SansTitre

Astronomical Ephemeris (7) for the HP-41

Overview

1°) 4 Subroutines: "L" "K" "Z" "M"
2°) Local Sidereal Time - Sun - Moon - Mercury - Venus - Mars
3°) Jupiter - Saturn - Uranus - Neptune - Pluto
4°) Numerical Examples
5°) A Single Program

-These programs calculate the positions of the Sun, the major planets and the Moon over the interval [ 1700 , 2300 ].
-For Pluto the interval is only [ 1880 , 2100 ]

-The precision is about 0°01 for the heliocentric longitudes & latitudes.
-They are referred to the mean ecliptic & equinox of the date:
-Aberration, nutation and light-time are taken into account for the geocentric coordinates

-Correction for parallax is only taken into account for the height.

Registers

R00 = Time from 2000/01/01 0h TT ( unit = 300 Julian years ) ( Registers R16-R17-R18 are to be initialized before computing the coordinates )

R01 = X Rectangular
R02 = Y coordinates of the Sun,

R03 = Geocentric longitude ( ° ' " )
R04 = Geocentric latitude ( ° ' " )
R05 = Distance Earth-Planet ( AU )

R06 = Right-ascension ( hh.mnss )
R07 = Declination ( ° ' " )

R08 = Azimuth ( ° ' " ) ( reckoned clockwise from North )
R09 = height ( ° ' " )
R10 = height corrected for refraction ( ° ' " )

R11 = Heliocentric longitude ( decimal degrees )
R12 = Heliocentric latitude ( decimal degrees )
R13 = Radius vector ( AU )

R14 = Elongation ( ° ' " )
R15 = height without parallax correction

• R16 = Longitude of the observer ( ° ' " ) positive East
• R17 = Latitude of the observer ( ° ' " )
• R18 = DeltaT = TT - UT ( 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 )

1°) 4 Subroutines: "L" "K" "Z" "M"

01 LBL "L"
02 102
03 RCL 00
04 6.179973
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 9
60 STO 15
61 RCL 12
62 RCL 13
63 -
64 360
65 STO 08
66 MOD
67 ENTER
68 ENTER
69 LBL 13
70 SIN
71 RCL 10
72 R-D
73 *
74 +
75 DSE 15
76 GTO 13
77 2
78 /
79 1
80 RCL 10
81 +
82 1
83 LASTX
84 -

85 /
86 SQRT
87 P-R
88 LASTX
89 /
90 R-P
91 RDN
92 ST+ X
93 1
94 R^
95 ST+ X
96 COS
97 RCL 10
98 *
99 -
100 RCL 09
101 *
102 RCL 05
103 +
104 X<> 13
105 +
106 RCL 14
107 -
108 COS
109 RCL 11
110 LASTX
111 SIN
112 P-R
113 X<>Y
114 ASIN
115 RCL 04
116 +
117 STO 12
118 X<> Z
119 R-P
120 CLX
121 RCL 14
122 +
123 RCL 03
124 +
125 RCL 08
126 MOD

127 STO 11
128 LBL "Z"
129 RCL 12
130 RCL 11
131 RCL 13
132 XEQ 07
133 RCL 02
134 ST+ Z
135 CLX
136 RCL 01
137 +
138 XEQ 06
139 STO 05
140 CLX
141 RCL 21
142 +
143 STO 03
144 X<>Y
145 STO 04
146 RCL 05
147 X^2
148 RCL 23
149 X^2
150 STO 08
151 -
152 RCL 13
153 X^2
154 +
155 RCL 05
156 ST+ X
157 /
158 RCL 09
159 1
160 RCL 10
161 X^2
162 -
163 *
164 SQRT
165 RCL 13
166 X^2
167 /
168 RCL 08

169 1/X
170 -
171 *
172 RCL 05
173 RCL 08
174 /
175 +
176 176
177 /
178 ST- 03
179 LBL "M"
180 RCL 20
181 CHS
182 RCL 04
183 RCL 03
184 XEQ 05
185 RCL 05
186 X<> Z
187 HMS
188 STO 07
189 X<>Y
190 15
191 /
192 24
193 MOD
194 HMS
195 STO 06
196 RCL 19
197 X<>Y
198 HMS-
199 HR
200 15
201 *
202 RCL 17
203 HR
204 RCL 07
205 HR
206 90
207 STO 15
208 ST- Z
209 R^
210 -

211 XEQ 05
212 RCL 15
213 +
214 CHS
215 360
216 MOD
217 HMS
218 STO 08
219 X<>Y
220 HMS
221 STO 15
222 LASTX
223 ENTER
224 COS
225 RCL 05
226 23455
227 *
228 /
229 ASIN
230 -
231 HMS
232 STO 09
233 LASTX
234 17.964
235 RCL Y
236 6.6
237 +
238 /
239 +
240 5.267
241 X<>Y
242 /
243 +
244 TAN
245 61.921
246 *
247 1/X
248 +
249 HMS
250 STO 10
251 RCL 03
252 RCL 22

253 -
254 COS
255 RCL 04
256 COS
257 *
258 ACOS
259 HMS
260 STO 14
261 X<>Y
262 RCL 09
263 RCL 08
264 RTN
265 LBL 05
266 1
267 XEQ 07
268 RDN
269 R-P
270 X<> Z
271 ST- Y
272 X<> Z
273 P-R
274 R^
275 XEQ 06
276 RDN
277 RTN
278 LBL 06
279 R-P
280 X<>Y
281 RDN
282 R-P
283 R^
284 X<>Y
285 RTN
286 LBL 07
287 X<>Y
288 RDN
289 P-R
290 R^
291 X<>Y
292 P-R
293 END

( 401 bytes / SIZE 024 )

Notes:

-The refraction uses a formula for a latitude of about 48°41' , temperature = 10°C , pressure = 1010 mbar and humidity = 8 mbar
-Lines 234 to 249 may be replaced by another formula ( cf for example "Astronomical Refraction for the HP41" paragraph 1°) )

2°) Local Sidereal Time - Sun - Moon - Mercury - Venus - Mars

01 LBL "TS"
02 DEG
03 HR
04 X<>Y
05 ENTER
06 INT
07 ST- Y
08 X<>Y
09 E2
10 *
11 ENTER
12 INT
13 STO 00
14 -
15 E2
16 *
17 X<> 00
18 1
19 E^X
20 -
21 12
22 /
23 +
24 INT
25 ST- 00
26 LASTX
27 367
28 *
29 INT
30 ST+ 00
31 SIGN
32 %
33 INT
34 .75
35 ST* Z
36 *
37 X<>Y
38 RCL 00
39 -
40 CHS
41 INT
42 X<>Y
43 -
44 INT
45 730434
46 -
47 24
48 *
49 +
50 2629800
51 /
52 STO 00
53 .023
54 %
55 7200.15401
56 +
57 *
58 6.66452
59 +
60 +
61 23.43928
62 RCL 00
63 .039
64 *
65 -
66 5802
67 RCL 00
68 *
69 125
70 -
71 STO 20
72 COS
73 391
74 /
75 +
76 COS
77 LASTX
78 X<> 20
79 SIN
80 209
81 /
82 STO 21
83 *
84 RCL 16
85 HR
86 +
87 15
88 /
89 +
90 RCL 18
91 3590
92 /
93 -
94 24
95 MOD
96 HMS
97 STO 19
98 RTN
99 LBL "SOL"
100 RCL 00
101 1335801
102 *
103 68
104 -
105 PI
106 P-R
107 STO 03
108 CLX
109 RCL 00
110 98894
111 *
112 67
113 +
114 5
115 LN
116 P-R
117 ST+ 03
118 CLX
119 9
120 LN
121 *
122 -
123 RCL 00
124 61
125 *
126 18
127 -
128 COS
129 3.4
130 *
131 -
132 RCL 00
133 67555
134 *
135 81
136 +
137 STO Z
138 SIN
139 2.3
140 *
141 +
142 X<>Y
143 ST+ X
144 5
145 LN
146 P-R

147 ST+ 03
148 X<> L
149 *
150 -
151 RCL 00
152 197787
153 *
154 48
155 -
156 1
157 P-R
158 ST+ 03
159 CLX
160 RCL 00
161 9105
162 *
163 63
164 -
165 COS
166 +
167 1.3
168 *
169 -
170 RCL 00
171 27113
172 *
173 63
174 +
175 COS
176 +
177 RCL 00
178 101154
179 *
180 61
181 -
182 COS
183 +
184 RCL 00
185 452
186 *
187 63
188 -
189 COS
190 -
191 RCL 00
192 6844
193 *
194 21
195 +
196 COS
197 -
198 RCL 00
199 7
200 *
201 9003
202 +
203 RCL 00
204 *
205 +
206 134500
207 -
208 R-D
209 STO 04
210 1671
211 RCL 00
212 13
213 *
214 -
215 E5
216 ST/ 03
217 ST/ 04
218 /
219 STO 01
220 XEQ 14
221 1
222 P-R
223 RCL 01
224 STO T
225 -
226 R-P
227 RDN
228 ENTER
229 COS
230 CHS
231 R^
232 *
233 1
234 +
235 X<>Y
236 2
237 /
238 TAN
239 1
240 ST- 01
241 R^
242 +
243 RCL 01
244 CHS
245 /
246 SQRT
247 *
248 ATAN
249 ST+ X
250 RCL 04
251 +
252 RCL 03
253 ST+ Z
254 CLX
255 360
256 MOD
257 X<>Y
258 STO 05
259 STO 23
260 X<>Y
261 STO 03
262 X<>Y
263 P-R
264 STO 01
265 X<>Y
266 STO 02
267 CLX
268 STO 04
269 RCL 03
270 176
271 1/X
272 -
273 RCL 21
274 +
275 STO 03
276 STO 22
277 XEQ "M"
278 RTN
279 LBL "LU"
280 XEQ 14
281 STO 08
282 CLX
283 59
284 /
285 CHS
286 1335801.334
287 +
288 *
289 68.245
290 -
291 STO 13
292 ST+ X

