Overview
1°) The Sun
2°) 4 subroutines ( to solve
Kepler's equation and calculate the geocentric coordinates )
3°) The Moon
4°) Mercury-Venus-Mars-Pluto
5°) Jupiter-Neptune
6°) Saturn
7°) Uranus-Xena/Lilah/Eris
8°) Position of the Sun ( faster
program , lesser accuracy )
9°) Position
of the Sun ( higher accuracy )
-Nowadays, it's easy to calculate the positions of the Sun, the Moon
and the planets with a great accuracy
by mean of Fourier series A.cos(B.T+C) and Poisson
series.
Unfortunately, this requires many bytes on an HP-41 and a more
economical approach is proposed in paragraphs 1 and 3 to 7:
-Kepler's equation is solved first and then, a few periodic terms are
added to the heliocentric longitude,
the heliocentric latitude and the radius vector. ( the Moon's
geocentric coordinates are computed directly )
-The result is an ephemeride over the interval 1000-3000 with an accuracy
of about 0.01° in the heliocentric longitudes.
( except for Pluto: its coordinates are obtained with this precision
over 1880-2110 only,
and for Xena/Lilah/Eris: the time-span is 1900-2100 )
-The Sun's coordinates are more accurate. However, errors in the geocentric
coordinates are increased when the distance between the Earth and the planet
is small and in this case, for Venus and Mars, the error in the
obtained geocentric longitude can reach 1 arcminute, perhaps a little more.
-All these coordinates are referred to the mean ecliptic and equinox
of the date.
-The elements of planetary orbits and the perturbations are taken from
the planetary theory VSOP87 by P. Bretagnon, JL. Simon and G. Francou,
improved by the new theories VSOP09 & TOP10.
-The Moon's coordinates are based on the series given by Jean Meeus
in "Astronomical Algorithms" - 2nd edition.
-Pluto's & Xena's positions are derived from simplified formulae
that I constructed myself
( thanks to a numerical integration of the JPL DE406 and to my
HP-48 ! )
-In order to save bytes, perturbations are written under the form
S sin µ + K cos µ instead of A.cos(B.T+C)
The phase µ is actually a linear combination of the mean
mean longitudes of the planets.
Furthermore, the R-P is quite useful: for instance, if the phase
µ is in register R10 , 2 sin µ + 4 cos µ
is computed by:
RCL 10
2
P-R
ST+ X
+
-This trick is extensively used troughout most of these programs.
-I also made several approximations which are satisfactory here, but
would be inadequate to obtain a great accuracy.
-However, the whole set of programs occupies more than 3000 bytes and
therefore, some of these routines are to be saved in extended memory.
DATA REGISTERS:
-Registers R00 thru R15 are used by every program.
R00 = T = the time expressed in thousands of years since 2000/01/01
0h ET is to be initialized before executing any program
R01 and R02 contain the Sun's rectangular ecliptic coordinates.
They are calculated and stored by the "SUN" program.
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.
-And for each program ( in paragraphs 1-3-4-5-6-7 ), you have:
| STACK | INPUTS | OUTPUTS |
| Z | / | distance to the earth* ( AU ) |
| Y | / | declination ( ° ' '' ) |
| X | / | right ascension ( hh.mnss ) |
* or Moon's parallax ( ° ' " )
INSTRUCTIONS:
1-Store the time T ( in thousands of years since 2000/01/01 0h ET
( not 12h ) ) into register R00.
This can be performed by one of these short routines:
| 01 LBL "T1"
02 HR 03 24 04 / 05 X<>Y 06 1.012 07 DDAYS 08 - 09 365250 10 / 11 STO 00 12 END |
01 LBL "T2"
02 HR 03 24 04 / 05 X<>Y 06 XEQ "J0" 07 + 08 365250 09 / 10 STO 00 11 END |
See "Julian & Gregorian Calendars for the HP-41" for a listing
of "J0" ( which can be replaced by "J1" or "J2" )
LBL "T1" if you have a TIME modue
LBL "T2" if you don't have
a TIME module and for dates before 1582/10/15
date
ENTER^
hh.mnss XEQ "T1" or
XEQ "T2"
2-XEQ "SUN" first: This is needed to calculate
the geocentric coordinates of the planets
( this doesn't apply to the Moon, except if you want to obtain the elongation
from the Sun ).
3-XEQ "MO" for the Moon and "ME" "VE" "MA" "JU" "SA" "UR"
"NE" "PL" for Mercury, Venus, Mars, Jupiter, Saturn, Uranus, Neptune
and Pluto.
NB: The HP-41 must be set in DEG mode.
1°) The Sun
| 01 LBL "SUN"
02 XEQ "O" 03 COS 04 RCL 08 05 RCL 05 06 - 07 SIN 08 + 09 RCL 13 10 SIN 11 + 12 ST+ X 13 RCL 12 14 SIN |
15 LASTX
16 ST+ X 17 SIN 18 + 19 2 20 SQRT 21 * 22 - 23 STO 03 24 RCL 13 25 COS 26 PI 27 % 28 STO 04 |
29 RCL 00
30 17195 31 RCL 00 32 46 33 * 34 + 35 * 36 77063 37 - 38 STO 09 39 CLX 40 42 41 + 42 * |
43 CHS
44 1671 45 + 46 STO 06 47 SIGN 48 STO 05 49 CLX 50 33 51 / 52 * 53 ST+ 08 54 CLST 55 STO 01 56 STO 02 |
57 STO 07
58 XEQ "L" 59 RCL 03 60 RCL 05 61 P-R 62 STO 01 63 X<>Y 64 STO 02 65 RCL 05 66 RCL 07 67 RCL 06 68 END |
( 97 bytes / SIZE 016 )
| STACK | INPUTS | OUTPUTS |
| Z | / | distance to the earth ( AU ) |
| Y | / | declination ( ° ' '' ) |
| X | / | right ascension ( hh.mnss ) |
Example: Calculate the Sun's position on
2100 January 1st at 0h TT ( Ephemeris Time )
thus T = 0.1 0.1 STO 00 ( or 1.012100 ENTER^ 0 XEQ "T1" or 2100.0101 ENTER^ 0 XEQ "T2" )
XEQ "SUN" yields 18h46m09s
( right ascension ) = R06 ( execution
time = 36s )
RDN
-23°00'10''
( declination ) = R07
RDN
0.983356 AU ( radius vector
) = R05
we have also:
R01 = 0.181015
the Sun's rectangular coordinates
R02 = -0.966552
coordinates x and y
R03 = -79.393°
the Sun's longitude
R04 = 0
the Sun's latitude is always 0 in these programs
2°) 4 Subroutines: "L" "N" "O" "K"
-These subroutines are called by all the other programs - except in paragraph 8 - so they must stay in main memory.
