hp41programs

Astro Ephem 2 Astronomical Ephemeris (II) for the HP41

Overview

0°) 4 Subroutines: "L" "N" "O" "K"
1°) The Sun
2°) The Moon
3°) Mercury
4°) Venus
5°) Mars
6°) Jupiter
7°) Saturn
8°) Uranus
9°) Neptune
10°) Pluto

-The programs listed in "Astronomical Ephemeris for the HP-41" give a good accuracy
( about 0.01° in the heliocentric longitudes ) over the time span [1000,3000]
-In this page, the same accuracy is obtained over the interval [0,4000]
( except for Pluto whose coordinates are accurate between 1880 and 2110 only )
-The same method is used: we first solve Kepler's equation and then, a few perturbations are added.
-But of course, more terms have been taken into account ( Fourier & Poisson series )

-This precision of the order of 0.01° is probably achieved over [-1000,5000] for the Sun, Mercury and Venus.
-But for Jupiter, Saturn and Uranus - even between 0 and 4000 - errors may sometimes slightly exceed 0.01°
-The precision of the Moon's coordinates is more doubtful outside [1000-3000].

-The instructions are identical, except that the unit of time is 2000 Julian years ( from 2000/01/01 0h TT )
-The effects of nutation and aberration have been neglected and all the coordinates are referred to the mean ecliptic and equinox of the date.

-For the Sun and the planets - except Pluto - these programs employ the series VSOP87D
with improvements from the new theories VSOP09 & TOP2010 for Uranus and Neptune.

DATA REGISTERS:

-Registers R00 thru R15 are used by every program.

R00 = T = time since 2000/01/01 0h TT is to be initialized before executing any program    ( Unit = 2000 years = 730500 days )
R01 and R02 contain the Sun's rectangular ecliptic coordinates. They are calculated and stored by the "SUN" program which must be executed first.
R03 = geocentric longitude in decimal degrees
R04 = geocentric latitude    ------------------
R05 = distance to the Earth in Astronomical Units ( except for the Moon: R05 = the Moon's parallax in sexagesimal degrees )
R06 = Right Ascension in hh.mnss
R07 = Declination in ° ' ''
R08 = heliocentric longitude in decimal degrees   ( except for the Sun and the Moon )
R09 = heliocentric latitude   -------------------    ---------------------------------
R10 = radius vector in Astronomical Units            ---------------------------------

-Registers are also used for temporary data storage, for instance:

R05 thru R10 contain the mean elements of the planets: semi-major axis, eccentricity, inclination,
mean longitude, longitude of perihelion, longitude of the ascending node.
R03 , R04 , R11 contain the perturbations in longitude, radius vector and latitude respectively.

STACK	INPUTS	OUTPUTS
T	/	elongation from the Sun* ( deg )
Z	/	distance to the earth** ( AU )
Y	/	declination ( ° ' '' )
X	/	right ascension ( hh.mnss )

* except for the Sun
** or Moon's parallax ( ° ' " )

-The following routine may be used to store T in R00
-Line 06 may be replaced by XEQ "J1" or XEQ "J2" ( cf "Julian & Gregorian Calendar" )

01 LBL "TT"
02 HR
03 24
04 /
05 X<>Y
06 XEQ "J0"
07 +
08 730500
09 /
10 STO 00
11 END

-For example: 5000/01/23 at 0h TT

5000.0123 ENTER^
0 XEQ "TT" >>>> T = R00 = 1.5

>>>> The HP-41 must be set in DEG mode.

0°) 4 Subroutines: "L" "N" "O" "K"

-LBL 00 solves Kepler's Equation
-Line 97 is used for the Moon only
-LBL 01 = Spherical-Rectangular conversion
-LBL 02 = Rectangular-Spherical conversion

01 LBL "L"
02 +
03   E3
04 ST/ 03
05 ST/ 04
06 ST/ 07
07 ST/ 09
08 ST/ 11
09 /
10 STO 10
11   E5
12 ST/ 06
13 9
14 STO 15
15 RCL 08
16 360
17 MOD
18 27.942
19 RCL 00
20 *
21 +
22 RCL 09
23 -
24 ENTER^
25 ENTER^
26 LBL 00
27 SIN
28 RCL 06
29 R-D
30 *
31 +
32 DSE 15
33 GTO 00
34 2
35 /
36 1
37 RCL 06
38 +
39 1
40 LASTX
41 -
42 /
43 SQRT
44 P-R
45 LASTX

46 /
47 R-P
48 RDN
49 ST+ X
50 1
51 R^
52 ST+ X
53 COS
54 RCL 06
55 *
56 -
57 RCL 05
58 *
59 RCL 04
60 +
61 X<> 10
62 STO 04
63 -
64 RCL 09
65 +
66 COS
67 RCL 07
68 LASTX
69 SIN
70 P-R
71 X<>Y
72 ASIN
73 RCL 11
74 +
75 STO 09
76 X<> Z
77 R-P
78 CLX
79 RCL 04
80 +
81 RCL 03
82 +
83 STO 08
84 RCL 10
85 XEQ 01
86 RCL 02
87 ST+ Z
88 CLX
89 RCL 01
90 +

91 XEQ 02
92 STO 05
93 RDN
94 STO 03
95 X<>Y
96 STO 04
97 LBL "N"
98 RCL 00
99 15
100 /
101 X^2
102 .2602
103 -
104 RCL 00
105 *
106 23.4393
107 +
108 CHS
109 RCL 04
110 RCL 03
111 RCL 05
112 XEQ 01
113 RDN
114 R-P
115 X<> Z
116 ST- Y
117 X<> Z
118 P-R
119 R^
120 XEQ 02
121 CLX
122 15
123 /
124 24
125 MOD
126 RCL 02
127 RCL 01
128 R-P
129 CLX
130 RCL 03
131 -
132 COS
133 RCL 04
134 COS
135 *

