Heliocentric latitude ( deg )
R08 = Radius vector ( AU )
R09 = Right-ascension ( deg )
R10 = Declination ( deg )
R11 = Azimuth ( deg ) ( reckoned clockwise from South )
R12 = height ( deg )
R13 = height corrected for refraction ( deg )
R14 & R15: temp
• R16 = Longitude of the observer ( ° ' " ) positive East
• R17 = Latitude of the observer ( ° ' " )
• R18 = DeltaT = TT - UT ( seconds )
R19 = local true sidereal time ( deg )
R20-R21-R22: temp
Flags: /
Subroutine: "J" or "J1" ( cf "Julian & Gregorian Calendars for the HP-41" )
-With an HP41CX or a TIME module, lines 08-09 may be replaced by 1.012 DDAYS -
| 01 LBL "EPH" 02 DEG 03 HR 04 STO 15 05 24 06 / 07 X<>Y 08 XEQ "J" 09 + 10 36525 11 / 12 STO 00 13 36000770 14 STO 06 15 * 16 E3 17 STO 09 18 / 19 99.9678 20 + 21 RCL 15 22 15 23 * 24 + 25 RCL 16 26 HR 27 + 28 STO 19 29 RCL 18 30 315576 E4 31 / 32 ST+ 00 33 RCL 00 34 1934 35 * 36 125 37 - 38 1 39 P-R 40 391 41 / 42 549.4 43 SQRT 44 + 45 RCL 00 46 77 47 / 48 - 49 STO 20 50 COS 51 X<>Y 52 209 53 / 54 STO 21 55 * 56 ST+ 19 57 1671 58 STO 10 59 48 60 + 61 STO 15 62 4 63 CHS 64 STO 14 65 80026 66 CHS 67 STO 12 68 2963 69 + 70 STO 13 71 RCL 00 72 445267 73 * 74 68 75 - 76 STO 03 77 SIN 78 RCL 00 79 20 80 * 81 18 82 - 83 COS 84 - 85 RCL 00 86 32964 87 * 88 23 89 - 90 COS 91 - 92 ST+ X 93 X<> 03 94 COS 95 PI 96 % 97 STO 05 98 CLST 99 STO 01 100 STO 02 101 STO 04 102 STO 11 103 XEQ 14 104 RCL 22 105 RCL 05 106 P-R 107 STO 01 108 X<>Y 109 STO 02 110 RCL 13 111 RCL 12 112 RCL 11 113 RTN 114 LBL 03 115 RCL 00 116 RCL 00 117 3599905 118 % 119 2.96 120 - 121 STO 11 122 STO 12 123 CLX 124 44526711 125 % 126 68.25 127 - 128 STO 13 129 ST+ X 130 STO 03 131 STO 10 132 ST- 11 133 STO 14 134 CLX 135 47719887 136 + 137 % 138 128.43 139 + 140 ST- 03 141 STO 07 142 ST+ 10 143 ST+ X 144 STO 08 145 STO 15 146 CLX 147 48320202 148 % 149 86.66 150 + 151 STO 09 152 ST+ 15 153 ST+ X 154 STO 06 155 2574 156 RCL 07 157 COS 158 28 159 * 160 RCL 03 161 COS 162 5 163 * 164 + 165 RCL 14 166 COS 167 4 168 * 169 + 170 5 171 * 172 - 173 E6 174 / 175 STO 05 176 RCL 07 177 RCL 09 178 + 179 SIN 180 281 181 * 182 RCL 07 183 RCL 09 184 - 185 SIN 186 278 187 * 188 + 189 RCL 14 190 RCL 09 191 - 192 SIN 193 173 194 * 195 + 196 RCL 03 197 RCL 09 198 + 199 SIN 200 55 201 * 202 + 203 RCL 03 204 RCL 09 205 - 206 SIN 207 46 208 * 209 + 210 RCL 09 211 RCL 14 212 + 213 SIN 214 33 215 * |