-LBL 00 solves Kepler's equation
-Line 97 LBL "N" is useful for the Moon only
-LBL 01 = Spherical-Rectangular conversion
-LBL 02 = Rectangular-Spherical conversion
-If you want to get the elongation from the Sun in register T, replace
lines 115 to 125 by
| CLX
15 / 24 MOD HMS |
RCL 02
RCL 01 R-P CLX RCL 03 - |
COS
RCL 04 COS * ACOS RCL 05 |
R^
HMS STO 07 R^ STO 06 RTN |
| 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 12 14 STO 15 15 RCL 08 16 360 17 MOD 18 13.971 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 13.01 100 % 101 23.4393 102 - 103 RCL 04 104 RCL 03 105 RCL 05 106 XEQ 01 107 RDN 108 R-P 109 X<> Z 110 ST- Y 111 X<> Z 112 P-R 113 R^ 114 XEQ 02 115 X<> Z 116 HMS 117 STO 07 118 X<>Y 119 15 120 / 121 24 122 MOD 123 HMS 124 STO 06 125 RTN 126 LBL 01 |
127 X<>Y
128 RDN 129 P-R 130 R^ 131 X<>Y 132 P-R 133 RTN 134 LBL 02 135 R-P 136 X<>Y 137 RDN 138 R-P 139 R^ 140 X<>Y 141 RTN 142 LBL "O" 143 XEQ "K" 144 CLX 145 STO 04 146 STO 11 147 4452671.114 148 RCL 00 149 .177 150 * 151 - 152 RCL 00 153 * 154 68.245 155 - 156 STO 13 157 ST+ X 158 STO 14 159 585178.159 160 RCL 00 161 * 162 181.179 163 + 164 STO 07 165 359993.727 166 RCL 00 167 * 168 80.027 |
169 -
170 STO 08 171 - 172 STO 12 173 LASTX 174 191402.993 175 RCL 00 176 * 177 4.829 178 - 179 STO 09 180 ST+ X 181 - 182 4 183 * 184 RCL 05 185 3 186 * 187 + 188 STO 10 189 RTN 190 LBL "K" 191 30349.057 192 RCL 00 193 * 194 34.31 195 + 196 STO 05 197 12221.14 198 RCL 00 199 * 200 50.061 201 + 202 STO 06 203 - 204 STO 10 205 LASTX 206 - 207 STO 11 208 RCL 10 209 + 210 STO 12 |
211 RCL 06
212 ST+ X 213 - 214 STO 09 215 ST+ X 216 STO 03 217 4284.673 218 RCL 00 219 * 220 45.955 221 - 222 STO 07 223 2184.856 224 RCL 00 225 * 226 55.654 227 - 228 STO 08 229 - 230 STO 14 231 LASTX 232 - 233 STO 15 234 RCL 06 235 RCL 07 236 3 237 * 238 - 239 STO 04 240 LASTX 241 RCL 09 242 RCL 06 243 - 244 + 245 STO 13 246 RCL 09 247 5 248 END |
( 427 bytes / SIZE 016 )
3°) The Moon
| 01 LBL "MO"
02 XEQ "O" 03 RCL 00 04 3.22 05 RCL 00 06 65 07 / 08 + 09 * 10 77.06 11 - 12 ST- 08 13 CLX 14 89 15 + 16 * 17 477198868 18 + 19 % 20 128.43 21 + 22 STO 07 23 ST+ X 24 STO 12 25 CLX 26 35 27 * 28 483202017 29 - 30 % 31 86.66 32 - 33 STO 09 34 ST+ X 35 STO 06 36 6036 37 RCL 14 38 RCL 07 39 - 40 STO 03 41 COS 42 58 43 * 44 - 45 RCL 14 46 COS 47 46 48 * 49 - 50 RCL 12 51 COS 52 9 53 * 54 - 55 RCL 14 56 RCL 12 57 - 58 STO 15 59 COS 60 RCL 07 61 COS 62 82 63 * 64 - 65 4 66 * 67 + 68 RCL 14 69 RCL 08 70 - 71 STO 11 72 COS 73 RCL 14 74 RCL 07 75 + 76 STO 10 77 COS 78 + 79 3 |
80 *
81 - 82 1 83 % 84 1/X 85 ASIN 86 HMS 87 STO 05 88 RCL 07 89 RCL 09 90 - 91 SIN 92 281 93 * 94 RCL 07 95 RCL 09 96 + 97 SIN 98 278 99 * 100 + 101 RCL 14 102 RCL 09 103 + 104 SIN 105 173 106 * 107 + 108 RCL 03 109 RCL 09 110 - 111 SIN 112 55 113 * 114 + 115 RCL 03 116 RCL 09 117 + 118 SIN 119 46 120 * 121 + 122 RCL 14 123 RCL 09 124 - 125 SIN 126 33 127 * 128 + 129 RCL 12 130 RCL 09 131 - 132 SIN 133 17 134 * 135 + 136 RCL 10 137 RCL 09 138 + 139 SIN 140 RCL 12 141 RCL 09 142 + 143 SIN 144 + 145 9 146 * 147 + 148 RCL 11 149 RCL 09 150 + 151 SIN 152 RCL 09 153 SIN 154 641 155 * 156 - 157 8 158 * |
159 +