293 STO 14
294 CLX
295 .079
296 *
297 1431596.603
298 +
299 *
300 128.431
301 +
302 STO 07
303 ST+ X
304 STO 12
305 CLX
306 30
307 /
308 1449606.053
309 -
310 *
311 86.657
312 -
313 STO 09
314 ST+ X
315 STO 06
316 2574
317 RCL 07
318 COS
319 28
320 *
321 RCL 14
322 RCL 07
323 -
324 STO 03
325 COS
326 5
327 *
328 +
329 RCL 14
330 COS
331 4
332 *
333 +
334 5
335 *
336 -
337 RCL 12
338 COS
339 4
340 *
341 -
342 RCL 14
343 RCL 12
344 -
345 STO 15
346 COS
347 RCL 14
348 RCL 08
349 -
350 STO 11
351 COS
352 -
353 2
354 SQRT
355 *
356 +
357 RCL 07
358 RCL 14
359 +
360 STO 10
361 COS
362 -
363 RCL 03
364 RCL 08
365 -
366 COS
367 -
368 E6
369 /
370 STO 05
371 RCL 07
372 RCL 09
373 -
374 SIN
375 281
376 *
377 RCL 07
378 RCL 09
379 +
380 SIN
381 278
382 *
383 +
384 RCL 14
385 RCL 09
386 +
387 SIN
388 173
389 *
390 +
391 RCL 03
392 RCL 09
393 -
394 SIN
395 55
396 *
397 +
398 RCL 03
399 RCL 09
400 +
401 SIN
402 46
403 *
404 +
405 RCL 14
406 RCL 09
407 -
408 SIN
409 33
410 *
411 +
412 RCL 12
413 RCL 09
414 -
415 SIN
416 17
417 *
418 +
419 RCL 10
420 RCL 09
421 +
422 SIN
423 RCL 12
424 RCL 09
425 +
426 SIN
427 +
428 9
429 *
430 +
431 RCL 11
432 RCL 09
433 +
434 SIN
435 RCL 09
436 SIN
437 641
438 *

439 -
440 8
441 *
442 +
443 RCL 15
444 RCL 09
445 +
446 SIN
447 RCL 10
448 RCL 09
449 -
450 SIN
451 +
452 4
453 *
454 +
455 RCL 14
456 RCL 08
457 +
458 RCL 09
459 +
460 SIN
461 PI
462 *
463 -
464 RCL 11
465 RCL 09
466 -
467 STO 04
468 RCL 07
469 -
470 SIN
471 LASTX
472 RCL 06
473 +
474 SIN
475 +
476 RCL 04
477 SIN
478 +
479 RCL 09
480 RCL 07
481 -
482 STO 04
483 RCL 08
484 +
485 SIN
486 -
487 RCL 04
488 RCL 14
489 ST+ X
490 +
491 SIN
492 +
493 RCL 08
494 RCL 09
495 -
496 SIN
497 -
498 RCL 06
499 RCL 09
500 +
501 SIN
502 +
503 ST+ X
504 +
505 STO 04
506 RCL 07
507 SIN
508 6289
509 *
510 RCL 14
511 SIN
512 658
513 *
514 +
515 RCL 12
516 SIN
517 214
518 *
519 +
520 RCL 06
521 SIN
522 114
523 *
524 +
525 RCL 15
526 SIN
527 59
528 *
529 +
530 RCL 03
531 RCL 08
532 -
533 SIN
534 57
535 *
536 +
537 RCL 10
538 SIN
539 53
540 *
541 +
542 RCL 11
543 SIN
544 46
545 *
546 +
547 RCL 08
548 RCL 07
549 -
550 SIN
551 41
552 *
553 -
554 RCL 03
555 SIN
556 98
557 *
558 RCL 07
559 RCL 06
560 -
561 SIN
562 -
563 13
564 *
565 +
566 RCL 07
567 RCL 06
568 +
569 SIN
570 RCL 14
571 ST+ X
572 RCL 07
573 -
574 SIN
575 +
576 11
577 *
578 +
579 RCL 03
580 ST+ X
581 SIN
582 9
583 *
584 +

585 RCL 03
586 RCL 08
587 +
588 SIN
589 8
590 *
591 -
592 RCL 14
593 RCL 08
594 +
595 SIN
596 7
597 *
598 -
599 RCL 08
600 SIN
601 RCL 00
602 .3
603 *
604 37
605 -
606 *
607 RCL 13
608 SIN
609 7
610 *
611 -
612 RCL 07
613 RCL 08
614 +
615 SIN
616 6
617 *
618 -
619 RCL 14
620 RCL 06
621 +
622 SIN
623 3
624 *
625 +
626 RCL 07
627 RCL 12
628 +
629 SIN
630 ST+ X
631 +
632 RCL 13
633 RCL 07
634 -
635 SIN
636 -
637 RCL 13
638 RCL 08
639 +
640 SIN
641 +
642 5
643 *
644 +
645 RCL 10
646 RCL 08
647 -
648 SIN
649 RCL 14
650 RCL 12
651 +
652 SIN
653 +
654 RCL 14
655 ST+ X
656 SIN
657 +
658 RCL 03
659 RCL 12
660 -
661 SIN
662 +
663 RCL 00
664 7
665 *
666 1
667 -
668 R-D
669 SIN
670 -
671 4
672 *
673 +
674 RCL 08
675 RCL 12
676 -
677 SIN
678 RCL 03
679 RCL 06
680 -
681 SIN
682 +
683 3
684 *
685 -
686 RCL 11
687 RCL 08
688 -
689 SIN
690 LASTX
691 RCL 07
692 -
693 SIN
694 +
695 RCL 11
696 RCL 12
697 -
698 SIN
699 +
700 RCL 13
701 RCL 07
702 +
703 SIN
704 -
705 RCL 12
706 RCL 08
707 +
708 SIN
709 -
710 RCL 08
711 ST+ X
712 SIN
713 -
714 RCL 06
715 RCL 10
716 +
717 SIN
718 -
719 RCL 14
720 RCL 06
721 -
722 SIN
723 -
724 RCL 00
725 14
726 *
727 CHS
728 1443803644
729 +
730 RCL 00

731 *
732 211728
733 +
734 E3
735 /
736 360
737 MOD
738 SIN
739 ST+ X
740 ST- 04
741 X<> L
742 STO 03
743 RCL 09
744 +
745 SIN
746 +
747 ST+ X
748 +
749 E3
750 ST/ 04
751 /
752 RCL 21
753 +
754 ST+ 03
755 XEQ "M"
756 RTN
757 LBL "ME"
758 RCL 00
759 19069
760 *
761 SIN
762 ST+ X
763 CHS
764 STO 03
765 CLX
766 STO 04
767 STO 05
768 .3871
769 STO 09
770 RCL 00
771 448422216
772 RCL 00
773 367
774 /
775 +
776 *
777 250205
778 +
779 STO 12
780 CLX
781 5
782 *
783 7005
784 +
785 STO 11
786 CLX
787 6
788 *
789 20563
790 +
791 STO 10
792 CLX
793 7
794 SQRT
795 *
796 4669
797 +
798 *
799 77456
800 +
801 STO 13
802 CLX
803 2
804 SQRT
805 *
806 3558
807 +
808 *
809 48331
810 XEQ "K"
811 RTN
812 LBL "VE"
813 RCL 00
814 67555
815 *
816 81
817 +
818 STO 03
819 3
820 *
821 SIN
822 ST+ X
823 RCL 03
824 ST+ X
825 SIN
826 PI
827 *
828 -
829 RCL 03
830 SIN
831 2
832 SQRT
833 *
834 -
835 STO 03
836 CLX
837 STO 04
838 STO 05
839 .72333
840 STO 09
841 RCL 00
842 175557639
843 RCL 00
844 8
845 SQRT
846 *
847 +
848 *
849 181178
850 +
851 STO 12
852 CLX
853 14
854 *
855 CHS
856 677
857 +
858 STO 10
859 CLX
860 3
861 *
862 3395
863 +
864 STO 11
865 CLX
866 10
867 *
868 CHS
869 4206
870 +
871 *
872 131564
873 +
874 STO 13
875 CLX
876 4
877 *