136 ACOS
137 RCL 05
138 R^
139 HMS
140 STO 07
141 R^
142 HMS
143 STO 06
144 RTN
145 LBL 01
146 X<>Y
147 RDN
148 P-R
149 R^
150 X<>Y
151 P-R
152 RTN
153 LBL 02
154 R-P
155 X<>Y
156 RDN
157 R-P
158 R^
159 X<>Y
160 RTN
161 LBL "O"
162 XEQ "K"
163 CLX
164 STO 04
165 STO 11
166 8905342.229
167 RCL 00
168 .708
169 *
170 -
171 RCL 00
172 *
173 68.245
174 -
175 STO 13
176 ST+ X
177 STO 14
178 1170356.317
179 RCL 00
180 *

181 181.179
182 +
183 STO 07
184 719987.453
185 RCL 00
186 *
187 80.027
188 -
189 STO 08
190 -
191 STO 12
192 LASTX
193 382805.985
194 RCL 00
195 *
196 4.829
197 -
198 STO 09
199 ST+ X
200 -
201 4
202 *
203 RCL 05
204 3
205 *
206 +
207 STO 10
208 RTN
209 LBL "K"
210 60698.113
211 RCL 00
212 *
213 34.31
214 +
215 STO 05
216 24442.279
217 RCL 00
218 *
219 50.061
220 +
221 STO 06
222 -
223 STO 10
224 LASTX
225 -

226 STO 11
227 RCL 10
228 +
229 STO 12
230 RCL 06
231 ST+ X
232 -
233 STO 09
234 ST+ X
235 STO 03
236 8569.345
237 RCL 00
238 *
239 45.955
240 -
241 STO 07
242 4369.712
243 RCL 00
244 *
245 55.654
246 -
247 STO 08
248 -
249 STO 14
250 LASTX
251 -
252 STO 15
253 RCL 06
254 RCL 07
255 3
256 *
257 -
258 STO 04
259 LASTX
260 RCL 09
261 RCL 06
262 -
263 +
264 STO 13
265 RCL 09
266 END

( 446 bytes / SIZE 016 )

1°) The Sun

01 LBL "SUN"
02 XEQ "O"
03 COS
04 RCL 08
05 RCL 05
06 -
07 STO 03
08 SIN
09 +
10 RCL 13
11 SIN
12 +
13 ST+ X
14 RCL 12
15 SIN
16 LASTX
17 ST+ X
18 SIN
19 +
20 2

21 SQRT
22 *
23 -
24 RCL 03
25 ST+ X
26 SIN
27 RCL 05
28 SIN
29 -
30 2
31 SQRT
32 /
33 +
34 STO 03
35 RCL 13
36 COS
37 PI
38 %
39 RCL 08
40 RCL 05

41 -
42 COS
43 61
44 /
45 -
46 RCL 12
47 ST+ X
48 COS
49 63
50 /
51 +
52 STO 04
53 RCL 00
54 34389
55 RCL 00
56 183
57 *
58 +
59 *
60 77063

61 -
62 STO 09
63 CLX
64 5
65 *
66 84
67 +
68 *
69 CHS
70 1671
71 +
72 STO 06
73 SIGN
74 STO 05
75 RDN
76 X^2
77 CHS
78 121
79 +
80 *

81 *
82 E3
83 /
84 ST+ 08
85 CLST
86 STO 01
87 STO 02
88 STO 07
89 XEQ "L"
90 RCL 03
91 RCL 05
92 P-R
93 STO 01
94 X<>Y
95 STO 02
96 RCL 05
97 RCL 07
98 RCL 06
99 END

( 135 bytes / SIZE 016 )

STACK	INPUTS	OUTPUTS
Z	/	distance to the earth ( AU )
Y	/	declination ( ° ' '' )
X	/	right ascension ( hh.mnss )

Example: T = 1.5 ( 5000/01/23 0h TT ) 1.5 STO 00

XEQ "SUN"   >>>> R.A. = 20h18m22s                       = R06                   R03 = l = -57.604° = 302.396°                Ecliptic Longitude
                         RDN Decl = -19°18'60" = -19°19'00" = R07       and       R04 = b = 0°                                            Ecliptic Latitude is always 0°
                         RDN    r     = 0.986964                         = R05

and the rectangular ecliptic coordinates of the Sun:

R01 = X = 0.528784 UA
R02 = Y = -0.833359 UA

2°) The Moon

01 LBL "MO"
02 XEQ "O"
03 RCL 00
04 6.451
05 RCL 00
06 .061
07 *
08 +
09 *
10 77.063
11 -
12 ST- 08
13 CLX
14 11
15 *
16 CHS
17 115
18 +
19 *
20 3542
21 +
22 *
23 9543977351
24 +
25 *
26 128341
27 +
28   E3
29 /
30 STO 07
31 ST+ X
32 STO 12
33 RDN
34 ST+X
35 1417
36 +
37 *
38 9664040349
39 -
40 *
41 86657
42 -
43   E3
44 /
45 STO 09
46 ST+ X
47 STO 06
48 6036
49 RCL 14
50 RCL 07
51 -
52 STO 03
53 COS
54 58
55 *
56 -
57 RCL 14
58 COS
59 46
60 *
61 -
62 RCL 12
63 COS
64 9
65 *
66 -
67 RCL 14
68 RCL 12
69 -
70 STO 15
71 COS
72 RCL 07
73 COS
74 82
75 *
76 -
77 4
78 *
79 +
80 RCL 14
81 RCL 08
82 -