160 RCL 15 161 RCL 09 162 + 163 SIN 164 RCL 10 165 RCL 09 166 - 167 SIN 168 + 169 4 170 * 171 + 172 RCL 14 173 RCL 08 174 + 175 RCL 09 176 + 177 SIN 178 3 179 * 180 - 181 RCL 11 182 RCL 09 183 - 184 STO 04 185 RCL 07 186 - 187 SIN 188 LASTX 189 RCL 06 190 + 191 SIN 192 + 193 RCL 04 194 SIN 195 + 196 RCL 09 197 RCL 07 198 - 199 STO 04 200 RCL 08 201 + 202 SIN 203 - 204 RCL 04 205 RCL 14 206 ST+ X 207 + 208 SIN 209 + 210 RCL 08 211 RCL 09 212 - 213 SIN 214 - 215 RCL 06 216 RCL 09 217 + 218 SIN 219 + 220 ST+ X 221 + 222 STO 04 223 RCL 07 224 SIN 225 6289 226 * 227 RCL 14 228 SIN 229 658 230 * 231 + 232 RCL 12 233 SIN 234 214 235 * 236 + 237 RCL 06 |
238 SIN
239 114 240 * 241 + 242 RCL 15 243 SIN 244 59 245 * 246 + 247 RCL 03 248 RCL 08 249 - 250 SIN 251 57 252 * 253 + 254 RCL 10 255 SIN 256 53 257 * 258 + 259 RCL 11 260 SIN 261 46 262 * 263 + 264 RCL 08 265 RCL 07 266 - 267 SIN 268 41 269 * 270 - 271 RCL 03 272 SIN 273 98 274 * 275 RCL 07 276 RCL 06 277 - 278 SIN 279 - 280 13 281 * 282 + 283 RCL 07 284 RCL 06 285 + 286 SIN 287 RCL 14 288 ST+ X 289 RCL 07 290 - 291 SIN 292 + 293 11 294 * 295 + 296 RCL 03 297 ST+ X 298 SIN 299 9 300 * 301 + 302 RCL 03 303 RCL 08 304 + 305 SIN 306 8 307 * 308 - 309 RCL 14 310 RCL 08 311 + 312 SIN 313 7 314 * 315 - 316 RCL 08 |
317 SIN
318 RCL 00 319 37 320 - 321 * 322 RCL 13 323 SIN 324 7 325 * 326 - 327 RCL 07 328 RCL 08 329 + 330 SIN 331 6 332 * 333 - 334 RCL 14 335 RCL 06 336 + 337 SIN 338 3 339 * 340 + 341 RCL 07 342 RCL 12 343 + 344 SIN 345 ST+ X 346 + 347 RCL 13 348 RCL 07 349 - 350 SIN 351 - 352 RCL 13 353 RCL 08 354 + 355 SIN 356 + 357 5 358 * 359 + 360 RCL 10 361 RCL 08 362 - 363 SIN 364 RCL 14 365 RCL 12 366 + 367 SIN 368 + 369 RCL 14 370 ST+ X 371 SIN 372 + 373 RCL 03 374 RCL 12 375 - 376 SIN 377 + 378 RCL 00 379 23 380 * 381 1 382 - 383 R-D 384 SIN 385 - 386 4 387 * 388 + 389 RCL 08 390 RCL 12 391 - 392 SIN 393 RCL 03 394 RCL 06 395 - |
396 SIN
397 + 398 3 399 * 400 - 401 RCL 11 402 RCL 08 403 - 404 SIN 405 LASTX 406 RCL 07 407 - 408 SIN 409 + 410 RCL 11 411 RCL 12 412 - 413 SIN 414 + 415 RCL 13 416 RCL 07 417 + 418 SIN 419 - 420 RCL 12 421 RCL 08 422 + 423 SIN 424 - 425 RCL 08 426 ST+ X 427 SIN 428 - 429 RCL 06 430 RCL 10 431 + 432 SIN 433 - 434 RCL 14 435 RCL 06 436 - 437 SIN 438 - 439 RCL 00 440 ST+ X 441 157 442 - 443 RCL 00 444 * 445 4812678813 446 + 447 RCL 00 448 * 449 211728 450 + 451 E3 452 / 453 360 454 MOD 455 SIN 456 ST+ X 457 ST- 04 458 X<> L 459 STO 03 460 RCL 09 461 + 462 SIN 463 + 464 ST+ X 465 + 466 E3 467 ST/ 04 468 / 469 ST+ 03 470 XEQ "N" 471 END |
( 581 bytes / SIZE 016 )
| STACK | INPUTS | OUTPUTS |
| Z | / | Moon's parallax ( ° ' '' ) |
| Y | / | declination ( ° ' '' ) |
| X | / | right ascension ( hh.mnss ) |
Example:
( 2100/0101 0h TT ) ( T = 0.1 )
XEQ "MO"
>>>> 10h38m02s
( right ascension ) = R06
( execution time = 70s )
RDN
9°48'13" ( declination
)
= R07
RDN
0°59'01" ( Moon's
parallax ) = R05
RDN yields elongation from the Sun = 123°20 if you've modified the subroutines as suggested in §2.
R03 = 157.399°
( geocentric longitude )
R04 =
1.093° ( geocentric
latitude )
4°) Mercury-Venus-Mars-Pluto
-All the perturbations have been neglected in the motion of Mercury.