878 2703
879 +
880 *
881 76680
882 XEQ "K"
883 RTN
884 LBL "MA"
885 XEQ "L"
886 RCL 15
887 2215
888 *
889 71
890 -
891 COS
892 RCL 15
893 9301
894 *
895 STO 05
896 COS
897 +
898 RCL 05
899 RCL 11
900 -
901 37
902 +
903 COS
904 +
905 2
906 SQRT
907 *
908 RCL 11
909 28
910 *
911 49
912 +
913 COS
914 RCL 03
915 264
916 *
917 STO 05
918 13
919 +
920 COS
921 +
922 RCL 15
923 7077
924 *
925 ST- 05
926 SIN
927 -
928 ST+ X
929 +
930 RCL 09
931 22
932 *
933 RCL 03
934 +
935 ST+ 06
936 12
937 -
938 COS
939 6
940 *
941 -
942 RCL 05
943 21
944 +
945 COS
946 RCL 06
947 ST+ X
948 11
949 +
950 COS
951 -
952 4
953 *
954 +
955 RCL 06
956 48
957 +
958 COS
959 7
960 *
961 +
962 RCL 15
963 10
964 *
965 18
966 -
967 COS
968 15
969 *
970 +
971 STO 03
972 CLX
973 STO 04
974 STO 05
975 1.5237
976 STO 09
977 RCL 00
978 57425089
979 RCL 00
980 8
981 SQRT
982 *
983 +
984 *
985 4830
986 -
987 STO 12
988 CLX
989 27
990 *
991 9340
992 +
993 STO 10
994 RDN
995 ST+ X
996 CHS
997 1850
998 +
999 STO 11
1000 CLX
1001 5523
1002 +
1003 *
1004 23940
1005 -
1006 STO 13
1007 CLX
1008 2316
1009 *
1010 49558
1011 XEQ "K"
1012 RTN
1013 GTO "JU"
1014 LBL 14
1015 RCL 00
1016 107997.151
1017 RCL 00
1018 722
1019 /
1020 -
1021 *
1022 2.964
1023 -
1024 END

( 1528 bytes / SIZE 024 )

3°) Jupiter - Saturn - Uranus - Neptune - Pluto

01 LBL "JU"
02 XEQ "L"
03 RCL 06
04 RCL 11
05 -
06 STO 15
07 23
08 -
09 COS
10 RCL 11
11 32
12 -
13 COS
14 12
15 *
16 +
17 RCL 00
18 *
19 RCL 06
20 39
21 -
22 COS
23 2
24 SQRT
25 *
26 +
27 RCL 07
28 ST+ X
29 67
30 +
31 COS
32 ST+ X
33 -
34 RCL 04
35 RCL 05
36 +
37 SIN
38 RCL 14
39 3
40 *
41 76
42 +
43 COS
44 +
45 RCL 11
46 ST+ X
47 75
48 +
49 COS
50 +
51 RCL 06
52 RCL 15
53 +
54 30
55 -
56 SIN
57 +
58 RCL 06
59 RCL 10
60 +
61 11
62 -
63 SIN
64 +
65 3
66 *
67 +
68 RCL 07
69 COS
70 RCL 09
71 RCL 10
72 +
73 69
74 -
75 COS
76 +
77 4
78 *
79 +
80 RCL 09
81 ST+ X
82 65
83 -
84 SIN
85 RCL 08
86 RCL 10
87 +
88 62
89 -
90 SIN
91 +
92 5
93 *
94 +
95 RCL 06
96 RCL 11
97 +
98 STO 04
99 12
100 +
101 SIN
102 16
103 *
104 -
105 RCL 08
106 73
107 +
108 COS
109 22
110 *
111 +
112 RCL 10
113 RCL 07
114 -
115 41
116 +
117 SIN
118 23
119 *
120 -
121 RCL 09
122 75
123 -
124 SIN
125 37
126 *
127 +
128 RCL 15
129 61
130 -
131 SIN
132 42
133 *
134 +
135 RCL 10
136 33
137 -
138 SIN
139 56
140 *
141 +
142 RCL 11
143 7.3
144 -
145 SIN
146 329
147 *
148 -
149 STO 03
150 RCL 04

151 18
152 +
153 COS
154 4
155 *
156 RCL 15
157 63
158 -
159 SIN
160 5
161 *
162 +
163 STO 04
164 RCL 15
165 29
166 +
167 SIN
168 ST+ X
169 RCL 10
170 57
171 +
172 SIN
173 3
174 *
175 +
176 CHS
177 STO 05
178 5.203
179 STO 09
180 RCL 00
181 1303
182 RCL 00
183 16
184 *
185 -
186 STO 11
187 RDN
188 ST+ X
189 9108908
190 +
191 *
192 34310
193 +
194 STO 12
195 CLX
196 49
197 *
198 4849
199 +
200 STO 10
201 CLX
202 9
203 *
204 4838
205 +
206 *
207 14331
208 +
209 STO 13
210 CLX
211 4
212 *
213 3063
214 +
215 *
216 100464
217 XEQ "K"
218 RTN
219 LBL "SA"
220 XEQ "L"
221 RCL 11
222 41
223 +
224 COS
225 RCL 00
226 *
227 RCL 09
228 COS
229 RCL 07
230 RCL 11
231 +
232 4
233 -
234 SIN
235 -
236 ST+ X
237 +
238 RCL 09
239 ST+ X
240 27
241 -
242 COS
243 6
244 *
245 -
246 RCL 11
247 32
248 -
249 COS
250 30
251 *
252 -
253 RCL 00
254 *
255 RCL 09
256 RCL 11
257 -
258 56
259 +
260 COS
261 RCL 08
262 RCL 10
263 +
264 44
265 +
266 COS
267 +
268 RCL 07
269 RCL 12
270 -
271 STO 14
272 ST+ 14
273 COS
274 -
275 RCL 14
276 RCL 15
277 +
278 78
279 -
280 COS
281 +
282 RCL 12
283 RCL 03
284 -
285 39
286 +
287 SIN
288 -
289 ST+ X
290 +
291 RCL 07
292 RCL 11
293 ST+ X
294 STO 13
295 -
296 36
297 +
298 COS
299 RCL 10
300 RCL 07

301 -
302 STO 05
303 RCL 13
304 +
305 STO 04
306 COS
307 -
308 RCL 15
309 7
310 *
311 28
312 -
313 SIN
314 +
315 RCL 07
316 59
317 +
318 COS
319 -
320 RCL 06
321 14
322 +
323 COS
324 +
325 PI
326 *
327 +
328 RCL 14
329 11
330 +
331 SIN
332 RCL 07
333 RCL 03
334 -
335 COS
336 +
337 6
338 *
339 -
340 RCL 03
341 21
342 -
343 COS
344 RCL 13
345 15
346 -
347 SIN
348 +
349 RCL 03
350 RCL 11
351 -
352 SIN
353 -
354 RCL 08
355 30
356 -
357 COS
358 +
359 8
360 *
361 +
362 RCL 10
363 54
364 +
365 COS
366 RCL 05
367 25
368 +
369 COS
370 +
371 9
372 *
373 +
374 RCL 09
375 RCL 11
376 +
377 STO 06
378 2
379 -
380 SIN
381 14
382 *
383 +
384 RCL 07
385 RCL 11
386 +
387 STO 14
388 50
389 -
390 SIN
391 45
392 *
393 +
394 RCL 09
395 14
396 +
397 COS
398 118
399 *
400 +
401 RCL 07
402 RCL 11
403 -
404 30
405 +
406 COS
407 228
408 *
409 +
410 RCL 11
411 7.3
412 -
413 SIN
414 810
415 *
416 +
417 STO 03
418 RCL 06
419 76
420 -
421 COS
422 RCL 08
423 48
424 -
425 COS
426 +
427 3
428 *
429 RCL 04
430 67
431 +
432 SIN
433 ST+ X
434 -
435 RCL 11
436 SIN
437 4
438 *
439 +
440 RCL 09
441 ST+ X
442 STO 13
443 46
444 +
445 SIN
446 RCL 00
447 *
448 -
449 RCL 05
450 28

451 -
452 COS
453 6
454 *
455 +
456 RCL 14
457 20
458 +
459 COS
460 18
461 *
462 -
463 RCL 13
464 33
465 +
466 COS
467 20
468 *
469 +
470 STO 04
471 RCL 09
472 73
473 -
474 COS
475 6
476 *
477 RCL 11
478 COS
479 RCL 14
480 50
481 -
482 COS
483 +
484 4
485 *
486 -
487 RCL 08
488 20
489 -
490 COS
491 8
492 *
493 +
494 RCL 13
495 60
496 -
497 COS
498 19
499 *
500 +
501 12
502 -
503 STO 05
504 9.555
505 STO 09
506 RCL 00
507 3670533
508 RCL 00
509 22
510 SQRT
511 *
512 +
513 *
514 50061
515 +
516 STO 12
517 CLX
518 104
519 *
520 CHS
521 5551
522 +
523 STO 10
524 CLX
525 11
526 *
527 CHS
528 2489
529 +
530 STO 11
531 CLX
532 8
533 *
534 5891
535 +
536 *
537 93057
538 +
539 STO 13
540 RDN
541 CHS
542 2631
543 +
544 *
545 113665
546 XEQ "K"
547 RTN
548 LBL "UR"
549 XEQ "L"
550 RCL 12
551 RCL 03
552 -
553 65
554 +
555 COS
556 RCL 03
557 44
558 +
559 COS
560 +
561 6
562 SQRT
563 *
564 RCL 12
565 RCL 05
566 -
567 21
568 +
569 COS
570 3
571 *
572 +
573 RCL 05
574 52
575 -
576 COS
577 8
578 *
579 +
580 RCL 00
581 *
582 RCL 03
583 RCL 05
584 -
585 SIN
586 RCL 03
587 RCL 12
588 +
589 59
590 -
591 COS
592 +
593 RCL 04
594 RCL 12
595 +
596 SIN
597 +
598 RCL 14
599 ST+ X
600 STO 11