83 STO 11
84 COS
85 RCL 07
86 RCL 14
87 +
88 STO 10
89 COS
90 +
91 3
92 *
93 -
94 1
95 %
96 1/X
97 ASIN
98 HMS
99 STO 05
100 RCL 07
101 RCL 09
102 -
103 SIN
104 281
105 *
106 RCL07
107 RCL 09
108 +
109 SIN
110 278
111 *
112 +
113 RCL 09
114 RCL 14
115 +
116 STO 04
117 SIN
118 173
119 *
120 +
121 RCL 03
122 RCL 09
123 -
124 SIN
125 55
126 *
127 +
128 RCL 03
129 RCL 09
130 +
131 SIN
132 46
133 *
134 +
135 RCL 14
136 RCL 09
137 -
138 SIN
139 33
140 *
141 +
142 RCL 12
143 RCL 09
144 -
145 SIN
146 17
147 *
148 +
149 RCL 09
150 RCL 10
151 +
152 SIN
153 RCL 09
154 RCL 12
155 +
156 SIN
157 +
158 9
159 *
160 +
161 RCL 09
162 RCL 11
163 +
164 SIN

165 RCL 09
166 SIN
167 641
168 *
169 -
170 8
171 *
172 +
173 RCL 09
174 RCL 15
175 +
176 SIN
177 RCL 10
178 RCL 09
179 -
180 SIN
181 +
182 4
183 *
184 +
185 RCL 04
186 RCL 08
187 +
188 SIN
189 3
190 *
191 -
192 RCL 11
193 RCL 09
194 -
195 STO 04
196 RCL 07
197 -
198 SIN
199 LASTX
200 RCL 06
201 +
202 SIN
203 +
204 RCL 04
205 SIN
206 +
207 RCL 09
208 RCL 07
209 -
210 STO 04
211 RCL 08
212 +
213 SIN
214 -
215 RCL 04
216 RCL 14
217 ST+ X
218 +
219 SIN
220 +
221 RCL 08
222 RCL 09
223 -
224 SIN
225 -
226 RCL 06
227 RCL 09
228 +
229 SIN
230 +
231 ST+ X
232 +
233 STO 04
234 RCL 03
235 RCL 08
236 -
237 SIN
238 57
239 *
240 RCL 08
241 SIN
242 185
243 *
244 -
245 RCL 11
246 SIN

247 46
248 *
249 +
250 RCL 08
251 RCL 07
252 -
253 SIN
254 41
255 *
256 -
257 RCL 07
258 RCL 08
259 +
260 SIN
261 30
262 *
263 -
264 RCL 03
265 RCL 08
266 +
267 SIN
268 8
269 *
270 -
271 RCL 08
272 RCL 14
273 +
274 SIN
275 7
276 *
277 -
278 1
279 RCL 00
280 20
281 /
282 -
283 *
284 RCL 07
285 SIN
286 6289
287 *
288 +
289 RCL 14
290 SIN
291 658
292 *
293 +
294 RCL 12
295 SIN
296 214
297 *
298 +
299 RCL 06
300 SIN
301 114
302 *
303 +
304 RCL 15
305 SIN
306 59
307 *
308 +
309 RCL 10
310 SIN
311 53
312 *
313 +
314 RCL 03
315 SIN
316 98
317 *
318 RCL 07
319 RCL 06
320 -
321 SIN
322 -
323 13
324 *
325 +
326 RCL 06
327 RCL 07
328 +

329 SIN
330 RCL 14
331 ST+ X
332 RCL 07
333 -
334 SIN
335 +
336 11
337 *
338 +
339 RCL 03
340 ST+ X
341 SIN
342 9
343 *
344 +
345 RCL 13
346 SIN
347 7
348 *
349 RCL 06
350 RCL 14
351 +
352 SIN
353 3
354 *
355 -
356 RCL 07
357 RCL 12
358 +
359 SIN
360 ST+ X
361 -
362 RCL 13
363 RCL 07
364 -
365 SIN
366 +
367 RCL 08
368 RCL 13
369 +
370 SIN
371 -
372 5
373 *
374 -
375 RCL 10
376 RCL 08
377 -
378 SIN
379 RCL 12
380 RCL 14
381 +
382 SIN
383 +
384 RCL 14
385 ST+ X
386 SIN
387 +
388 RCL 03
389 RCL 12
390 -
391 SIN
392 +
393 RCL 00
394 46
395 *
396 1
397 -
398 R-D
399 SIN
400 -
401 4
402 *
403 +
404 RCL 08
405 RCL 12
406 -
407 SIN
408 RCL 03
409 RCL 06
410 -

411 SIN
412 +
413 3
414 *
415 -
416 RCL 11
417 RCL 08
418 -
419 SIN
420 LASTX
421 RCL 07
422 -
423 SIN
424 +
425 RCL 11
426 RCL 12
427 -
428 SIN
429 +
430 RCL 07
431 RCL 13
432 +
433 SIN
434 -
435 RCL 08
436 RCL 12
437 +
438 SIN
439 -
440 RCL 08
441 ST+ X
442 SIN
443 -
444 RCL 06
445 RCL 10
446 +
447 SIN
448 -
449 RCL 14
450 RCL 06
451 -
452 SIN
453 -
454 RCL 00
455 ENTER^
456 +
457 CHS
458 15
459 +
460 RCL 00
461 *
462 631
463 -
464 RCL 00
465 *
466 9625357624
467 +
468 RCL 00
469 *
470 211728
471 +
472   E3
473 /
474 360
475 MOD
476 SIN
477 ST+ X
478 ST- 04
479 X<> L
480 STO 03
481 RCL 09
482 +
483 SIN
484 +
485 ST+ X
486 +
487   E3
488 ST/ 04
489 /
490 ST+ 03
491 XEQ "N"
492 END

( 631 bytes / SIZE 016 )

STACK	INPUTS	OUTPUTS
T	/	elongation from the Sun* ( deg )
Z	/	Moon's parallax ( ° ' '' )
Y	/	declination ( ° ' '' )
X	/	right ascension ( hh.mnss )

Example: T = 1.5 ( 5000/01/23 0h TT ) ( geocentric )

XEQ "MO" >>>>   R.A. = 5h28m58s = R06                       R03 = l = 82.940°
                      RDN    Decl = 24°30'13" = R07                      R04 = b = 1.627°
                      RDN    Paral = 1°00'38" = R05
                      RDN    Elong = 140.52°