-If you want to take the most important one into account,
add 63563 RCL 00 * 87 +
COS ST+ X STO 03 after line 05 and delete line
03
-Lines 49-113-252 are synthetic 3-byte GTO 14
| 01 LBL "ME"
02 CLX 03 STO 03 04 STO 04 05 STO 11 06 .3871 07 STO 05 08 RCL 00 09 18 10 RCL 00 11 2 12 * 13 - 14 * 15 7005 16 + 17 STO 07 18 CLX 19 3 20 % 21 1494726.751 22 + 23 * 24 250.205 25 + 26 STO 08 27 CLX 28 20 29 * 30 20563 31 + 32 STO 06 33 CLX 34 30 35 * 36 15564 37 + 38 * 39 77456 40 + 41 STO 09 42 CLX 43 18 44 * 45 11861 46 + 47 * 48 48331 49 GTO 14 50 LBL "VE" 51 XEQ "O" 52 RCL 12 53 SIN 54 2 55 SQRT 56 * |
57 RCL 12
58 3 59 * 60 SIN 61 ST+ X 62 - 63 RCL 12 64 ST+ X 65 SIN 66 PI 67 * 68 - 69 STO 03 70 .72333 71 STO 05 72 RCL 00 73 RCL 07 74 RCL 00 75 X^2 76 32 77 / 78 + 79 STO 08 80 CLX 81 48 82 - 83 * 84 677 85 + 86 STO 06 87 CLX 88 18 89 + 90 * 91 CHS 92 2337 93 + 94 * 95 6 96 * 97 131564 98 + 99 STO 09 100 CLX 101 10 102 * 103 3395 104 + 105 STO 07 106 CLX 107 41 108 * 109 9010 110 + 111 * 112 76680 |
113 GTO 14
114 LBL "MA" 115 XEQ "O" 116 5 117 P-R 118 3 119 * 120 - 121 RCL 10 122 SIN 123 ST+ X 124 RCL 00 125 * 126 + 127 RCL 09 128 RCL 05 129 - 130 STO 13 131 SIN 132 7 133 * 134 - 135 RCL 13 136 RCL 05 137 - 138 5 139 P-R 140 2 141 / 142 - 143 + 144 RCL 07 145 ST+ X 146 RCL 13 147 7 148 * 149 - 150 RCL 05 151 + 152 RCL 06 153 6 154 * 155 - 156 3.6 157 P-R 158 - 159 + 160 RCL 08 161 RCL 09 162 - 163 STO 14 164 LASTX 165 - 166 STO 15 167 3 168 P-R |
169 -
170 - 171 RCL 13 172 ST+ X 173 SIN 174 4 175 * 176 + 177 RCL 14 178 RCL 15 179 + 180 SIN 181 RCL 14 182 SIN 183 - 184 ST+ X 185 + 186 RCL 09 187 3 188 * 189 RCL 07 190 - 191 COS 192 RCL 03 193 2 194 / 195 RCL 10 196 ST+ X 197 - 198 COS 199 + 200 RCL 10 201 RCL 09 202 - 203 COS 204 + 205 2 206 SQRT 207 * 208 - 209 STO 03 210 1.52368 211 STO 05 212 RCL 00 213 RCL 09 214 RCL 00 215 X^2 216 32 217 / 218 + 219 STO 08 220 RDN 221 CHS 222 90 223 + 224 * |
225 9340
226 + 227 STO 06 228 CLX 229 13 230 * 231 18410 232 + 233 * 234 23940 235 - 236 STO 09 237 CLX 238 6 239 - 240 * 241 1850 242 + 243 STO 07 244 SIGN 245 + 246 * 247 ST+ X 248 7720 249 + 250 * 251 49558 252 GTO 14 253 LBL "PL" 254 XEQ "K" 255 RCL 05 256 1451.7 257 RCL 00 258 * 259 238.925 260 + 261 STO 08 262 - 263 STO 10 264 SIN 265 7 266 * 267 RCL 08 268 COS 269 4 270 * 271 - 272 RCL 08 273 ST+ X 274 STO 09 275 SIN 276 ST+ X 277 - 278 RCL 06 279 RCL 08 280 - |
281 STO 11
282 SIN 283 4 284 * 285 + 286 STO 03 287 RCL 09 288 1 289 P-R 290 RCL 08 291 SIN 292 - 293 ST+ X 294 + 295 RCL 10 296 COS 297 5 298 * 299 + 300 RCL 11 301 COS 302 ST+ X 303 + 304 STO 04 305 RCL 00 306 117 307 * 308 3 309 - 310 RCL 08 311 COS 312 5 313 * 314 - 315 STO 11 316 39.489 317 STO 05 318 24900 319 STO 06 320 17140 321 STO 07 322 13971 323 RCL 00 324 * 325 135925 326 - 327 STO 09 328 246232 329 LBL 14 330 XEQ "L" 331 END |
( 528 bytes / SIZE 016 )
| STACK | INPUTS | OUTPUTS |
| Z | / | distance to the earth ( AU ) |
| Y | / | declination ( ° ' '' ) |
| X | / | right ascension ( hh.mnss ) |
Example: with T =
0.1 ( 2100/01/01 0h TT )
1°) Mercury:
XEQ "ME" >>>>
19h19m18s ( right ascension )
= R06 ( execution time
= 25s )
RDN
-24°18'31" ( declination
)
= R07
RDN
1.38603 AU ( Mercury's distance to the Earth
) = R05
RDN yields elongation from the Sun = 7°70 if you've modified the subroutines as suggested above ( in §2 ).
R03 = -71.984°
( geocentric longitude )
R08 = -54.797° ( heliocentric
longitude ) R10 = 0.43213 AU
( radius vector )
R04 = -2.113°
( geocentric latitude )
R09 = -6.791°
( heliocentric latitude )
2°) Venus:
XEQ "VE"
>>>> 21h32m22s
( right ascension )
= R06 ( execution time
= 36s )
RDN
-16°32'22" ( declination
)
= R07
RDN
1.1256 AU ( Venus' distance
to the Earth ) = R05
RDN yields elongation from the Sun = 39°51
R03 = -39.923°
( geocentric longitude )
R08 = 19.733°
( heliocentric longitude ) R10
= 0.7252 AU ( radius vector )
R04 = -1.853°
( geocentric latitude )
R09 = -2.876°
( heliocentric latitude )
3°) Mars:
XEQ "MA"
>>>> 1h48m30s
( right ascension )
= R06 ( execution time
= 43s )
RDN
12°11'29" ( declination )
= R07
RDN
0.8699 AU ( Mars' distance to the Earth
) = R05
RDN yields elongation from the Sun = 108°92
R03 = 29.535°
( geocentric longitude )
R08 = 67.577°