601 ST+ X
602 STO 15
603 46
604 -
605 COS
606 +
607 RCL 15
608 RCL 04
609 -
610 50
611 -
612 COS
613 -
614 RCL 12
615 65
616 +
617 COS
618 +
619 ST+ X
620 +
621 RCL 11
622 RCL 04
623 -
624 63
625 -
626 SIN
627 PI
628 *
629 +
630 RCL 11
631 RCL 14
632 +
633 60
634 -
635 COS
636 4
637 *
638 +
639 RCL 14
640 RCL 05
641 -
642 78
643 +
644 SIN
645 5
646 *
647 -
648 RCL 09
649 RCL 14
650 +
651 RCL 05
652 -
653 STO 10
654 28
655 +
656 COS
657 6
658 *
659 +
660 RCL 04
661 RCL 05
662 +
663 80
664 -
665 COS
666 7
667 *
668 +
669 RCL 14
670 10
671 +
672 SIN
673 10
674 *
675 -
676 RCL 11
677 RCL 12
678 +
679 20
680 -
681 SIN
682 12
683 *
684 +
685 RCL 06
686 RCL 12
687 -
688 10
689 -
690 COS
691 RCL 12
692 RCL 04
693 -
694 COS
695 -
696 15
697 *
698 +
699 RCL 03
700 73
701 +
702 SIN
703 RCL 04
704 39
705 +
706 SIN
707 +
708 35
709 *
710 -
711 RCL 05
712 RCL 12
713 +
714 STO 07
715 11
716 -
717 COS
718 39
719 *
720 +
721 RCL 12
722 RCL 03
723 -
724 STO 15
725 51
726 -
727 COS
728 40
729 *
730 +
731 RCL 11
732 19
733 +
734 SIN
735 209
736 *
737 -
738 RCL 05
739 62.2
740 -
741 SIN
742 858
743 *
744 +
745 STO 03
746 RCL 11
747 33
748 +
749 COS
750 RCL 07

751 SIN
752 -
753 6
754 *
755 RCL 05
756 39
757 +
758 SIN
759 ST+ X
760 -
761 STO 04
762 RCL 06
763 RCL 12
764 -
765 80
766 +
767 COS
768 5
769 *
770 RCL 10
771 SIN
772 PI
773 *
774 -
775 RCL 11
776 RCL 05
777 -
778 SIN
779 ST+ X
780 -
781 RCL 07
782 11
783 -
784 SIN
785 RCL 15
786 49
787 -
788 SIN
789 +
790 6
791 *
792 +
793 RCL 11
794 19
795 +
796 COS
797 34
798 *
799 +
800 26
801 -
802 STO 05
803 19.218
804 STO 09
805 RCL 00
806 1289593
807 RCL 00
808 7
809 SQRT
810 *
811 +
812 *
813 45955
814 -
815 STO 12
816 RDN
817 ST+ X
818 773
819 +
820 STO 11
821 CLX
822 8
823 *
824 CHS
825 4630
826 +
827 STO 10
828 RDN
829 ST+ X
830 4459
831 +
832 *
833 172993
834 +
835 STO 13
836 CLX
837 12
838 *
839 1563
840 +
841 *
842 74005
843 XEQ "K"
844 RTN
845 LBL "NE"
846 XEQ "L"
847 RCL 05
848 38
849 +
850 SIN
851 5
852 *
853 CHS
854 RCL 00
855 *
856 RCL 07
857 RCL 13
858 -
859 STO 10
860 16
861 +
862 COS
863 RCL 05
864 RCL 13
865 +
866 77
867 -
868 COS
869 +
870 5
871 *
872 +
873 RCL 06
874 RCL 13
875 -
876 STO 08
877 COS
878 9
879 *
880 +
881 RCL 14
882 RCL 05
883 -
884 STO 09
885 11
886 -
887 COS
888 22
889 *
890 +
891 RCL 04
892 50
893 -
894 COS
895 24
896 *
897 +
898 RCL 14
899 7
900 +

901 SIN
902 71
903 *
904 +
905 RCL 05
906 27.8
907 +
908 COS
909 584
910 *
911 +
912 STO 03
913 RCL 04
914 RCL 14
915 +
916 69
917 -
918 SIN
919 RCL 14
920 54
921 +
922 SIN
923 -
924 9
925 *
926 STO 04
927 RCL 09
928 11
929 -
930 SIN
931 RCL 08
932 SIN
933 -
934 5
935 *
936 RCL 10
937 16
938 +
939 SIN
940 3
941 *
942 -
943 RCL 05
944 63
945 -
946 COS
947 8
948 *
949 +
950 RCL 14
951 6
952 +
953 COS
954 17
955 *
956 -
957 41
958 -
959 STO 05
960 30.11
961 STO 09
962 RCL 00
963 1770
964 RCL 00
965 28
966 *
967 -
968 STO 11
969 RDN
970 ST+ X
971 899
972 +
973 STO 10
974 CLX
975 8
976 SQRT
977 *
978 659648
979 +
980 *
981 55654
982 -
983 STO 12
984 CLX
985 PI
986 *
987 4278
988 +
989 *
990 48124
991 +
992 STO 13
993 RDN
994 ST+ X
995 3306
996 +
997 *
998 131784
999 XEQ "K"
1000 RTN
1001 LBL "PL"
1002 RCL 00
1003 8669
1004 *
1005 65
1006 +
1007 COS
1008 7
1009 *
1010 RCL 00
1011 3231
1012 *
1013 76
1014 +
1015 COS
1016 4
1017 *
1018 +
1019 STO 03
1020 RCL 00
1021 26
1022 *
1023 4
1024 -
1025 STO 04
1026 RCL 00
1027 6
1028 *
1029 STO 05
1030 39.489
1031 STO 09
1032 24900
1033 STO 10
1034 17140
1035 STO 11
1036 439701
1037 RCL 00
1038 *
1039 238927
1040 +
1041 STO 12
1042 RCL 00
1043 4191
1044 *
1045 135925
1046 -
1047 STO 13
1048 246232
1049 XEQ "K"
1050 END

( 1448 bytes / SIZE 024 )

4°) Numerical Examples

LOCAL SIDEREAL TIME:

STACK	INPUTS	OUTPUTS
Y	YYYY.MNDD	/
X	hh.mnss (TT)	HH.MNSS (LST)

-Suppose we are at the US Naval Observatory at Washington ( D.C. ) on 2021/07/16 7h41m TT , assuming TT-UT1 = 69.3 seconds

•       Longitude = 77°03'56" W = -77.0356   STO 16
•       Latitude = 38°55'17" N = +38.5517   STO 17
•              DELTA T = TT - UT =   69.3 s     STO 18

2021.0716 ENTER^
7.41 XEQ "TS" >>>> 22h09m03s = R19

-We also have obliquity of the ecliptic = R20 = 23°4374
and nutation in longitude = R21 = -0°0044

Note:

-Cf reference [5] for accurate TT-UT1 values

THE SUN - THE MOON - THE PLANETS

STACK	INPUT	OUTPUTS
T	/	Elg = elongation from the Sun ( ° ' " )
Z	/	h₀ = apparent altitude ( ° ' '' )
Y	/	h = true altitude ( ° ' '' )
X	/	Az = Azimuth ( ° ' '' )

THE SUN

>>> After executing "TS" simply press R/S ( or XEQ "SOL" )

Az = 36°13'56" = R08 ---Execution time = 31s---
RDN h = -20°49'04" = R09
RDN h₀ = -20°51'35" = R10 ( often meaningless when < 0 )
RDN Elg = 0 = R14

and R01 = X = -0.41365 AU
R02 = Y = 0.92842 AU

R03 = 114.°005 = Geocentric longitude = R22 R06 = 7h43m34s = right-ascension
R04 = 0 = Geocentric latitude R07 = 21°18'21" = declination
R05 = 1.01640 AU = distance Earth-Sun

Note:

-Always execute "SOL" before the planets to get the correct geocentric coordinates.