3°) Mercury

01 LBL "ME"
02 RCL 00
03 127125
04 *
05 87
06 +
07 COS
08 ST+ X
09 STO 03
10 CLX
11 STO 04

12 STO 11
13 .3871
14 STO 05
15 RCL 00
16 36
17 RCL 00
18 7
19 *
20 -
21 *
22 7005

23 +
24 STO 07
25 RDN
26 X^2
27 CHS
28 121
29 +
30 *
31 2989453501
32 +
33 *

34 250205
35 +
36 E3
37 /
38 STO 08
39 RDN
40 CHS
41 41
42 +
43 *
44 20563

45 +
46 STO 06
47 CLX
48 118
49 *
50 31128
51 +
52 *
53 77456
54 +
55 STO 09

56 RDN
57 ST+ X
58 70
59 +
60 *
61 23722
62 +
63 *
64 48331
65 XEQ "L"
66 END

( 132 bytes / SIZE 016 )

STACK	INPUTS	OUTPUTS
T	/	elongation from the Sun ( deg )
Z	/	distance to the earth ( AU )
Y	/	declination ( ° ' '' )
X	/	right ascension ( hh.mnss )

Example: T = 1.5 ( 5000/01/23 0h TT ) ( geocentric ) ( heliocentric )

XEQ "ME"   >>>>   R.A. = 20h29m40s = R06                       R03 = l = -55.257° = 304.743°                R08 = L = -50.267° = 309.733°
                      RDN    Decl = -20°21'19" = R07                      R04 = b = -1.623°                                     R09 = B = -5.049°
                      RDN       r    = 1.4495 UA = R05                                                                                       R10 = R = 0.46636 UA
                      RDN    Elong = 2.85°

4°) Venus

01 LBL "VE"
02 XEQ "O"
03 RCL 12
04 SIN
05 2
06 SQRT
07 *
08 RCL 12
09 3
10 *
11 SIN
12 ST+ X
13 -
14 RCL 12
15 ST+ X
16 SIN

17 PI
18 *
19 -
20 STO 03
21 .72333
22 STO 05
23 RCL 00
24 96
25 CHS
26 RCL 00
27 4
28 *
29 +
30 *
31 677
32 +

33 STO 06
34 CLX
35 4
36 *
37 CHS
38 45
39 -
40 *
41 430
42 -
43 *
44 28043
45 +
46 *
47 131564
48 +

49 STO 09
50 RDN
51 X^2
52 CHS
53 124
54 +
55 *
56 *
57 E3
58 /
59 RCL 07
60 +
61 STO 08
62 CLX
63 20
64 *

65 3395
66 +
67 STO 07
68 CLX
69 162
70 *
71 18021
72 +
73 *
74 76680
75 XEQ "L"
76 END

( 126 bytes / SIZE 016 )

STACK	INPUTS	OUTPUTS
T	/	elongation from the Sun* ( deg )
Z	/	distance to the earth** ( AU )
Y	/	declination ( ° ' '' )
X	/	right ascension ( hh.mnss )

Example: T = 1.5 ( 5000/01/23 0h TT ) ( geocentric ) ( heliocentric )

XEQ "VE"   >>>>   R.A. = 22h50m30s = R06                       R03 = l = -19.568° = 340.432°                R08 = L = 37.443°
                      RDN    Decl = -9°20'44"    = R07                      R04 = b = -1.946°                                     R09 = B = -3.145°
                      RDN       r    = 1.1728 UA = R05                                                                                        R10 = R = 0.7261 UA
                      RDN    Elong = 38.08°

5°) Mars

01 LBL "MA"
02 XEQ "O"
03 5
04 P-R
05 3
06 *
07 -
08 RCL 10
09 SIN
10 4
11 *
12 RCL 00
13 *
14 +
15 RCL 09
16 RCL 05
17 -
18 STO 13
19 SIN
20 7
21 *
22 -
23 RCL 13
24 RCL 05
25 -

26 5
27 P-R
28 2
29 /
30 -
31 +
32 RCL 07
33 ST+ X
34 RCL 13
35 7
36 *
37 -
38 RCL 05
39 +
40 RCL 06
41 6
42 *
43 -
44 3.6
45 P-R
46 -
47 +
48 RCL 08
49 RCL 09
50 -

51 STO 14
52 LASTX
53 -
54 STO 15
55 3
56 P-R
57 -
58 -
59 RCL 13
60 ST+ X
61 SIN
62 4
63 *
64 +
65 RCL 14
66 RCL 15
67 +
68 SIN
69 RCL 14
70 SIN
71 -
72 ST+ X
73 +
74 RCL 09
75 3

76 *
77 RCL 07
78 -
79 COS
80 RCL 03
81 2
82 /
83 RCL 10
84 ST+ X
85 -
86 COS
87 +
88 RCL 10
89 RCL 09
90 -
91 COS
92 +
93 2
94 SQRT
95 *
96 -
97 STO 03
98 1.5237
99 STO 05
100 RCL 00

101 RCL 09
102 RCL 00
103 X^2
104 .124
105 *
106 +
107 STO 08
108 CLX
109 PI
110 *
111 CHS
112 181
113 +
114 *
115 9340
116 +
117 STO 06
118 CLX
119 4
120 *
121 54
122 +
123 *
124 36819
125 +

126 *
127 23940
128 -
129 STO 09
130 CLX
131 5
132 *
133 12
134 -
135 *
136 1850
137 +
138 STO 07
139 CLX
140 18
141 *
142 6
143 +
144 *
145 15440
146 +
147 *
148 49558
149 XEQ "L"
150 END

( 202 bytes / SIZE 016 )

STACK	INPUTS	OUTPUTS
T	/	elongation from the Sun* ( deg )
Z	/	distance to the earth** ( AU )
Y	/	declination ( ° ' '' )
X	/	right ascension ( hh.mnss )