( heliocentric longitude )
R10 = 1.5095 AU ( radius vector )
R04 = 0.950°
( geocentric latitude )
R09 = 0.548°
( heliocentric latitude )
4°) Pluto:
XEQ "PL"
>>>> 2h23m50s
( right ascension )
= R06 ( execution time
= 33s )
RDN
-3°37'43" ( declination )
= R07
RDN
48.576 AU ( Pluto's distance to the Earth
) = R05
RDN yields elongation from the Sun = 110°80
R03 = 32.394°
( geocentric longitude )
R08 = 33.511°
( heliocentric longitude )
R10 = 48.934 AU ( radius
vector )
R04 = -16.921°
( geocentric latitude )
R09 = -16.794°
( heliocentric latitude )
5°) Jupiter-Neptune
| 01 LBL "JU"
02 XEQ "K" 03 X^2 04 P-R 05 5 06 SQRT 07 / 08 + 09 RCL 09 10 RCL 00 11 ST+ X 12 P-R 13 5 14 LN 15 * 16 - 17 - 18 RCL 00 19 * 20 RCL 09 21 37 22 P-R 23 3.4 24 * 25 - 26 + 27 RCL 05 28 RCL 09 29 + 30 STO 08 31 12 32 P-R 33 6 34 / 35 + 36 - 37 RCL 11 38 6 39 SQRT 40 P-R 41 + 42 + 43 RCL 12 44 2 45 P-R 46 + 47 + 48 RCL 09 49 RCL 05 50 - 51 STO 07 52 PI 53 P-R 54 ST+ X 55 - 56 + 57 RCL 03 58 COS 59 ST+ X 60 + 61 RCL 00 62 * 63 RCL 09 64 325 65 P-R 66 9 67 D-R 68 * 69 + |
70 -
71 RCL 10 72 ST+ X 73 STO 14 74 SIN 75 56 76 * 77 + 78 RCL 08 79 3 80 P-R 81 14 82 * 83 + 84 + 85 RCL 11 86 36 87 P-R 88 6 89 / 90 - 91 + 92 RCL 12 93 12 94 P-R 95 5 96 LN 97 * 98 - 99 + 100 RCL 10 101 SIN 102 22 103 * 104 - 105 RCL 07 106 15 107 P-R 108 5 109 SQRT 110 / 111 + 112 - 113 RCL 11 114 ST+ X 115 2 116 P-R 117 ST+ X 118 + 119 + 120 RCL 10 121 RCL 14 122 + 123 SIN 124 5 125 * 126 + 127 RCL 10 128 RCL 12 129 + 130 2 131 P-R 132 ST+ X 133 - 134 - 135 RCL 06 136 7 137 SQRT 138 P-R |
139 +
140 + 141 RCL 05 142 RCL 14 143 + 144 SIN 145 RCL 12 146 RCL 14 147 + 148 COS 149 + 150 RCL 13 151 SIN 152 + 153 RCL 03 154 SIN 155 + 156 3 157 * 158 + 159 RCL 11 160 RCL 06 161 - 162 2 163 P-R 164 - 165 - 166 RCL 05 167 73 168 - 169 COS 170 1.3 171 * 172 + 173 STO 03 174 RCL 08 175 SIN 176 ST+ X 177 RCL 14 178 COS 179 3 180 * 181 - 182 RCL 12 183 SIN 184 - 185 RCL 07 186 COS 187 - 188 RCL 10 189 COS 190 + 191 STO 04 192 RCL 08 193 COS 194 5 195 * 196 RCL 07 197 COS 198 PI 199 * 200 - 201 STO 11 202 RCL 00 203 1303 204 RCL 00 205 55 206 * 207 - |
208 STO 07
209 CLX 210 45 211 / 212 * 213 RCL 05 214 + 215 STO 08 216 CLX 217 5.203 218 STO 05 219 INT 220 CHS 221 * 222 163 223 + 224 * 225 4849 226 + 227 STO 06 228 CLX 229 4 230 * 231 CHS 232 103 233 + 234 * 235 16126 236 + 237 * 238 14331 239 + 240 STO 09 241 CLX 242 40 243 * 244 10210 245 + 246 * 247 100464 248 XEQ "L" 249 RTN 250 LBL "NE" 251 XEQ "K" 252 RCL 15 253 583 254 P-R 255 18 256 / 257 - 258 RCL 15 259 3 260 RCL 00 261 * 262 P-R 263 3 264 * 265 - 266 - 267 RCL 14 268 3 269 - 270 SIN 271 71 272 * 273 + 274 RCL 15 275 ST+ X 276 24 |
277 P-R
278 6 279 / 280 + 281 + 282 RCL 14 283 RCL 15 284 + 285 STO 13 286 SIN 287 22 288 * 289 + 290 RCL 05 291 RCL 08 292 - 293 STO 10 294 SIN 295 9 296 * 297 + 298 RCL 15 299 RCL 08 300 - 301 STO 12 302 4 303 P-R 304 + 305 + 306 RCL 06 307 RCL 08 308 - 309 STO 09 310 SIN 311 5 312 * 313 + 314 RCL 14 315 ST+ X 316 STO 11 317 SIN 318 RCL 13 319 RCL 15 320 + 321 SIN 322 - 323 ST+ X 324 - 325 STO 03 326 RCL 15 327 COS 328 8 329 * 330 RCL 14 331 1 332 P-R 333 17 334 * 335 + 336 - 337 RCL 10 338 COS 339 RCL 13 340 COS 341 - 342 5 343 * 344 + 345 RCL 09 |
346 COS
347 3 348 * 349 + 350 RCL 12 351 1 352 P-R 353 - 354 - 355 RCL 11 356 COS 357 + 358 STO 04 359 RCL 14 360 6 361 P-R 362 + 363 CHS 364 RCL 12 365 5 366 P-R 367 .7 368 / 369 - 370 - 371 STO 11 372 30.07 373 STO 05 374 RCL 00 375 899 376 RCL 00 377 6 378 * 379 + 380 STO 06 381 RDN 382 CHS 383 93 384 - 385 * 386 1770 387 + 388 STO 07 389 CLX 390 32 391 / 392 * 393 ST+ 08 394 CLX 395 38 396 * 397 14263 398 + 399 * 400 48124 401 + 402 STO 09 403 CLX 404 26 405 * 406 11022 407 + 408 * 409 131784 410 XEQ "L" 411 END |
( 530 bytes / SIZE 016 )
| STACK | INPUTS | OUTPUTS |
| Z | / | distance to the earth ( AU ) |
| Y | / | declination ( ° ' '' ) |
| X | / | right ascension ( hh.mnss ) |
Example: T = 0.1
( 2100/01/01 0h TT )
1°) Jupiter:
XEQ "JU"
>>>> 13h20m20s
( right ascension )
= R06 ( execution time
= 53s )
RDN
-7°05'08" ( declination
)
= R07
RDN
5.546 AU ( Jupiter's distance
to the Earth ) = R05
and RDN yields elongation from the
Sun = 79°40
if you've modified the subroutines as suggested above ( in §2 ).