THE MOON

R/S or XEQ "LU" >>>> Az = 308°32'40" ---Execution time = 71s---
   RDN h = -38°06'43"
   RDN h₀ = -38°07'56" ( often meaningless when < 0 )
   RDN Elg = 75°47'15"

R03 = 189°748 = Geocentric longitude R06 = 12h42m51s = right-ascension
R04 = 4°471 = Geocentric latitude R07 = 0°15'04" = declination
R05 = 0.002514 AU = distance Earth-Moon

MERCURY

R/S or XEQ "ME" >>>>    Az = 49°53'15"        ---Execution time = 36s---
   RDN h = -9°59'43"
   RDN h₀ = -10°05'02" ( often meaningless when < 0 )
   RDN Elg = 17°01'19"

R03 = 96°995 = Geocentric longitude R06 = 6h30m19s = right-ascension R11 = 30°834 = heliocentric longitude
R04 = -0°632 = Geocentric latitude R07 = 22°37'16" = declination R12 = -2°146 = heliocentric latitude
R05 = 1.10329 AU = distance Earth-Mercury R13 = 0.32520 AU = radius vector

VENUS

R/S or XEQ "VE"    >>>> Az = 7°22'60"        ---Execution time = 37s---
   RDN h = -35°25'17"
   RDN h₀ = -35°26'39" ( often meaningless when < 0 )
   RDN Elg = 29°10'22"

R03 = 143°136 = Geocentric longitude    R06 = 9h44m07s = right-ascension    R11 = 186°615 = heliocentric longitude
R04 = 29°102 = Geocentric latitude R07 = 15°20'46" = declination     R12 = 3°196 = heliocentric latitude
R05 = 1.4105 AU = distance Earth-Venus    R13 = 0.7205 AU = radius vector

MARS

R/S or XEQ "MA" >>>>    Az =    9°23'49"        ---Execution time = 46s---
   RDN h = -35°08'14"
   RDN h₀ = -35°09'36" ( often meaningless when < 0 )
   RDN Elg = 27°33'01"

R03 = 141°532 = Geocentric longitude    R06 = 9h37m12s = right-ascension          R11 = 157°933 = heliocentric longitude
R04 = 1°171 = Geocentric latitude R07 = 15°26'03" = declination R12 = 1°757 = heliocentric latitude
R05 = 2.4994 AU = distance Earth-Mars       R13 = 1.6660 AU = radius vector

JUPITER

R/S or XEQ "JU" >>>>    Az = 178°21'22"        ---Execution time = 56s---
   RDN h = 38°59'22"
   RDN h₀ = 39°00'33"
   RDN Elg = 142°51'01"

R03 = -28°859 = Geocentric longitude    R06 = 22h14m16s = right-ascension       R11 = 324°143 = heliocentric longitude
R04 = -1°077 = Geocentric latitude    R07 = -12°04'27" = declination R12 = -0°895 = heliocentric latitude
R05 = 4.187 AU = distance Earth-Jupiter       R13 = 5.034 AU = radius vector

SATURN

R/S or XEQ "SA" >>>> Az = 200°07'44"     ---Execution time = 69s---
   RDN h = 30°30'59"
   RDN h₀ = 30°32'37"
   RDN Elg = 162°34'26"

R03 = -48°585 = Geocentric longitude    R06 = 20h56m22s = right-ascension       R11 = 309°666 = heliocentric longitude
R04 = -0°751 = Geocentric latitude    R07 = -18°04'35" = declination R12 = -0°677 = heliocentric latitude
R05 = 8.977 AU = distance Earth-Saturn             R13 = 9.952 AU = radius vector

URANUS

R/S or XEQ "UR" >>>> Az = 89°54'58"        ---Execution time = 64s---
RDN h = 25°28'32"
    RDN h₀ = 25°30'33"
    RDN Elg = 69°42'06"

R03 = 44°304 = Geocentric longitude       R06 = 2h47m53s = right-ascension       R11 = 41°544 = heliocentric longitude
R04 = -0°409 = Geocentric latitude       R07 = 15°44'21" = declination R12 = -0°416 = heliocentric latitude
R05 = 20.074 AU = distance Earth-Uranus             R13 = 19.745 AU = radius vector

NEPTUNE

R/S or XEQ "NE" >>>> Az = 149°36'56"     ---Execution time = 49s---
   RDN h = 42°46'04"
   RDN h₀ = 42°47'07"
   RDN Elg = 120°54'23"

R03 = -6°908 = Geocentric longitude       R06 = 23h36m26s = right-ascension       R11 = 351°424 = heliocentric longitude
R04 = -1°141 = Geocentric latitude       R07 = -3°47'23" = declination    R12 = -1°120 = heliocentric latitude
R05 = 29.390 AU = distance Earth-Neptune             R13 = 29.925 AU = radius vector

PLUTO

R/S or XEQ "PL" >>>> Az = 213°50'52"     ---Execution time = 37s---
   RDN h = 20°36'25"
   RDN h₀ = 20°38'57"
   RDN Elg = 177°45'36"

R03 = -64°397 = Geocentric longitude       R06 = 19h51m34s = right-ascension       R11 = 295°556 = heliocentric longitude
R04 = -1°570 = Geocentric latitude       R07 = -22°33'45" = declination    R12 = -1°523 = heliocentric latitude
R05 = 33.300 AU = distance Earth-Pluto                R13 = 34.316 AU = radius vector

REMARK:

-Actually, there is no XEQ "Z" in these programs
-But if you store the heliocentric longitude, latitude & the radius vector into R11-R12-R13 and the semi-major axis & the eccentricity into R09 & R10, you can call "Z" to get the geocentric coordinates.
-For example, with Sedna:

01 LBL "SD"
02 506
03 STO 09
04 .8496
05 STO 10
06 RCL 00
07 3
08 *
09 457
10 RCL Y
11 1085
12 *

13 +
14 *
15 3844
16 -
17 *
18 5222
19 -
20 *
21 2029
22 +
23 *
24 20363

25 +
26 *
27 54245
28 +
29 *
30 45874
31 +
32 STO 11
33 CLX
34 647
35 *
36 1139

37 +
38 *
39 CHS
40 752
41 +
42 *
43 3874
44 +
45 *
46 4365
47 +
48 *

49 1573
50 -
51 *
52 11803
53 -
54 STO 12
55 CLX
56 775
57 *
58 1127
59 +
60 *

61 CHS
62 1819
63 +
64 *
65 8084
66 +
67 *
68 13210
69 +
70 *
71 34295

72 -
73 *
74 90898
75 +
76 E3
77 ST/ 11
78 ST/ 12
79 /
80 STO 13
81 XEQ "Z"
82 END

( 170 bytes )

SEDNA

R/S or XEQ "SD" >>>> Az = 85°11'38"     ---Execution time = 24s---
   RDN h = 7°26'52"
   RDN h₀ = 7°33'43"
   RDN Elg = 55°46'24"

R03 = 59°080 = Geocentric longitude       R06 = 3h57m46s = right-ascension       R11 = 58°510 = heliocentric longitude
R04 = -11°819 = Geocentric latitude         R07 = 8°23'57" = declination       R12 = -11°900 = heliocentric latitude
R05 = 84.775 AU = distance Earth-Sedna                R13 = 84.208 AU = radius vector

5°) A Single Program

-This ( very long ) program may be used with free42 or DM42...
-Unfortunately, not enough room with an HP41

01 LBL "EPH"
02 DEG
03 HR
04 X<>Y
05 ENTER
06 INT
07 ST- Y
08 X<>Y
09 E2
10 *
11 ENTER
12 INT
13 STO 00
14 -
15 E2
16 *
17 X<> 00
18 1
19 E^X
20 -
21 12
22 /
23 +
24 INT
25 ST- 00
26 LASTX
27 367
28 *
29 INT
30 ST+ 00
31 SIGN
32 %
33 INT
34 .75
35 ST* Z
36 *
37 X<>Y
38 RCL 00
39 -
40 CHS
41 INT
42 X<>Y
43 -
44 INT
45 730434
46 -
47 24
48 *
49 +
50 2629800
51 /
52 STO 00
53 .023
54 %
55 7200.15401
56 +
57 *
58 6.66452
59 +
60 +
61 23.43928
62 RCL 00
63 .039
64 *
65 -
66 5802
67 RCL 00
68 *
69 125
70 -
71 STO 20
72 COS
73 391
74 /
75 +
76 COS
77 LASTX
78 X<> 20
79 SIN
80 209
81 /
82 STO 21
83 *
84 RCL 16
85 HR
86 +
87 15
88 /
89 +
90 RCL 18
91 3590
92 /
93 -
94 24
95 MOD
96 HMS
97 STO 19
98 RCL 00
99 1335801
100 *
101 68
102 -
103 PI
104 P-R
105 STO 03
106 CLX
107 RCL 00
108 98894
109 *
110 67
111 +
112 5
113 LN
114 P-R
115 ST+ 03
116 CLX
117 9
118 LN
119 *
120 -
121 RCL 00
122 61
123 *
124 18
125 -
126 COS
127 3.4
128 *
129 -
130 RCL 00
131 67555
132 *
133 81
134 +
135 STO Z
136 SIN
137 2.3
138 *
139 +
140 X<>Y
141 ST+ X
142 5
143 LN
144 P-R
145 ST+ 03
146 X<> L
147 *
148 -
149 RCL 00
150 197787
151 *
152 48
153 -
154 1
155 P-R
156 ST+ 03
157 CLX
158 RCL 00
159 9105
160 *
161 63
162 -
163 COS
164 +
165 1.3
166 *
167 -
168 RCL 00
169 27113
170 *
171 63
172 +
173 COS
174 +
175 RCL 00
176 101154
177 *
178 61
179 -
180 COS
181 +
182 RCL 00
183 452
184 *
185 63
186 -
187 COS
188 -
189 RCL 00
190 6844
191 *
192 21
193 +
194 COS
195 -
196 RCL 00
197 7
198 *
199 9003
200 +
201 RCL 00
202 *
203 +
204 134500
205 -
206 R-D
207 STO 04
208 1671
209 RCL 00
210 13
211 *
212 -
213 E5
214 ST/ 03
215 ST/ 04
216 /
217 STO 01
218 XEQ 16
219 1
220 P-R
221 RCL 01
222 STO T
223 -
224 R-P
225 RDN
226 ENTER
227 COS
228 CHS
229 R^
230 *
231 1
232 +
233 X<>Y
234 2
235 /
236 TAN
237 1
238 ST- 01
239 R^
240 +
241 RCL 01
242 CHS
243 /
244 SQRT
245 *
246 ATAN
247 ST+ X
248 RCL 04
249 +
250 RCL 03
251 ST+ Z
252 CLX
253 360
254 MOD
255 X<>Y
256 STO 05
257 STO 23
258 X<>Y
259 STO 03
260 X<>Y
261 P-R
262 STO 01
263 X<>Y
264 STO 02
265 CLX
266 STO 04
267 RCL 03
268 176
269 1/X
270 -
271 RCL 21
272 +
273 STO 03
274 STO 22
275 XEQ 00
276 RTN
277 LBL 03
278 XEQ 16
279 STO 08
280 CLX
281 59
282 /
283 CHS
284 1335801.334
285 +
286 *
287 68.245
288 -
289 STO 13
290 ST+ X
291 STO 14
292 CLX
293 .079
294 *
295 1431596.603
296 +
297 *
298 128.431
299 +
300 STO 07
301 ST+ X
302 STO 12
303 CLX
304 30
305 /
306 1449606.053
307 -
308 *
309 86.657
310 -
311 STO 09
312 ST+ X
313 STO 06
314 2574
315 RCL 07
316 COS
317 28
318 *
319 RCL 14
320 RCL 07
321 -
322 STO 03
323 COS
324 5
325 *
326 +
327 RCL 14
328 COS
329 4
330 *
331 +
332 5
333 *
334 -
335 RCL 12
336 COS
337 4
338 *