Example: T = 1.5 ( 5000/01/23 0h TT ) ( geocentric ) ( heliocentric )

XEQ "MA"   >>>>   R.A. = 0h33m15s = R06                       R03 = l = 8.729°                                     R08 = L = 49.535°
                      RDN    Decl =   2°45'57"    = R07                      R04 = b = -0.697°                                     R09 = B = -0.728°
                      RDN       r    = 1.4433 UA = R05                                                                                        R10 = R = 1.3834 UA
                      RDN    Elong = 66.34°

6°) Jupiter

01 LBL "JU"
02 XEQ "K"
03 4
04 P-R
05 +
06 CHS
07 RCL 00
08 *
09 RCL 09
10 16
11 P-R
12 6
13 SQRT
14 SQRT
15 *
16 -
17 -
18 RCL 00
19 *
20 RCL 09
21 99
22 P-R
23 5
24 SQRT
25 /
26 +
27 +
28 RCL 05
29 RCL 09
30 +
31 STO 08
32 PI
33 P-R
34 ST+ X
35 -
36 +
37 RCL 09
38 RCL 05
39 -
40 STO 07
41 6
42 P-R
43 2
44 /
45 +
46 +
47 RCL 03
48 3
49 P-R
50 4
51 LN
52 /

53 +
54 -
55 RCL 00
56 *
57 RCL 09
58 74
59 P-R
60 3.4
61 *
62 -
63 +
64 RCL 08
65 23
66 P-R
67 6
68 /
69 +
70 -
71 RCL 11
72 5
73 P-R
74 +
75 +
76 RCL 12
77 5
78 P-R
79 .8
80 *
81 +
82 +
83 RCL 07
84 6
85 P-R
86 ST+ X
87 -
88 +
89 RCL 06
90 RCL 09
91 +
92 SIN
93 6
94 SQRT
95 *
96 -
97 RCL 03
98 2
99 P-R
100 ST+ X
101 -
102 -
103 RCL 00
104 *

105 RCL 09
106 325
107 P-R
108 9
109 D-R
110 *
111 +
112 -
113 RCL 10
114 ST+ X
115 STO 14
116 SIN
117 56
118 *
119 +
120 RCL 08
121 3
122 P-R
123 14
124 *
125 +
126 +
127 RCL 11
128 36
129 P-R
130 6
131 /
132 -
133 +
134 RCL 12
135 12
136 P-R
137 5
138 LN
139 *
140 -
141 +
142 RCL 10
143 SIN
144 22
145 *
146 -
147 RCL 07
148 15
149 P-R
150 5
151 SQRT
152 /
153 +
154 -
155 RCL 11
156 ST+ X

157 2
158 P-R
159 ST+ X
160 +
161 +
162 RCL 10
163 RCL 14
164 +
165 SIN
166 5
167 *
168 +
169 RCL 10
170 RCL 12
171 +
172 2
173 P-R
174 ST+ X
175 -
176 -
177 RCL 06
178 7
179 SQRT
180 P-R
181 +
182 +
183 RCL 05
184 RCL 14
185 +
186 SIN
187 RCL 12
188 RCL 14
189 +
190 COS
191 +
192 RCL 13
193 SIN
194 +
195 RCL 03
196 SIN
197 +
198 3
199 *
200 +
201 RCL 11
202 RCL 06
203 -
204 2
205 P-R
206 -
207 -
208 STO 03

209 RCL 08
210 2
211 P-R
212 LASTX
213 /
214 RCL 00
215 *
216 +
217 RCL 14
218 COS
219 3
220 *
221 -
222 RCL 12
223 SIN
224 -
225 RCL 07
226 COS
227 -
228 RCL 10
229 COS
230 +
231 STO 04
232 RCL 08
233 COS
234 5
235 *
236 RCL 08
237 RCL 00
238 PI
239 *
240 P-R
241 RCL 00
242 *
243 2
244 /
245 +
246 -
247 RCL 07
248 COS
249 PI
250 *
251 -
252 STO 11
253 RCL 00
254 110
255 CHS
256 RCL 00
257 2
258 *
259 +
260 *

261 1303
262 +
263 STO 07
264 CLX
265 .089
266 *
267 *
268 RCL 05
269 +
270 STO 08
271 CLX
272 5.203
273 STO 05
274 RDN
275 ST+ X
276 19
277 +
278 *
279 CHS
280 326
281 +
282 *
283 4849
284 +
285 STO 06
286 CLX
287 36
288 *
289 CHS
290 412
291 +
292 *
293 32253
294 +
295 *
296 14331
297 +
298 STO 09
299 CLX
300 3
301 *
302 161
303 +
304 *
305 20420
306 +
307 *
308 100464
309 XEQ "L"
310 END

( 384 bytes / SIZE 016 )

STACK	INPUTS	OUTPUTS
T	/	elongation from the Sun* ( deg )
Z	/	distance to the earth** ( AU )
Y	/	declination ( ° ' '' )
X	/	right ascension ( hh.mnss )

Example: T = 1.5 ( 5000/01/23 0h TT ) ( geocentric ) ( heliocentric )

XEQ "JU"   >>>>   R.A. = 1h52m13s   = R06                       R03 = l = 29.655°                                     R08 = L = 41.156°
                      RDN    Decl = 10°05'22"   = R07                      R04 = b = -1.159°                                     R09 = B = -1.147°
                      RDN       r    = 4.893 UA   = R05                                                                                        R10 = R = 4.945 UA
                      RDN    Elong = 87.26°