216 + 217 RCL 15 218 SIN 219 17 220 * 221 + 222 RCL 10 223 RCL 09 224 - 225 SIN 226 RCL 08 227 RCL 09 228 - 229 SIN 230 + 231 9 232 * 233 + 234 RCL 09 235 RCL 11 236 + 237 SIN 238 RCL 09 239 SIN 240 641 241 * 242 - 243 8 244 * 245 - 246 RCL 14 247 RCL 15 248 - 249 SIN 250 RCL 09 251 RCL 10 252 + 253 SIN 254 + 255 4 256 * 257 + 258 RCL 12 259 RCL 14 260 + 261 RCL 09 262 - 263 SIN 264 3 265 * 266 - 267 STO 04 268 RCL 07 269 SIN 270 6289 271 * 272 RCL 14 273 SIN 274 658 275 * 276 + 277 RCL 08 278 SIN 279 214 280 * 281 + 282 RCL 06 283 SIN 284 114 285 * 286 - 287 RCL 14 288 RCL 08 289 - 290 SIN 291 59 292 * 293 + 294 RCL 03 295 RCL 12 296 - 297 SIN 298 57 299 * 300 + 301 RCL 10 302 SIN 303 53 304 * 305 + 306 RCL 11 307 SIN 308 46 309 * 310 - 311 RCL 12 312 RCL 07 313 - 314 SIN 315 41 316 * 317 - 318 RCL 03 319 SIN 320 98 321 * 322 RCL 06 323 RCL 07 324 + 325 SIN 326 - 327 13 328 * 329 + 330 RCL 07 331 RCL 06 332 - 333 SIN 334 RCL 14 335 ST+ X 336 STO 15 337 RCL 07 338 - 339 SIN 340 + 341 11 342 * 343 + 344 RCL 03 345 ST+ X 346 SIN 347 9 348 * 349 + 350 RCL 03 351 RCL 12 352 + 353 SIN 354 8 355 * 356 - 357 RCL 12 358 RCL 14 359 + 360 SIN 361 7 362 * 363 - 364 RCL 12 365 SIN 366 37 367 * 368 RCL 13 369 SIN 370 7 371 * 372 + 373 RCL 07 374 RCL 12 375 + 376 SIN 377 6 378 * 379 + 380 RCL 14 381 RCL 06 382 - 383 SIN 384 3 385 * 386 - 387 RCL 07 388 RCL 08 389 + 390 SIN 391 ST+ X 392 - 393 RCL 13 394 RCL 07 395 - 396 SIN 397 + 398 RCL 12 399 ST- 10 400 RCL 13 401 + 402 SIN 403 - 404 5 405 * 406 - 407 RCL 10 408 SIN 409 RCL 08 410 ST- 12 411 RCL 14 412 + 413 SIN 414 + 415 RCL 15 416 SIN 417 + 418 RCL 03 419 RCL 08 420 - 421 SIN 422 + 423 RCL 00 424 132 425 * 426 60 427 - 428 SIN 429 - 430 4 |
431 * 432 + 433 RCL 12 434 SIN 435 RCL 03 436 RCL 06 437 + 438 SIN 439 + 440 3 441 * 442 - 443 481267881 444 RCL 00 445 ST+ X 446 - 447 RCL 00 448 * 449 211728 450 + 451 + 452 E3 453 ST/ 04 454 / 455 360 456 MOD 457 STO 03 458 XEQ 00 459 RTN 460 LBL 01 461 387.1 462 STO 09 463 20563 464 STO 10 465 7005 466 RCL 00 467 2 468 STO 14 469 * 470 + 471 STO 11 472 1556 473 STO 15 474 77456 475 STO 13 476 250205 477 STO 12 478 149474072 479 STO 06 480 48331 481 1186 482 XEQ 13 483 RTN 484 LBL 02 485 723.33 486 STO 09 487 677 488 STO 10 489 5 490 CHS 491 STO 14 492 3395 493 RCL 00 494 + 495 STO 11 496 1402 497 STO 15 498 131564 499 STO 13 500 181179 501 STO 12 502 58519213 503 STO 06 504 76680 505 901 506 XEQ 13 507 RTN 