339 -
340 RCL 14
341 RCL 12
342 -
343 STO 15
344 COS
345 RCL 14
346 RCL 08
347 -
348 STO 11
349 COS
350 -
351 2
352 SQRT
353 *
354 +
355 RCL 07
356 RCL 14
357 +
358 STO 10
359 COS
360 -
361 RCL 03
362 RCL 08
363 -
364 COS
365 -
366 E6
367 /
368 STO 05
369 RCL 07
370 RCL 09
371 -
372 SIN
373 281
374 *
375 RCL 07
376 RCL 09
377 +
378 SIN
379 278
380 *
381 +
382 RCL 14
383 RCL 09
384 +
385 SIN
386 173
387 *
388 +
389 RCL 03
390 RCL 09
391 -
392 SIN
393 55
394 *
395 +
396 RCL 03
397 RCL 09
398 +
399 SIN
400 46
401 *
402 +
403 RCL 14
404 RCL 09
405 -
406 SIN
407 33
408 *
409 +
410 RCL 12
411 RCL 09
412 -
413 SIN
414 17
415 *
416 +
417 RCL 10
418 RCL 09
419 +
420 SIN
421 RCL 12
422 RCL 09
423 +
424 SIN
425 +
426 9
427 *
428 +
429 RCL 11
430 RCL 09
431 +
432 SIN
433 RCL 09
434 SIN
435 641
436 *
437 -
438 8
439 *
440 +
441 RCL 15
442 RCL 09
443 +
444 SIN
445 RCL 10
446 RCL 09
447 -
448 SIN
449 +
450 4
451 *
452 +
453 RCL 14
454 RCL 08
455 +
456 RCL 09
457 +
458 SIN
459 PI
460 *
461 -
462 RCL 11
463 RCL 09
464 -
465 STO 04
466 RCL 07
467 -
468 SIN
469 LASTX
470 RCL 06
471 +
472 SIN
473 +
474 RCL 04
475 SIN
476 +
477 RCL 09
478 RCL 07
479 -
480 STO 04
481 RCL 08
482 +
483 SIN
484 -
485 RCL 04
486 RCL 14
487 ST+ X
488 +
489 SIN
490 +
491 RCL 08
492 RCL 09
493 -
494 SIN
495 -
496 RCL 06
497 RCL 09
498 +
499 SIN
500 +
501 ST+ X
502 +
503 STO 04
504 RCL 07
505 SIN
506 6289
507 *
508 RCL 14
509 SIN
510 658
511 *
512 +
513 RCL 12
514 SIN
515 214
516 *
517 +
518 RCL 06
519 SIN
520 114
521 *
522 +
523 RCL 15
524 SIN
525 59
526 *
527 +
528 RCL 03
529 RCL 08
530 -
531 SIN
532 57
533 *
534 +
535 RCL 10
536 SIN
537 53
538 *
539 +
540 RCL 11
541 SIN
542 46
543 *
544 +
545 RCL 08
546 RCL 07
547 -
548 SIN
549 41
550 *
551 -
552 RCL 03
553 SIN
554 98
555 *
556 RCL 07
557 RCL 06
558 -
559 SIN
560 -
561 13
562 *
563 +
564 RCL 07
565 RCL 06
566 +
567 SIN
568 RCL 14
569 ST+ X
570 RCL 07
571 -
572 SIN
573 +
574 11
575 *
576 +
577 RCL 03
578 ST+ X
579 SIN
580 9
581 *
582 +
583 RCL 03
584 RCL 08
585 +
586 SIN
587 8
588 *
589 -
590 RCL 14
591 RCL 08
592 +
593 SIN
594 7
595 *
596 -
597 RCL 08
598 SIN
599 RCL 00
600 .3
601 *
602 37
603 -
604 *
605 RCL 13
606 SIN
607 7
608 *
609 -
610 RCL 07
611 RCL 08
612 +
613 SIN
614 6
615 *
616 -
617 RCL 14
618 RCL 06
619 +
620 SIN
621 3
622 *
623 +
624 RCL 07
625 RCL 12
626 +
627 SIN
628 ST+ X
629 +
630 RCL 13
631 RCL 07
632 -
633 SIN
634 -
635 RCL 13
636 RCL 08
637 +
638 SIN
639 +
640 5
641 *
642 +
643 RCL 10
644 RCL 08
645 -
646 SIN
647 RCL 14
648 RCL 12
649 +
650 SIN
651 +
652 RCL 14
653 ST+ X
654 SIN
655 +
656 RCL 03
657 RCL 12
658 -
659 SIN
660 +
661 RCL 00
662 7
663 *
664 1
665 -
666 R-D
667 SIN
668 -
669 4
670 *
671 +
672 RCL 08
673 RCL 12
674 -
675 SIN
676 RCL 03

677 RCL 06
678 -
679 SIN
680 +
681 3
682 *
683 -
684 RCL 11
685 RCL 08
686 -
687 SIN
688 LASTX
689 RCL 07
690 -
691 SIN
692 +
693 RCL 11
694 RCL 12
695 -
696 SIN
697 +
698 RCL 13
699 RCL 07
700 +
701 SIN
702 -
703 RCL 12
704 RCL 08
705 +
706 SIN
707 -
708 RCL 08
709 ST+ X
710 SIN
711 -
712 RCL 06
713 RCL 10
714 +
715 SIN
716 -
717 RCL 14
718 RCL 06
719 -
720 SIN
721 -
722 RCL 00
723 14
724 *
725 CHS
726 1443803644
727 +
728 RCL 00
729 *
730 211728
731 +
732 E3
733 /
734 360
735 MOD
736 SIN
737 ST+ X
738 ST- 04
739 X<> L
740 STO 03
741 RCL 09
742 +
743 SIN
744 +
745 ST+ X
746 +
747 E3
748 ST/ 04
749 /
750 RCL 21
751 +
752 ST+ 03
753 XEQ 00
754 RTN
755 LBL 01
756 RCL 00
757 19069
758 *
759 SIN
760 ST+ X
761 CHS
762 STO 03
763 CLX
764 STO 04
765 STO 05
766 .3871
767 STO 09
768 RCL 00
769 448422216
770 RCL 00
771 367
772 /
773 +
774 *
775 250205
776 +
777 STO 12
778 CLX
779 5
780 *
781 7005
782 +
783 STO 11
784 CLX
785 6
786 *
787 20563
788 +
789 STO 10
790 CLX
791 7
792 SQRT
793 *
794 4669
795 +
796 *
797 77456
798 +
799 STO 13
800 CLX
801 2
802 SQRT
803 *
804 3558
805 +
806 *
807 48331
808 XEQ 14
809 RTN
810 LBL 02
811 RCL 00
812 67555
813 *
814 81
815 +
816 STO 03
817 3
818 *
819 SIN
820 ST+ X
821 RCL 03
822 ST+ X
823 SIN
824 PI
825 *
826 -
827 RCL 03
828 SIN
829 2
830 SQRT
831 *
832 -
833 STO 03
834 CLX
835 STO 04
836 STO 05
837 .72333
838 STO 09
839 RCL 00
840 175557639
841 RCL 00
842 8
843 SQRT
844 *
845 +
846 *
847 181178
848 +
849 STO 12
850 CLX
851 14
852 *
853 CHS
854 677
855 +
856 STO 10
857 CLX
858 3
859 *
860 3395
861 +
862 STO 11
863 CLX
864 10
865 *
866 CHS
867 4206
868 +
869 *
870 131564
871 +
872 STO 13
873 CLX
874 4
875 *
876 2703
877 +
878 *
879 76680
880 XEQ 14
881 RTN
882 LBL 04
883 XEQ 12
884 RCL 15
885 2215
886 *
887 71
888 -
889 COS
890 RCL 15
891 9301
892 *
893 STO 05
894 COS
895 +
896 RCL 05
897 RCL 11
898 -
899 37
900 +
901 COS
902 +
903 2
904 SQRT
905 *
906 RCL 11
907 28
908 *
909 49
910 +
911 COS
912 RCL 03
913 264
914 *
915 STO 05
916 13
917 +
918 COS
919 +
920 RCL 15
921 7077
922 *
923 ST- 05
924 SIN
925 -
926 ST+ X
927 +
928 RCL 09
929 22
930 *
931 RCL 03
932 +
933 ST+ 06
934 12
935 -
936 COS
937 6
938 *
939 -
940 RCL 05
941 21
942 +
943 COS
944 RCL 06
945 ST+ X
946 11
947 +
948 COS
949 -
950 4
951 *
952 +
953 RCL 06
954 48
955 +
956 COS
957 7
958 *
959 +
960 RCL 15
961 10
962 *
963 18
964 -
965 COS
966 15
967 *
968 +
969 STO 03
970 CLX
971 STO 04
972 STO 05
973 1.5237
974 STO 09
975 RCL 00
976 57425089
977 RCL 00
978 8
979 SQRT
980 *
981 +
982 *
983 4830
984 -
985 STO 12
986 CLX
987 27
988 *
989 9340
990 +
991 STO 10
992 RDN
993 ST+ X
994 CHS
995 1850
996 +
997 STO 11
998 CLX
999 5523
1000 +
1001 *
1002 23940
1003 -
1004 STO 13
1005 CLX
1006 2316
1007 *
1008 49558
1009 XEQ 14
1010 RTN
1011 LBL 05
1012 XEQ 12
1013 RCL 06
1014 RCL 11