7°) Saturn

01 LBL "SA"
02 XEQ "K"
03 3
04 SQRT
05 P-R
06 +
07 CHS
08 RCL 00
09 *
10 RCL 09
11 11
12 P-R
13 +
14 +
15 RCL 00
16 *
17 RCL 09
18 40
19 P-R
20 1.54
21 *
22 -
23 +
24 RCL 11
25 ST+ X
26 STO 08
27 6
28 P-R
29 3
30 /
31 +
32 -
33 RCL 09
34 RCL 06
35 -
36 STO 14
37 6
38 P-R
39 +
40 +
41 RCL 03
42 3
43 P-R
44 +
45 -
46 RCL 00
47 *
48 RCL 09
49 244
50 P-R
51 5
52 SQRT
53 /
54 +
55 -
56 RCL 08
57 3
58 P-R
59 11.6
60 *
61 -
62 -
63 RCL 11
64 2
65 P-R
66 -
67 +
68 RCL 14
69 15
70 P-R
71 1.3
72 *
73 -
74 +
75 RCL 03
76 8
77 P-R
78 1.5
79 /
80 +
81 +
82 RCL 00
83 *

84 RCL 09
85 182
86 P-R
87 3.41
88 *
89 -
90 -
91 RCL 08
92 122
93 P-R
94 .14
95 *
96 -
97 +
98 RCL 11
99 15
100 P-R
101 .87
102 /
103 +
104 -
105 RCL 14
106 42
107 P-R
108 5
109 SQRT
110 /
111 +
112 -
113 RCL 11
114 RCL 06
115 -
116 STO 15
117 PI
118 P-R
119 +
120 +
121 RCL 12
122 4
123 P-R
124 -
125 +
126 RCL 13
127 PI
128 P-R
129 -
130 +
131 RCL 03
132 28
133 SQRT
134 P-R
135 ST+ X
136 -
137 +
138 RCL 03
139 RCL 04
140 -
141 SIN
142 RCL 14
143 RCL 06
144 -
145 COS
146 +
147 PI
148 *
149 -
150 RCL 03
151 RCL 06
152 +
153 4
154 P-R
155 2
156 /
157 RCL 00
158 *
159 +
160 -
161 RCL 00
162 *
163 RCL 09
164 800
165 P-R
166 9

167 D-R
168 *
169 +
170 +
171 RCL 08
172 72
173 P-R
174 3
175 *
176 +
177 -
178 RCL 11
179 117
180 P-R
181 32
182 SQRT
183 /
184 -
185 -
186 RCL 14
187 9
188 P-R
189 5
190 *
191 -
192 -
193 RCL 15
194 6
195 P-R
196 ST+ X
197 -
198 +
199 RCL 12
200 9
201 P-R
202 PI
203 /
204 +
205 -
206 RCL 10
207 2
208 P-R
209 4
210 *
211 +
212 +
213 RCL 10
214 ST+ X
215 SIN
216 9
217 *
218 -
219 RCL 13
220 SIN
221 8
222 *
223 -
224 RCL 03
225 7
226 P-R
227 3
228 /
229 +
230 -
231 RCL 04
232 COS
233 7
234 *
235 -
236 RCL 04
237 RCL 06
238 +
239 5
240 P-R
241 .6
242 *
243 +
244 +
245 RCL 06
246 RCL 07
247 -
248 ST+ X
249 SIN

250 4
251 *
252 +
253 RCL 05
254 COS
255 RCL 14
256 RCL 06
257 -
258 SIN
259 -
260 RCL 08
261 RCL 09
262 +
263 COS
264 +
265 3
266 *
267 +
268 RCL 03
269 RCL 04
270 -
271 2
272 P-R
273 +
274 +
275 RCL 04
276 RCL 07
277 +
278 COS
279 RCL 06
280 RCL 07
281 -
282 SIN
283 -
284 RCL 05
285 RCL 12
286 +
287 SIN
288 -
289 ST+ X
290 +
291 STO 03
292 RCL 08
293 SIN
294 3
295 *
296 RCL 00
297 *
298 RCL 08
299 1
300 P-R
301 10
302 *
303 +
304 -
305 RCL 14
306 3
307 SQRT
308 P-R
309 ST+ X
310 -
311 +
312 RCL 09
313 SIN
314 3
315 *
316 -
317 RCL 00
318 *
319 RCL 08
320 18
321 P-R
322 3
323 /
324 -
325 -
326 RCL 10
327 COS
328 8
329 *
330 +
331 RCL 11
332 1

333 P-R
334 5
335 *
336 +
337 +
338 RCL 14
339 4
340 P-R
341 6
342 /
343 +
344 -
345 RCL 09
346 COS
347 4
348 *
349 +
350 RCL 10
351 ST+ X
352 COS
353 +
354 RCL 15
355 SIN
356 +
357 STO 04
358 RCL 08
359 SIN
360 3
361 *
362 CHS
363 RCL 00
364 *
365 RCL 14
366 3
367 P-R
368 2
369 SQRT
370 /
371 -
372 +
373 RCL 08
374 COS
375 8
376 *
377 +
378 RCL 12
379 SIN
380 3
381 SQRT
382 *
383 +
384 RCL 00
385 *
386 RCL 08
387 17
388 P-R
389 9
390 /
391 -
392 +
393 RCL 14
394 8
395 P-R
396 +
397 -
398 RCL 12
399 2
400 P-R
401 ST+ X
402 +
403 -
404 RCL 00
405 *
406 RCL 14
407 9
408 P-R
409 .6
410 /
411 -
412 -
413 RCL 08
414 5
415 P-R

416 3.8
417 *
418 +
419 -
420 RCL 12
421 5
422 P-R
423 .7
424 *
425 -
426 -
427 RCL 09
428 SIN
429 4
430 *
431 +
432 RCL 10
433 COS
434 ST+ X
435 +
436 RCL 15
437 COS
438 3
439 *
440 -
441 STO 11
442 9.543
443 STO 05
444 RCL 00
445 335
446 RCL 00
447 39
448 *
449 +
450 *
451 39275
452 +
453 *
454 93057
455 +
456 STO 09
457 CLX
458 .208
459 *
460 *
461 RCL 06
462 +
463 STO 08
464 CLX
465 3
466 *
467 26
468 -
469 *
470 694
471 -
472 *
473 5553
474 +
475 STO 06
476 CLX
477 6
478 *
479 CHS
480 75
481 -
482 *
483 2489
484 +
485 STO 07
486 CLX
487 18
488 *
489 49
490 +
491 *
492 CHS
493 17542
494 +
495 *
496 113666
497 XEQ "L"
498 END