and R03 = -158.788°
( geocentric longitude )
R08 = 190.996° ( heliocentric
longitude )
R04 =
1.278° ( geocentric
latitude )
R09 = 1.300°
( heliocentric latitude )
R10 = 5.451 AU ( radius vector )
2°) Neptune:
XEQ "NE"
>>>> 11h14m44s
( right ascension )
= R06 ( execution time
= 45s )
RDN
5°54'26" ( declination
)
= R07
RDN
29.808 AU ( Neptune's
distance to the Earth ) = R05 and
RDN yields elongation from the Sun = 113°32
and R03 = 167.288°
( geocentric longitude )
R08 = 165.574° ( heliocentric
longitude )
R04 =
0.964° ( geocentric
latitude )
R09 = 0.951°
( heliocentric latitude )
R10 = 30.210 AU ( radius vector )
6°) Saturn
| 01 LBL "SA"
02 XEQ "K" 03 P-R 04 LASTX 05 LN 06 * 07 - 08 RCL 00 09 * 10 RCL 09 11 61 12 P-R 13 5 14 SQRT 15 / 16 + 17 - 18 RCL 11 19 ST+ X 20 STO 08 21 COS 22 9 23 * 24 + 25 RCL 09 26 RCL 06 27 - 28 STO 14 29 4 30 P-R 31 .8 32 / 33 - 34 + 35 RCL 03 36 SIN 37 ST+ X 38 + 39 RCL 00 40 * 41 RCL 09 42 91 43 P-R 44 3.41 45 * 46 - 47 - 48 RCL 08 49 61 50 P-R 51 7 52 / 53 - 54 + 55 RCL 11 56 7 57 P-R 58 .8 59 / 60 + 61 - 62 RCL 14 63 21 64 P-R 65 5 66 SQRT 67 / |
68 +
69 - 70 RCL 11 71 RCL 06 72 - 73 STO 15 74 SIN 75 RCL 13 76 COS 77 - 78 RCL 14 79 RCL 06 80 - 81 COS 82 - 83 RCL 08 84 RCL 09 85 + 86 SIN 87 - 88 ST+ X 89 + 90 RCL 12 91 2 92 P-R 93 - 94 + 95 RCL 03 96 7 97 SQRT 98 P-R 99 ST+ X 100 - 101 + 102 RCL 00 103 * 104 RCL 09 105 800 106 P-R 107 9 108 D-R 109 * 110 + 111 + 112 RCL 08 113 72 114 P-R 115 3 116 * 117 + 118 - 119 RCL 11 120 117 121 P-R 122 32 123 SQRT 124 / 125 - 126 - 127 RCL 14 128 9 129 P-R 130 5 131 * 132 - 133 - 134 RCL 15 |
135 6
136 P-R 137 ST+ X 138 - 139 + 140 RCL 12 141 9 142 P-R 143 PI 144 / 145 + 146 - 147 RCL 10 148 2 149 P-R 150 4 151 * 152 + 153 + 154 RCL 10 155 ST+ X 156 SIN 157 9 158 * 159 - 160 RCL 13 161 SIN 162 8 163 * 164 - 165 RCL 03 166 7 167 P-R 168 3 169 / 170 + 171 - 172 RCL 04 173 COS 174 7 175 * 176 - 177 RCL 04 178 RCL 06 179 + 180 5 181 P-R 182 .6 183 * 184 + 185 + 186 RCL 06 187 RCL 07 188 - 189 ST+ X 190 SIN 191 4 192 * 193 + 194 RCL 05 195 COS 196 RCL 14 197 RCL 06 198 - 199 SIN 200 - 201 RCL 08 |
202 RCL 09
203 + 204 COS 205 + 206 RCL 06 207 COS 208 - 209 3 210 * 211 + 212 RCL 03 213 RCL 04 214 - 215 2 216 P-R 217 + 218 + 219 RCL 04 220 RCL 07 221 + 222 COS 223 RCL 06 224 RCL 07 225 - 226 SIN 227 - 228 RCL 05 229 RCL 12 230 + 231 SIN 232 - 233 ST+ X 234 + 235 STO 03 236 RCL 14 237 RCL 00 238 P-R 239 ST+ X 240 - 241 RCL 08 242 RCL 00 243 P-R 244 5 245 * 246 + 247 - 248 RCL 09 249 SIN 250 RCL 00 251 * 252 - 253 RCL 08 254 18 255 P-R 256 3 257 / 258 - 259 - 260 RCL 10 261 COS 262 8 263 * 264 + 265 RCL 11 266 1 267 P-R 268 5 |
269 *
270 + 271 + 272 RCL 14 273 4 274 P-R 275 6 276 / 277 + 278 - 279 RCL 09 280 COS 281 4 282 * 283 + 284 RCL 10 285 ST+ X 286 COS 287 + 288 RCL 15 289 SIN 290 + 291 STO 04 292 RCL 08 293 8 294 P-R 295 4 296 / 297 RCL 00 298 * 299 + 300 RCL 14 301 4 302 P-R 303 + 304 - 305 RCL 12 306 COS 307 ST+ X 308 - 309 RCL 00 310 * 311 RCL 14 312 9 313 P-R 314 .6 315 / 316 - 317 - 318 RCL 08 319 5 320 P-R 321 3.8 322 * 323 + 324 - 325 RCL 12 326 5 327 P-R 328 .7 329 * 330 - 331 - 332 RCL 09 333 SIN 334 4 335 * |
336 +
337 RCL 10 338 COS 339 ST+ X 340 + 341 RCL 15 342 COS 343 3 344 * 345 - 346 STO 11 347 9.543 348 STO 05 349 RCL 00 350 84 351 RCL 00 352 5 353 * 354 + 355 * 356 19638 357 + 358 * 359 93057 360 + 361 STO 09 362 CLX 363 5.2 364 % 365 * 366 RCL 06 367 + 368 STO 08 369 CLX 370 6 371 * 372 CHS 373 347 374 - 375 * 376 5551 377 + 378 STO 06 379 RDN 380 ST+ X 381 CHS 382 37 383 - 384 * 385 2489 386 + 387 STO 07 388 CLX 389 6 390 + 391 * 392 ST+ X 393 CHS 394 8771 395 + 396 * 397 113666 398 XEQ "L" 399 END |
( 477 bytes / SIZE 016 )
| STACK | INPUTS | OUTPUTS |
| Z | / | distance to the earth ( AU ) |
| Y | / | declination ( ° ' '' ) |
| X | / | right ascension ( hh.mnss ) |
Example: ( T = 0.1
) ( 2100/01/01 0h TT )
XEQ "SA"
>>>> 13h38m36s
( right ascension )
= R06 ( execution time
= 71s )
RDN
-7°38'39" ( declination
)
= R07
RDN
9.875 AU ( Saturn's distance
to the Earth ) = R05
and RDN yields elongation from the
Sun = 74°99
if you've modified the subroutines as suggested above ( in §2 ).