1015 -
1016 STO 15
1017 23
1018 -
1019 COS
1020 RCL 11
1021 32
1022 -
1023 COS
1024 12
1025 *
1026 +
1027 RCL 00
1028 *
1029 RCL 06
1030 39
1031 -
1032 COS
1033 2
1034 SQRT
1035 *
1036 +
1037 RCL 07
1038 ST+ X
1039 67
1040 +
1041 COS
1042 ST+ X
1043 -
1044 RCL 04
1045 RCL 05
1046 +
1047 SIN
1048 RCL 14
1049 3
1050 *
1051 76
1052 +
1053 COS
1054 +
1055 RCL 11
1056 ST+ X
1057 75
1058 +
1059 COS
1060 +
1061 RCL 06
1062 RCL 15
1063 +
1064 30
1065 -
1066 SIN
1067 +
1068 RCL 06
1069 RCL 10
1070 +
1071 11
1072 -
1073 SIN
1074 +
1075 3
1076 *
1077 +
1078 RCL 07
1079 COS
1080 RCL 09
1081 RCL 10
1082 +
1083 69
1084 -
1085 COS
1086 +
1087 4
1088 *
1089 +
1090 RCL 09
1091 ST+ X
1092 65
1093 -
1094 SIN
1095 RCL 08
1096 RCL 10
1097 +
1098 62
1099 -
1100 SIN
1101 +
1102 5
1103 *
1104 +
1105 RCL 06
1106 RCL 11
1107 +
1108 STO 04
1109 12
1110 +
1111 SIN
1112 16
1113 *
1114 -
1115 RCL 08
1116 73
1117 +
1118 COS
1119 22
1120 *
1121 +
1122 RCL 10
1123 RCL 07
1124 -
1125 41
1126 +
1127 SIN
1128 23
1129 *
1130 -
1131 RCL 09
1132 75
1133 -
1134 SIN
1135 37
1136 *
1137 +
1138 RCL 15
1139 61
1140 -
1141 SIN
1142 42
1143 *
1144 +
1145 RCL 10
1146 33
1147 -
1148 SIN
1149 56
1150 *
1151 +
1152 RCL 11
1153 7.3
1154 -
1155 SIN
1156 329
1157 *
1158 -
1159 STO 03
1160 RCL 04
1161 18
1162 +
1163 COS
1164 4
1165 *
1166 RCL 15
1167 63
1168 -
1169 SIN
1170 5
1171 *
1172 +
1173 STO 04
1174 RCL 15
1175 29
1176 +
1177 SIN
1178 ST+ X
1179 RCL 10
1180 57
1181 +
1182 SIN
1183 3
1184 *
1185 +
1186 CHS
1187 STO 05
1188 5.203
1189 STO 09
1190 RCL 00
1191 1303
1192 RCL 00
1193 16
1194 *
1195 -
1196 STO 11
1197 RDN
1198 ST+ X
1199 9108908
1200 +
1201 *
1202 34310
1203 +
1204 STO 12
1205 CLX
1206 49
1207 *
1208 4849
1209 +
1210 STO 10
1211 CLX
1212 9
1213 *
1214 4838
1215 +
1216 *
1217 14331
1218 +
1219 STO 13
1220 CLX
1221 4
1222 *
1223 3063
1224 +
1225 *
1226 100464
1227 XEQ 14
1228 RTN
1229 LBL 06
1230 XEQ 12
1231 RCL 11
1232 41
1233 +
1234 COS
1235 RCL 00
1236 *
1237 RCL 09
1238 COS
1239 RCL 07
1240 RCL 11
1241 +
1242 4
1243 -
1244 SIN
1245 -
1246 ST+ X
1247 +
1248 RCL 09
1249 ST+ X
1250 27
1251 -
1252 COS
1253 6
1254 *
1255 -
1256 RCL 11
1257 32
1258 -
1259 COS
1260 30
1261 *
1262 -
1263 RCL 00
1264 *
1265 RCL 09
1266 RCL 11
1267 -
1268 56
1269 +
1270 COS
1271 RCL 08
1272 RCL 10
1273 +
1274 44
1275 +
1276 COS
1277 +
1278 RCL 07
1279 RCL 12
1280 -
1281 STO 14
1282 ST+ 14
1283 COS
1284 -
1285 RCL 14
1286 RCL 15
1287 +
1288 78
1289 -
1290 COS
1291 +
1292 RCL 12
1293 RCL 03
1294 -
1295 39
1296 +
1297 SIN
1298 -
1299 ST+ X
1300 +
1301 RCL 07
1302 RCL 11
1303 ST+ X
1304 STO 13
1305 -
1306 36
1307 +
1308 COS
1309 RCL 10
1310 RCL 07
1311 -
1312 STO 05
1313 RCL 13
1314 +
1315 STO 04
1316 COS
1317 -
1318 RCL 15
1319 7
1320 *
1321 28
1322 -
1323 SIN
1324 +
1325 RCL 07
1326 59
1327 +
1328 COS
1329 -
1330 RCL 06
1331 14
1332 +
1333 COS
1334 +
1335 PI
1336 *
1337 +
1338 RCL 14
1339 11
1340 +
1341 SIN
1342 RCL 07
1343 RCL 03
1344 -
1345 COS
1346 +
1347 6
1348 *
1349 -
1350 RCL 03
1351 21
1352 -