508 LBL 04 509 XEQ 12 510 RCL 15 511 10 512 * 513 18 514 - 515 COS 516 16 517 * 518 RCL 09 519 22 520 * 521 RCL 03 522 + 523 ST+ 06 524 12 525 - 526 COS 527 6 528 * 529 - 530 RCL 06 531 49 532 + 533 COS 534 7 535 * 536 + 537 RCL 08 538 RCL 11 539 + 540 RCL 12 541 + 542 21 543 + 544 COS 545 RCL 06 546 ST+ X 547 11 548 + 549 COS 550 - 551 4 552 * 553 + 554 STO 03 555 CLX 556 STO 04 557 STO 05 558 1523.7 559 STO 09 560 9340 561 STO 10 562 1850 563 STO 11 564 9 565 STO 14 566 - 567 STO 15 568 4829 569 CHS 570 STO 12 571 19141696 572 STO 06 573 23940 574 CHS 575 STO 13 576 49558 577 772 578 XEQ 14 579 RTN 580 LBL 05 581 XEQ 12 582 RCL 11 583 32 584 - 585 COS 586 4 587 * 588 RCL 00 589 * 590 RCL 08 591 73 592 + 593 COS 594 RCL 10 595 RCL 07 596 - 597 41 598 + 599 SIN 600 - 601 509 602 SQRT 603 * 604 + 605 RCL 06 606 RCL 11 607 + 608 STO 04 609 12 610 + 611 SIN 612 16 613 * 614 - 615 RCL 08 616 3 617 * 618 28 619 + 620 COS 621 RCL 09 622 ST+ X 623 STO 13 624 25 625 + 626 COS 627 + 628 5 629 * 630 - 631 RCL 13 632 RCL 06 633 + 634 69 635 - 636 COS 637 RCL 07 638 COS 639 + 640 RCL 06 641 ST+ X 642 STO 13 643 RCL 09 644 + 645 79 |
646 + 647 COS 648 - 649 4 650 * 651 + 652 RCL 11 653 ST- 06 654 ST- 13 655 ST+ X 656 75 657 ST- 09 658 + 659 COS 660 RCL 13 661 60 662 + 663 COS 664 - 665 3 666 * 667 + 668 RCL 09 669 SIN 670 37 671 * 672 + 673 RCL 06 674 61 675 - 676 SIN 677 42 678 * 679 + 680 RCL 10 681 33 682 - 683 STO 10 684 SIN 685 56 686 * 687 + 688 RCL 11 689 7.3 690 - 691 SIN 692 329 693 * 694 - 695 STO 03 696 RCL 04 697 18 698 + 699 COS 700 4 701 * 702 RCL 06 703 63 704 - 705 SIN 706 5 707 * 708 + 709 STO 04 710 RCL 10 711 COS 712 3 713 * 714 CHS 715 STO 05 716 5203 717 STO 09 718 1303 719 RCL 00 720 5 721 * 722 - 723 STO 11 724 4849 725 STO 10 726 16 727 STO 14 728 1613 729 STO 15 730 34310 731 STO 12 732 3036303 733 STO 06 734 14331 735 STO 13 736 86133 737 + 738 1021 739 XEQ 14 740 RTN 741 LBL 06 742 XEQ 12 743 21 744 - 745 COS 746 RCL 11 747 ST+ X 748 75 749 + 750 COS 751 - 752 RCL 04 753 ST+ 14 754 RCL 05 755 + 756 SIN 757 - 758 8 759 * 760 RCL 06 761 RCL 09 762 RCL 11 763 + 764 STO 13 765 - 766 25 767 + 768 COS 769 RCL 08 770 30 771 - 772 COS 773 + 774 RCL 10 775 54 776 + 777 COS 778 + 779 9 780 * 781 + 782 RCL 07 783 RCL 03 784 - 785 COS 786 RCL 08 787 RCL 14 788 - 789 79 790 - 791 COS 792 + 793 6 794 * 795 - 796 RCL 06 797 14 798 + 799 COS 800 RCL 15 801 7 802 * 803 62 804 + 805 COS 806 - 807 3 808 * 809 + 810 RCL 13 811 SIN 812 14 813 * 814 + 815 RCL 11 816 32 817 - 818 COS 819 10 820 * 821 RCL 00 822 * 823 - 824 RCL 07 825 RCL 11 826 + 827 STO 04 828 50 829 - 830 SIN 831 45 832 * 833 + 834 RCL 09 835 14 836 + 837 COS 838 118 839 * 840 + 841 RCL 09 842 ST+ X 843 STO 13 844 ST+ 07 845 30 846 + 847 COS 848 228 849 * 850 + 851 RCL 11 852 7.3 853 - 854 SIN 855 810 856 * 857 + 858 STO 03 859 RCL 13 860 33 |
861 + 862 COS 863 20 864 ST+ 04 865 ST- 08 866 * 867 RCL 04 868 COS 869 18 870 * 871 - 872 RCL 07 873 28 874 - 875 COS 876 6 877 * 878 + 879 RCL 11 880 SIN 881 4 882 * 883 + 884 STO 04 885 RCL 13 886 60 887 - 888 COS 889 19 890 * 891 RCL 08 892 COS 893 8 894 * 895 + 896 RCL 09 897 73 898 - 899 COS 900 6 901 * 902 + 903 STO 05 904 9543 905 STO 09 906 5553 907 STO 10 908 35 909 CHS 910 STO 14 911 2489 912 RCL 00 913 4 914 * 915 - 916 STO 11 917 1964 918 STO 15 919 50061 920 STO 12 921 1223511 922 STO 06 923 93057 924 STO 13 925 20609 926 + 927 877 928 XEQ 14 929 RTN 930 LBL 07 931 XEQ 12 932 RCL 12 933 ST- 07 934 RCL 14 935 ST+ X 936 STO 11 937 + 938 20 939 - 940 SIN 941 RCL 13 942 12 943 ST* Z 944 - 945 COS 946 5 947 * 948 - 949 RCL 04 950 RCL 05 951 + 952 STO 13 953 80 954 - 955 COS 956 7 957 * 958 + 959 RCL 07 960 28 961 + 962 COS 963 6 964 * 965 + 966 RCL 11 967 RCL 14 968 + 969 60 970 - 971 COS 972 4 973 * 974 + 975 RCL 12 976 ST- 06 977 RCL 13 978 - 979 27 980 + 981 COS 982 PI 983 * 984 - 985 RCL 14 986 10 987 STO 10 988 + 989 SIN 990 RCL 10 991 ST- 06 992 * 993 - 994 RCL 06 995 COS 996 RCL 12 997 RCL 04 998 - 999 COS 1000 - 1001 15 1002 * 1003 + 1004 RCL 05 1005 RCL 12 1006 + 1007 STO 13 1008 11 1009 - 1010 COS 1011 39 1012 * 1013 + 1014 RCL 12 1015 RCL 03 1016 - 1017 51 1018 - 1019 COS 1020 40 1021 * 1022 + 1023 RCL 03 1024 73 1025 + 1026 SIN 1027 RCL 04 1028 39 1029 + 1030 SIN 1031 + 1032 35 1033 * 1034 - 1035 RCL 11 1036 19 1037 + 1038 STO 11 1039 SIN 1040 209 1041 * 1042 - 1043 RCL 05 1044 62.2 1045 - 1046 SIN 1047 858 1048 * 1049 + 1050 STO 03 1051 RCL 11 1052 14 1053 + 1054 COS 1055 RCL 13 1056 SIN 1057 - 1058 6 1059 * 1060 STO 04 1061 RCL 11 1062 COS 1063 34 1064 * 1065 RCL 13 1066 79 1067 + 1068 COS 1069 7 1070 * 1071 - 1072 STO 05 1073 19192 1074 STO 09 1075 45955 |