and R03 = -154.370°
( geocentric longitude )
R08 = 199.987° ( heliocentric
longitude )
R04 =
2.424° ( geocentric
latitude )
R09 = 2.476°
( heliocentric latitude )
R10 = 9.667 AU ( radius vector
)
7°) Uranus-Xena
| 01 LBL "UR"
02 XEQ "K" 03 RCL 15 04 4 05 P-R 06 .3 07 / 08 - 09 RCL 04 10 RCL 07 11 + 12 STO 11 13 4 14 P-R 15 .7 16 * 17 + 18 + 19 RCL 04 20 3 21 P-R 22 .7 23 / 24 + 25 - 26 RCL 13 27 COS 28 ST+ X 29 + 30 RCL 00 31 * 32 RCL 15 33 856 34 P-R 35 18 36 / 37 - 38 - 39 RCL 14 40 2 41 ST* 08 42 * 43 STO 10 44 209 45 P-R 46 E2 47 / 48 - 49 - 50 RCL 11 51 9 52 P-R 53 .23 54 / 55 + 56 - |
57 RCL 08
58 39 59 P-R 60 5.5 61 / 62 + 63 - 64 RCL 04 65 5 66 P-R 67 7 68 * 69 - 70 - 71 RCL 15 72 ST+ X 73 35 74 P-R 75 6 76 / 77 + 78 - 79 RCL 13 80 6 81 P-R 82 3 83 / 84 + 85 + 86 RCL 05 87 RCL 07 88 - 89 SIN 90 RCL 10 91 RCL 15 92 + 93 STO 09 94 SIN 95 - 96 3 97 * 98 RCL 14 99 RCL 15 100 + 101 SIN 102 - 103 5 104 * 105 + 106 RCL 14 107 RCL 10 108 + 109 STO 06 110 SIN 111 4 112 * |
113 +
114 RCL 10 115 RCL 07 116 + 117 STO 12 118 SIN 119 6 120 * 121 RCL 14 122 SIN 123 5 124 * 125 - 126 RCL 07 127 RCL 08 128 + 129 SIN 130 + 131 RCL 10 132 ST+ X 133 SIN 134 + 135 RCL 09 136 RCL 08 137 - 138 SIN 139 - 140 RCL 15 141 RCL 08 142 - 143 SIN 144 + 145 RCL 07 146 21 147 + 148 SIN 149 - 150 ST+ X 151 + 152 RCL 13 153 RCL 07 154 - 155 3 156 P-R 157 2 158 / 159 + 160 - 161 RCL 11 162 RCL 07 163 + 164 STO 13 165 6 166 P-R 167 3 168 / |
169 +
170 + 171 STO 03 172 RCL 10 173 COS 174 34 175 * 176 RCL 08 177 1 178 P-R 179 6 180 * 181 - 182 - 183 RCL 11 184 6 185 P-R 186 LASTX 187 / 188 - 189 - 190 RCL 05 191 RCL 07 192 - 193 COS 194 5 195 * 196 + 197 RCL 13 198 COS 199 PI 200 * 201 + 202 RCL 09 203 COS 204 RCL 15 205 COS 206 - 207 RCL 12 208 COS 209 - 210 ST+ X 211 + 212 RCL 04 213 SIN 214 - 215 RCL 14 216 COS 217 + 218 RCL 06 219 COS 220 - 221 STO 04 222 RCL 08 223 2 224 P-R |
225 .4
226 / 227 - 228 RCL 10 229 COS 230 6 231 * 232 + 233 STO 11 234 19.192 235 STO 05 236 RCL 00 237 14863 238 RCL 00 239 21 240 * 241 + 242 * 243 172993 244 + 245 STO 09 246 CLX 247 33 248 / 249 * 250 RCL 07 251 + 252 STO 08 253 CLX 254 27 255 - 256 * 257 4630 258 + 259 STO 06 260 CLX 261 4 262 * 263 8 264 + 265 * 266 773 267 + 268 STO 07 269 CLX 270 18 271 - 272 * 273 CHS 274 134 275 + 276 * 277 5211 278 + 279 * 280 74005 |
281 XEQ "L"
282 RTN 283 LBL "XE" 284 RCL 00 285 1358 286 RCL 00 287 26587 288 * 289 + 290 * 291 124 292 - 293 * 294 STO 11 295 CLX 296 3080 297 * 298 1175 299 - 300 * 301 14 302 + 303 STO 03 304 CLX 305 11605 306 * 307 CHS 308 960 309 - 310 * 311 8 312 + 313 STO 04 314 CLX 315 641.294 316 * 317 20.862 318 + 319 STO 08 320 68.049 321 STO 05 322 43364 323 STO 06 324 43867 325 STO 07 326 RCL 00 327 13970 328 * 329 187249 330 + 331 STO 09 332 151210 333 CHS 334 XEQ "L" 335 END |
( 469 bytes / SIZE 016 )
| STACK | INPUTS | OUTPUTS |
| Z | / | distance to the earth ( AU ) |
| Y | / | declination ( ° ' '' ) |
| X | / | right ascension ( hh.mnss ) |
Example: ( T = 0.1 )
( 2100/01/01 0h TT )
1°) Uranus
XEQ "UR"
>>>> 1h06m24s
( right ascension )
= R06 ( execution time
= 57s )
RDN
6°22'41" ( declination
)
= R07
RDN
19.824 AU ( Uranus' distance to the
Earth ) = R05
and RDN yields elongation from the
Sun = 97°13
if you've modified the subroutines as suggested above ( in §2 ).
and R03 = 17.741°
( geocentric longitude )
R08 = 20.542°
( heliocentric longitude )
R04 =
-0.628° ( geocentric
latitude )
R09 = -0.623°
( heliocentric latitude )
R10 = 19.970 AU ( radius vector )
2°) Xena
XEQ "XE"
>>>> 2h34m58s
( right ascension )
= R06 ( execution time
= 37s )
RDN
21°40'24" ( declination
)
= R07
RDN
83.419 AU ( Xena's distance to the
Earth ) = R05
and RDN yields elongation from the
Sun = 122°37
if you've modified the subroutines as suggested above ( in §2 ).
and R03 = 43.192°
( geocentric longitude )
R08 = 43.761°
( heliocentric longitude )
R04 =
6.180° ( geocentric
latitude )
R09 = 6.141°
( heliocentric latitude )
R10 = 83.950 AU ( radius vector )
8°) Position of the Sun ( faster program
, lesser accuracy )
-The following routine neglects the perturbations except the main one
in the radius vector.