( 601 bytes / SIZE 016 )

STACK	INPUTS	OUTPUTS
T	/	elongation from the Sun* ( deg )
Z	/	distance to the earth** ( AU )
Y	/	declination ( ° ' '' )
X	/	right ascension ( hh.mnss )

Example: T = 1.5 ( 5000/01/23 0h TT ) ( geocentric ) ( heliocentric )

XEQ "SA"   >>>>   R.A. = 1h40m09s   = R06                      R03 = l = 26.063°                                     R08 = L = 31.844°
                      RDN    Decl = 7°49'05"     = R07                      R04 = b = -2.240°                                     R09 = B = -2.254°
                      RDN       r    = 9.806 UA   = R05                                                                                         R10 = R = 9.747 UA
                      RDN    Elong = 83.67°

8°) Uranus

01 LBL "UR"
02 XEQ "K"
03 RCL 04
04 SIN
05 ST+ X
06 RCL 00
07 *
08 RCL 15
09 8
10 P-R
11 .3
12 /
13 -
14 +
15 RCL 04
16 RCL 07
17 +
18 STO 11
19 8
20 P-R
21 .7
22 *
23 +
24 +
25 RCL 08
26 ST+ X
27 STO 08
28 COS
29 7
30 SQRT
31 *
32 +
33 RCL 04
34 6
35 P-R
36 1.5
37 *
38 +
39 -
40 RCL 15
41 ST+ X
42 COS
43 ST+ X
44 -
45 RCL 13
46 7
47 SQRT
48 P-R
49 2
50 SQRT
51 *
52 -

53 -
54 RCL 00
55 *
56 RCL 15
57 856
58 P-R
59 18
60 /
61 -
62 -
63 RCL 14
64 ST+ X
65 STO 10
66 209
67 P-R
68 E2
69 /
70 -
71 -
72 RCL 11
73 9
74 P-R
75 .23
76 /
77 +
78 -
79 RCL 08
80 39
81 P-R
82 5.5
83 /
84 +
85 -
86 RCL 04
87 5
88 P-R
89 7
90 *
91 -
92 -
93 RCL 15
94 ST+ X
95 35
96 P-R
97 6
98 /
99 +
100 -
101 RCL 13
102 6
103 P-R
104 3

105 /
106 +
107 +
108 RCL 05
109 RCL 07
110 -
111 SIN
112 RCL 10
113 RCL 15
114 +
115 STO 09
116 SIN
117 -
118 3
119 *
120 RCL 14
121 RCL 15
122 +
123 SIN
124 -
125 5
126 *
127 +
128 RCL 10
129 RCL 14
130 +
131 STO 06
132 SIN
133 4
134 *
135 +
136 RCL 07
137 RCL 10
138 +
139 STO 12
140 SIN
141 6
142 *
143 RCL 14
144 SIN
145 5
146 *
147 -
148 RCL 07
149 RCL 08
150 +
151 SIN
152 +
153 RCL 10
154 ST+ X
155 SIN
156 +

157 RCL 09
158 RCL 08
159 -
160 SIN
161 -
162 RCL 15
163 RCL 08
164 -
165 SIN
166 +
167 RCL 07
168 21
169 +
170 SIN
171 -
172 ST+ X
173 +
174 RCL 13
175 RCL 07
176 -
177 3
178 SQRT
179 P-R
180 +
181 -
182 RCL 07
183 RCL 11
184 +
185 STO 13
186 6
187 P-R
188 3
189 /
190 +
191 +
192 STO 03
193 RCL 10
194 COS
195 34
196 *
197 RCL 08
198 1
199 P-R
200 6
201 *
202 -
203 -
204 RCL 11
205 6
206 P-R
207 LASTX
208 /

209 -
210 -
211 RCL 05
212 RCL 07
213 -
214 COS
215 5
216 *
217 +
218 RCL 13
219 COS
220 PI
221 *
222 +
223 RCL 09
224 COS
225 RCL 15
226 COS
227 -
228 RCL 12
229 COS
230 -
231 ST+ X
232 +
233 RCL 04
234 SIN
235 -
236 RCL 14
237 COS
238 +
239 RCL 06
240 COS
241 -
242 STO 04
243 RCL 08
244 2
245 P-R
246 .4
247 /
248 -
249 RCL 10
250 COS
251 6
252 *
253 +
254 STO 11
255 19.192
256 STO 05
257 RCL 00
258 86
259 RCL 00
260 3

261 *
262 +
263 *
264 29726
265 +
266 *
267 172993
268 +
269 STO 09
270 CLX
271 .122
272 *
273 *
274 RCL 07
275 +
276 STO 08
277 CLX
278 PI
279 *
280 55
281 -
282 *
283 4630
284 +
285 STO 06
286 SIGN
287 +
288 15
289 *
290 *
291 773
292 +
293 STO 07
294 CLX
295 16
296 *
297 CHS
298 148
299 +
300 *
301 536
302 +
303 *
304 10423
305 +
306 *
307 74005
308 XEQ "L"
309 END

( 386 bytes / SIZE 016 )

STACK	INPUTS	OUTPUTS
T	/	elongation from the Sun* ( deg )
Z	/	distance to the earth** ( AU )
Y	/	declination ( ° ' '' )
X	/	right ascension ( hh.mnss )

Example: T = 1.5 ( 5000/01/23 0h TT ) ( geocentric ) ( heliocentric )