1076 CHS 1077 STO 12 1078 429864 1079 STO 06 1080 4630 1081 STO 10 1082 3 1083 CHS 1084 STO 14 1085 773 1086 RCL 00 1087 + 1088 STO 11 1089 1486 1090 STO 15 1091 172993 1092 STO 13 1093 74005 1094 521 1095 XEQ 14 1096 RTN 1097 LBL 08 1098 XEQ 12 1099 RCL 04 1100 50 1101 - 1102 COS 1103 24 1104 * 1105 RCL 13 1106 11 1107 - 1108 COS 1109 22 1110 * 1111 + 1112 RCL 06 1113 RCL 14 1114 ST+ 04 1115 RCL 05 1116 + 1117 ST- 07 1118 - 1119 COS 1120 9 1121 * 1122 + 1123 RCL 04 1124 77 1125 - 1126 COS 1127 RCL 07 1128 16 1129 + 1130 COS 1131 + 1132 5 1133 * 1134 + 1135 RCL 14 1136 7 1137 + 1138 SIN 1139 71 1140 * 1141 + 1142 RCL 05 1143 27.8 1144 + 1145 COS 1146 584 1147 * 1148 + 1149 STO 03 1150 RCL 04 1151 69 1152 - 1153 SIN 1154 RCL 14 1155 36 1156 - 1157 COS 1158 - 1159 9 1160 * 1161 STO 04 1162 RCL 05 1163 63 1164 - 1165 COS 1166 8 1167 * 1168 RCL 14 1169 6 1170 + 1171 COS 1172 17 1173 * 1174 - 1175 STO 05 1176 30070 1177 STO 09 1178 899 1179 STO 10 1180 CLX 1181 STO 14 1182 1770 1183 RCL 00 1184 9 1185 * 1186 - 1187 STO 11 1188 1426 1189 STO 15 1190 55654 1191 CHS 1192 STO 12 1193 219883 1194 STO 06 1195 48124 1196 STO 13 1197 83660 1198 + 1199 1102 1200 XEQ 14 1201 RTN 1202 LBL 09 1203 RCL 00 1204 2890 1205 * 1206 65 1207 + 1208 COS 1209 7 1210 * 1211 RCL 00 1212 1077 1213 * 1214 76 1215 + 1216 COS 1217 4 1218 * 1219 + 1220 STO 03 1221 RCL 00 1222 9 1223 * 1224 4 1225 - 1226 STO 04 1227 RCL 00 1228 ST+ X 1229 STO 05 1230 39489 1231 STO 09 1232 24900 1233 STO 10 1234 CLX 1235 STO 14 1236 17140 1237 STO 11 1238 224075 1239 STO 13 1240 238927 1241 STO 12 1242 146567 1243 STO 06 1244 36260 1245 - 1246 1397 1247 STO 15 1248 GTO 14 1249 LBL 12 1250 98 1251 RCL 00 1252 2.06 1253 * 1254 STO 15 1255 * 1256 STO 13 1257 4 1258 LASTX 1259 * 1260 STO 04 1261 ST+ 04 1262 STO 05 1263 + 1264 STO 14 1265 208 1266 RCL 15 1267 * 1268 STO 12 1269 19 1270 LASTX 1271 * 1272 STO 11 1273 593 1274 LASTX 1275 * 1276 STO 07 1277 LASTX 1278 880 1279 * 1280 STO 08 1281 + 1282 STO 06 1283 LASTX 1284 RCL 07 1285 - 1286 STO 09 1287 + 1288 STO 10 1289 RCL 15 1290 31 |
1291 * 1292 STO 03 1293 RTN 1294 LBL 13 1295 0 1296 STO 03 1297 STO 04 1298 STO 05 1299 RDN 1300 LBL 14 1301 RCL 00 1302 ST* 06 1303 ST* 14 1304 ST* 15 1305 * 1306 + 1307 X<> 14 1308 ST+ 10 1309 E5 1310 ST/ 10 1311 9 1312 STO 08 1313 RCL 06 1314 RCL 12 1315 + 1316 RCL 13 1317 RCL 15 1318 + 1319 E3 1320 ST/ 03 1321 ST/ 04 1322 ST/ 05 1323 ST/ 09 1324 ST/ 11 1325 ST/ 14 1326 ST/ Z 1327 / 1328 STO 13 1329 - 1330 ENTER 1331 ENTER 1332 LBL 11 1333 SIN 1334 RCL 10 1335 R-D 1336 * 1337 + 1338 DSE 08 1339 GTO 11 1340 STO 15 1341 2 1342 / 1343 RCL 10 1344 1 1345 ST+ Y 1346 RCL 10 1347 - 1348 / 1349 SQRT 1350 P-R 1351 LASTX 1352 / 1353 R-P 1354 X<>Y 1355 ST+ X 1356 1 1357 RCL 15 1358 COS 1359 RCL 10 1360 * 1361 - 1362 RCL 09 1363 * 1364 RCL 05 1365 + 1366 STO 08 1367 CLX 1368 RCL 13 1369 + 1370 RCL 14 1371 ST+ 03 1372 - 1373 COS 1374 RCL 11 1375 LASTX 1376 SIN 1377 P-R 1378 X<>Y 1379 ASIN 1380 RCL 04 1381 + 1382 STO 07 1383 X<> Z 1384 R-P 1385 CLX 1386 RCL 03 1387 + 1388 STO 06 1389 RCL 08 1390 XEQ 10 1391 RCL 02 1392 ST+ Z 1393 CLX 1394 RCL 01 1395 + 1396 XEQ 12 1397 STO 05 1398 RDN 1399 STO 03 1400 STO 22 1401 X<>Y 1402 STO 04 1403 RCL 08 1404 ENTER 1405 SQRT 1406 * 1407 1/X 1408 RCL 08 1409 X^2 1410 1 1411 - 1412 RCL 05 1413 X^2 1414 ST+ Y 1415 ST+ X 1416 / 1417 ST* Y 1418 - 1419 RCL 05 1420 176 1421 / 1422 ST* Y 1423 + 1424 ST- 03 1425 LBL 00 1426 RCL 20 1427 CHS 1428 RCL 04 1429 RCL 03 1430 RCL 21 1431 + 1432 XEQ 13 1433 STO 09 1434 X<>Y 1435 STO 10 1436 RCL 17 1437 HR 1438 90 1439 STO 11 1440 - 1441 RCL 10 1442 LASTX 1443 RCL 09 1444 + 1445 RCL 19 1446 - 1447 XEQ 13 1448 ST- 11 1449 X<>Y 1450 ENTER 1451 COS 1452 RCL 05 1453 409 1454 * 1455 / 1456 - 1457 STO 12 1458 19.272 1459 RCL 12 1460 6.942 1461 + 1462 / 1463 + 1464 5.459 1465 X<>Y 1466 / 1467 + 1468 TAN 1469 1/X 1470 62.6 1471 / 1472 + 1473 STO 13 1474 X<>Y 1475 RCL 11 1476 RTN 1477 LBL 13 1478 1 1479 XEQ 10 1480 RDN 1481 R-P 1482 X<> Z 1483 ST- Y 1484 X<> Z 1485 P-R 1486 R^ 1487 XEQ 12 1488 RDN 1489 RTN 1490 LBL 10 1491 X<>Y 1492 RDN 1493 P-R 1494 R^ 1495 X<>Y 1496 P-R 1497 RTN 1498 LBL 12 1499 R-P 1500 X<>Y 1501 RDN 1502 R-P 1503 R^ 1504 X<>Y 1505 END |
( 2220 bytes / SIZE 023 )
| STACK | INPUTS | OUTPUTS |
| Z | / | h0 = apparent altitude ( deg ) |
| Y | YYYY.MNDD | h = true altitude ( deg ) |
| X | hh.mnss (UT) | Az = Azimuth ( deg ) |
YYYY.MNDD ENTER^
hh.mnss XEQ "EPH" returns the azimuthal coordinates of the Sun.
-Then R/S or XEQ 03 gives the coordinates of the Moon
-Then R/S or XEQ 01 ------------------------ Mercury
............................................................................
-Then R/S or XEQ 09 ------------------------- Pluto.
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 & TOP2010 Series http://www.imcce.fr/~jlsimon
[4] A fantastic software by Aldo Vitagliano:
"SOLEX" which may be downloaded freely from http://chemistry.unina.it/~alvitagl/solex/