-The errors remain of the order of 0.01°, 2 or 3 centuries
around J2000
-"SUN2" calculates the ecliptic longitude and the radius vector only.
Data Registers:
• R00 = T expressed in millenia since 2000/01/01 0h TT
(
Register R00 is to be initialized before executing "SUN2" )
Flags: /
Subroutines: /
| 01 LBL "SUN2"
02 DEG 03 4452671 04 RCL 00 05 * 06 68 07 - 08 COS 09 PI 10 * 11 RCL 00 |
12 359990.503
13 * 14 2.964 15 - 16 STO M 17 ST+ X 18 14 19 ST+ Z 20 P-R 21 ST- Z 22 CLX |
23 .4
24 / 25 RCL 00 26 42 27 * 28 1671 29 - 30 RCL M 31 X<>Y 32 P-R 33 ST+ T |
34 RDN
35 ST+ X 36 - 37 E5 38 ST/ Z 39 / 40 R-D 41 17.195 42 RCL 00 43 * 44 + |
45 77.063
46 - 47 0 48 X<> M 49 + 50 360 51 MOD 52 X<>Y 53 1 54 + 55 END |
( 112 bytes / SIZE 001 )
| STACK | INPUTS | OUTPUTS |
| Y | / | L |
| X | / | R |
with R = radius vector
( in AU )
and L = ecliptic longitude
( in degrees )
Example: Calculate the Sun's position on 2100 January 1st at 0h TT.
T = 0.1 0.1 STO 00
XEQ "SUN2" >>>>
R = 0.983356 AU
( execution time = 5 seconds )
X<>Y L = 280.6097°
-If you want to get the rectangular coordinates, press X<>Y P-R it yields:
X = 0.181053
and Y = -0.966545
9°) Position of the Sun ( higher accuracy
)
-"SUN3" calculates the ecliptic longitude and the radius vector only.
-It uses more periodic terms than "SUN" and the results are valid -
at least - over the time span [ 1000 , 3000 ]
Data Registers:
• R00 = T expressed in millenia since 2000/01/01 0h TT
( Register R00 is to be initialized before executing "SUN3" )
Flags: /
Subroutines: /
| 01 LBL "SUN3"
02 DEG 03 RCL 00 04 65 05 / 06 359990.503 07 - 08 RCL 00 09 * 10 2.964 11 + 12 STO M 13 RCL 00 14 202 15 * 16 18 17 - 18 COS 19 23 20 RCL 00 21 329645 22 * 23 STO O 24 - 25 1 |
26 P-R
27 ST+ Z 28 CLX 29 3 30 SQRT 31 * 32 X<>Y 33 450369 34 RCL 00 35 * 36 17 37 - 38 STO N 39 2 40 SQRT 41 P-R 42 ST- T 43 X<> L 44 / 45 - 46 3 47 * 48 RCL N 49 2 50 / |
51 COS
52 ST+ X 53 X<>Y 54 - 55 RCL 00 56 .7 57 * 58 14 59 - 60 ST- Z 61 RCL M 62 ST+ X 63 X<>Y 64 P-R 65 ST+ T 66 CLX 67 .4 68 / 69 + 70 RCL 00 71 42 72 + 73 RCL 00 74 * 75 1671 |
76 -
77 RCL M 78 X<>Y 79 P-R 80 ST+ T 81 RDN 82 ST+ X 83 + 84 4452671 85 RCL 00 86 * 87 68 88 - 89 PI 90 P-R 91 ST+ T 92 RDN 93 + 94 RCL O 95 ST+ X 96 48 97 - 98 1 99 P-R 100 ST+ T |
101 RDN
102 - 103 RCL 00 104 80 105 * 106 30010 107 + 108 RCL 00 109 * 110 + 111 134500 112 - 113 E5 114 ST/ Z 115 / 116 R-D 117 RCL M 118 - 119 360 120 MOD 121 X<>Y 122 1 123 + 124 CLA 125 END |
( 212 bytes / SIZE 000 )
| STACK | INPUTS | OUTPUTS |
| Y | / | L |
| X | / | R |
R = radius vector
( in AU )
L = ecliptic longitude ( in degrees
)
Example: Calculate the Sun's position on 2100 January 1st at 0h TT
T = 0.1 0.1 STO 00
XEQ "SUN3" >>>> R = 0.983353
AU
( execution time = 11 seconds )
X<>Y L = 280.6081°
Note:
-If you want to use "SUN3" instead of "SUN", replace line 125 by
| STO 05
X<>Y STO 03 X<>Y |
P-R
STO 01 X<>Y STO 02 |
CLX
STO 04 XEQ "N" RTN |
References:
[1] Planetary Programs and tables from -4000 to +2800 - Bretagnon
and Simon - Willmann-Bell ISBN 0-943396-08-5
[2] Lunar Tables and Programs from 4000 B.C. to A.D. 8000 - Chapront-Touzé
and Chapront - Willmann-Bell ISBN 0-943396-33-6
[3] Jean Meeus - "Astronomical Algorithms" - Willmann-Bell
- ISBN 0-943396-61-1
[4] www.Moshier.net
this site is a treasure-trove of very interesting programs and data !
[5] VSOP87D Series ftp://ftp.imcce.fr/pub/ephem/planets/vsop87/
[6] VSOP09 & TOP10 Series http://www.imcce.fr/~jlsimon
[7] A fantastic software, "SOLEX" which may be downloaded from
http://chemistry.unina.it/~alvitagl/solex/
>>> "Planetary Programs and Tables from -4000 to +2800 " also
provides simple formulae for corrections of aberration and nutation.