XEQ "UR"   >>>>   R.A. = 16h55m56s = R06                      R03 = l = -104.822° = 255.178°               R08 = L = 252.934°
                      RDN    Decl = -22°00'17"   = R07                      R04 = b = 0.251°                                     R09 = B = 0.260°
                      RDN       r    = 19.158 UA = R05                                                                                        R10 = R = 18.502 UA
                      RDN    Elong = 47.22°

9°) Neptune

01 LBL "NE"
02 XEQ "K"
03 RCL 15
04 583
05 P-R
06 18
07 /
08 -
09 RCL 15
10 5
11 RCL 00
12 *
13 P-R
14 13
15 SQRT
16 *
17 -
18 -
19 RCL 14
20 3
21 -
22 SIN
23 71
24 *
25 +
26 RCL 15
27 ST+ X
28 24
29 P-R
30 6
31 /
32 +
33 +
34 RCL 14

35 RCL 15
36 +
37 STO 13
38 SIN
39 22
40 *
41 +
42 RCL 05
43 RCL 08
44 -
45 STO 10
46 SIN
47 9
48 *
49 +
50 RCL 15
51 RCL 08
52 -
53 STO 12
54 4
55 P-R
56 +
57 +
58 RCL 06
59 RCL 08
60 -
61 STO 09
62 SIN
63 5
64 *
65 +
66 RCL 14
67 ST+ X
68 STO 11

69 SIN
70 RCL 13
71 RCL 15
72 +
73 SIN
74 -
75 ST+ X
76 -
77 STO 03
78 RCL 15
79 COS
80 8
81 *
82 RCL 14
83 1
84 P-R
85 17
86 *
87 +
88 -
89 RCL 10
90 COS
91 RCL 13
92 COS
93 -
94 5
95 *
96 +
97 RCL 09
98 COS
99 3
100 *
101 +
102 RCL 12

103 1
104 P-R
105 -
106 -
107 RCL 11
108 COS
109 +
110 STO 04
111 RCL 14
112 6
113 P-R
114 +
115 CHS
116 RCL 12
117 5
118 P-R
119 .7
120 /
121 -
122 -
123 STO 11
124 30.07
125 STO 05
126 RCL 00
127 899
128 RCL 00
129 13
130 *
131 +
132 STO 06
133 CLX
134 3
135 *
136 186

137 +
138 *
139 CHS
140 1770
141 +
142 STO 07
143 CLX
144 .124
145 *
146 *
147 ST+ 08
148 CLX
149 152
150 *
151 28525
152 +
153 *
154 48124
155 +
156 STO 09
157 CLX
158 5
159 *
160 CHS
161 104
162 +
163 *
164 22044
165 +
166 *
167 131784
168 XEQ "L"
169 END

( 229 bytes / SIZE 016 )

STACK	INPUTS	OUTPUTS
T	/	elongation from the Sun* ( deg )
Z	/	distance to the earth** ( AU )
Y	/	declination ( ° ' '' )
X	/	right ascension ( hh.mnss )

Example: T = 1.5 ( 5000/01/23 0h TT ) ( geocentric ) ( heliocentric )

XEQ "NE"   >>>>   R.A. =   3h48m33s = R06                      R03 = l = 58.956°                                    R08 = L = 60.652°
                      RDN    Decl = 18°11'05"   = R07                      R04 = b = -1.461°                                     R09 = B = -1.439°
                      RDN       r    = 29.389 UA = R05                                                                                        R10 = R = 29.843 UA
                      RDN    Elong = 116.55°

10°) Pluto

01 LBL "PL"
02 XEQ "K"
03 RCL 05
04 2903.4
05 RCL 00
06 *
07 238.925
08 +
09 STO 08
10 -
11 STO 10
12 SIN
13 7
14 *
15 RCL 08
16 COS

17 4
18 *
19 -
20 RCL 08
21 ST+ X
22 STO 09
23 SIN
24 ST+ X
25 -
26 RCL 06
27 RCL 08
28 -
29 STO 11
30 SIN
31 4
32 *

33 +
34 STO 03
35 RCL 09
36 1
37 P-R
38 RCL 08
39 SIN
40 -
41 ST+ X
42 +
43 RCL 10
44 COS
45 5
46 *
47 +
48 RCL 11

49 COS
50 ST+ X
51 +
52 STO 04
53 RCL 00
54 234
55 *
56 3
57 -
58 RCL 08
59 COS
60 5
61 *
62 -
63 STO 11
64 39.489

65 STO 05
66 24900
67 STO 06
68 17140
69 STO 07
70 27942
71 RCL 00
72 *
73 135925
74 -
75 STO 09
76 246232
77 XEQ "L"
78 END

( 133 bytes / SIZE 016 )

STACK	INPUTS	OUTPUTS
T	/	elongation from the Sun* ( deg )
Z	/	distance to the earth** ( AU )
Y	/	declination ( ° ' '' )
X	/	right ascension ( hh.mnss )

Example: T = 0.05 ( 2100/01/01 0h TT ) ( geocentric ) ( heliocentric )

XEQ "PL"   >>>>    R.A. = 2h23m50s   = R06                      R03 = l = 32.395°                                    R08 = L = 33.511°
                      RDN    Decl = -3°37'43"    = R07                      R04 = b = -16.921°                                  R09 = B = -16.794°
                      RDN       r    = 48.576 UA = R05                                                                                        R10 = R = 48.934 UA
                      RDN    Elong = 110.80°

( First execute "SUN" with T = 0.05 to get the correct geocentric coordinates )

References:

[1] Jean Meeus - "Astronomical Algorithms" - Willmann-Bell - ISBN 0-943396-35-2
[2] VSOP87D Series ftp://ftp.imcce.fr/pub/ephem/planets/vsop87/
[3] VSOP09 & TOP2010 Series http://www.imcce.fr/~jlsimon
[4] A fantastic software, "SOLEX" which may be downloaded from http://chemistry.unina.it/~alvitagl/solex/