1353 COS
1354 RCL 13
1355 15
1356 -
1357 SIN
1358 +
1359 RCL 03
1360 RCL 11
1361 -
1362 SIN
1363 -
1364 RCL 08
1365 30
1366 -
1367 COS
1368 +
1369 8
1370 *
1371 +
1372 RCL 10
1373 54
1374 +
1375 COS
1376 RCL 05
1377 25
1378 +
1379 COS
1380 +
1381 9
1382 *
1383 +
1384 RCL 09
1385 RCL 11
1386 +
1387 STO 06
1388 2
1389 -
1390 SIN
1391 14
1392 *
1393 +
1394 RCL 07
1395 RCL 11
1396 +
1397 STO 14
1398 50
1399 -
1400 SIN
1401 45
1402 *
1403 +
1404 RCL 09
1405 14
1406 +
1407 COS
1408 118
1409 *
1410 +
1411 RCL 07
1412 RCL 11
1413 -
1414 30
1415 +
1416 COS
1417 228
1418 *
1419 +
1420 RCL 11
1421 7.3
1422 -
1423 SIN
1424 810
1425 *
1426 +
1427 STO 03
1428 RCL 06
1429 76
1430 -
1431 COS
1432 RCL 08
1433 48
1434 -
1435 COS
1436 +
1437 3
1438 *
1439 RCL 04
1440 67
1441 +
1442 SIN
1443 ST+ X
1444 -
1445 RCL 11
1446 SIN
1447 4
1448 *
1449 +
1450 RCL 09
1451 ST+ X
1452 STO 13
1453 46
1454 +
1455 SIN
1456 RCL 00
1457 *
1458 -
1459 RCL 05
1460 28
1461 -
1462 COS
1463 6
1464 *
1465 +
1466 RCL 14
1467 20
1468 +
1469 COS
1470 18
1471 *
1472 -
1473 RCL 13
1474 33
1475 +
1476 COS
1477 20
1478 *
1479 +
1480 STO 04
1481 RCL 09
1482 73
1483 -
1484 COS
1485 6
1486 *
1487 RCL 11
1488 COS
1489 RCL 14
1490 50
1491 -
1492 COS
1493 +
1494 4
1495 *
1496 -
1497 RCL 08
1498 20
1499 -
1500 COS
1501 8
1502 *
1503 +
1504 RCL 13
1505 60
1506 -
1507 COS
1508 19
1509 *
1510 +
1511 12
1512 -
1513 STO 05
1514 9.555
1515 STO 09
1516 RCL 00
1517 3670533
1518 RCL 00
1519 22
1520 SQRT
1521 *
1522 +
1523 *
1524 50061
1525 +
1526 STO 12
1527 CLX
1528 104
1529 *
1530 CHS
1531 5551
1532 +
1533 STO 10
1534 CLX
1535 11
1536 *
1537 CHS
1538 2489
1539 +
1540 STO 11
1541 CLX
1542 8
1543 *
1544 5891
1545 +
1546 *
1547 93057
1548 +
1549 STO 13
1550 RDN
1551 CHS
1552 2631
1553 +
1554 *
1555 113665
1556 XEQ 14
1557 RTN
1558 LBL 07
1559 XEQ 12
1560 RCL 12
1561 RCL 03
1562 -
1563 65
1564 +
1565 COS
1566 RCL 03
1567 44
1568 +
1569 COS
1570 +
1571 6
1572 SQRT
1573 *
1574 RCL 12
1575 RCL 05
1576 -
1577 21
1578 +
1579 COS
1580 3
1581 *
1582 +
1583 RCL 05
1584 52
1585 -
1586 COS
1587 8
1588 *
1589 +
1590 RCL 00
1591 *
1592 RCL 03
1593 RCL 05
1594 -
1595 SIN
1596 RCL 03
1597 RCL 12
1598 +
1599 59
1600 -
1601 COS
1602 +
1603 RCL 04
1604 RCL 12
1605 +
1606 SIN
1607 +
1608 RCL 14
1609 ST+ X
1610 STO 11
1611 ST+ X
1612 STO 15
1613 46
1614 -
1615 COS
1616 +
1617 RCL 15
1618 RCL 04
1619 -
1620 50
1621 -
1622 COS
1623 -
1624 RCL 12
1625 65
1626 +
1627 COS
1628 +
1629 ST+ X
1630 +
1631 RCL 11
1632 RCL 04
1633 -
1634 63
1635 -
1636 SIN
1637 PI
1638 *
1639 +
1640 RCL 11
1641 RCL 14
1642 +
1643 60
1644 -
1645 COS
1646 4
1647 *
1648 +
1649 RCL 14
1650 RCL 05
1651 -
1652 78
1653 +
1654 SIN
1655 5
1656 *
1657 -
1658 RCL 09
1659 RCL 14
1660 +
1661 RCL 05
1662 -
1663 STO 10
1664 28
1665 +
1666 COS
1667 6
1668 *
1669 +
1670 RCL 04
1671 RCL 05
1672 +
1673 80
1674 -
1675 COS
1676 7
1677 *
1678 +
1679 RCL 14
1680 10
1681 +
1682 SIN
1683 10
1684 *
1685 -
1686 RCL 11
1687 RCL 12
1688 +
1689 20

1690 -
1691 SIN
1692 12
1693 *
1694 +
1695 RCL 06
1696 RCL 12
1697 -
1698 10
1699 -
1700 COS
1701 RCL 12
1702 RCL 04
1703 -
1704 COS
1705 -
1706 15
1707 *
1708 +
1709 RCL 03
1710 73
1711 +
1712 SIN
1713 RCL 04
1714 39
1715 +
1716 SIN
1717 +
1718 35
1719 *
1720 -
1721 RCL 05
1722 RCL 12
1723 +
1724 STO 07
1725 11
1726 -
1727 COS
1728 39
1729 *
1730 +
1731 RCL 12
1732 RCL 03
1733 -
1734 STO 15
1735 51
1736 -
1737 COS
1738 40
1739 *
1740 +
1741 RCL 11
1742 19
1743 +
1744 SIN
1745 209
1746 *
1747 -
1748 RCL 05
1749 62.2
1750 -
1751 SIN
1752 858
1753 *
1754 +
1755 STO 03
1756 RCL 11
1757 33
1758 +
1759 COS
1760 RCL 07
1761 SIN
1762 -
1763 6
1764 *
1765 RCL 05
1766 39
1767 +
1768 SIN
1769 ST+ X
1770 -
1771 STO 04
1772 RCL 06
1773 RCL 12
1774 -
1775 80
1776 +
1777 COS
1778 5
1779 *
1780 RCL 10
1781 SIN
1782 PI
1783 *
1784 -
1785 RCL 11
1786 RCL 05
1787 -
1788 SIN
1789 ST+ X
1790 -
1791 RCL 07
1792 11
1793 -
1794 SIN
1795 RCL 15
1796 49
1797 -
1798 SIN
1799 +
1800 6
1801 *
1802 +
1803 RCL 11
1804 19
1805 +
1806 COS
1807 34
1808 *
1809 +
1810 26
1811 -
1812 STO 05
1813 19.218
1814 STO 09
1815 RCL 00
1816 1289593
1817 RCL 00
1818 7
1819 SQRT
1820 *
1821 +
1822 *
1823 45955
1824 -
1825 STO 12
1826 RDN
1827 ST+ X
1828 773
1829 +
1830 STO 11
1831 CLX
1832 8
1833 *
1834 CHS
1835 4630
1836 +
1837 STO 10
1838 RDN
1839 ST+ X
1840 4459
1841 +
1842 *
1843 172993
1844 +
1845 STO 13
1846 CLX
1847 12
1848 *
1849 1563
1850 +
1851 *
1852 74005
1853 XEQ 14
1854 RTN
1855 LBL 08
1856 XEQ 12
1857 RCL 05
1858 38
1859 +
1860 SIN
1861 5
1862 *
1863 CHS
1864 RCL 00
1865 *
1866 RCL 07
1867 RCL 13
1868 -
1869 STO 10
1870 16
1871 +
1872 COS
1873 RCL 05
1874 RCL 13
1875 +
1876 77
1877 -
1878 COS
1879 +
1880 5
1881 *
1882 +
1883 RCL 06
1884 RCL 13
1885 -
1886 STO 08
1887 COS
1888 9
1889 *
1890 +
1891 RCL 14
1892 RCL 05
1893 -
1894 STO 09
1895 11
1896 -
1897 COS
1898 22
1899 *
1900 +
1901 RCL 04
1902 50
1903 -
1904 COS
1905 24
1906 *
1907 +
1908 RCL 14
1909 7
1910 +
1911 SIN
1912 71
1913 *
1914 +
1915 RCL 05
1916 27.8
1917 +
1918 COS
1919 584
1920 *
1921 +
1922 STO 03
1923 RCL 04
1924 RCL 14
1925 +
1926 69
1927 -
1928 SIN
1929 RCL 14
1930 54
1931 +
1932 SIN
1933 -
1934 9
1935 *
1936 STO 04
1937 RCL 09
1938 11
1939 -
1940 SIN
1941 RCL 08
1942 SIN
1943 -
1944 5
1945 *
1946 RCL 10
1947 16
1948 +
1949 SIN
1950 3
1951 *
1952 -
1953 RCL 05
1954 63
1955 -
1956 COS
1957 8
1958 *
1959 +
1960 RCL 14
1961 6
1962 +
1963 COS
1964 17
1965 *
1966 -
1967 41
1968 -
1969 STO 05
1970 30.11
1971 STO 09
1972 RCL 00
1973 1770
1974 RCL 00
1975 28
1976 *
1977 -
1978 STO 11
1979 RDN
1980 ST+ X
1981 899
1982 +
1983 STO 10
1984 CLX
1985 8
1986 SQRT
1987 *
1988 659648
1989 +
1990 *
1991 55654
1992 -
1993 STO 12
1994 CLX
1995 PI
1996 *
1997 4278
1998 +
1999 *
01 48124
02 +
03 STO 13
04 RDN
05 ST+ X
06 3306
07 +
08 *
09 131784
10 XEQ 14
11 RTN
12 LBL 09
13 RCL 00
14 8669
15 *
16 65
17 +
18 COS
19 7
20 *
21 RCL 00
22 3231
23 *
24 76
25 +
26 COS

27 4
28 *
29 +
30 STO 03
31 RCL 00
32 26
33 *
34 4
35 -
36 STO 04
37 RCL 00
38 6
39 *
40 STO 05
41 39.489
42 STO 09
43 24900
44 STO 10
45 17140
46 STO 11
47 439701
48 RCL 00
49 *
50 238927
51 +
52 STO 12
53 RCL 00
54 4191
55 *
56 135925
57 -
58 STO 13
59 246232
60 GTO 14
61 LBL 16
62 RCL 00
63 107997.151
64 RCL 00
65 722
66 /
67 -
68 *
69 2.964
70 -
71 RTN
72 LBL 12
73 102
74 RCL 00
75 6.179973
76 *
77 STO 15
78 *
79 STO 14
80 106
81 LASTX
82 *
83 STO 13
84 +
85 STO 12
86 19
87 RCL 15
88 *
89 STO 11
90 593
91 LASTX
92 *
93 STO 07
94 LASTX
95 880
96 *
97 STO 08
98 +
99 STO 06
100 LASTX
101 RCL 07
102 -
103 STO 09
104 +
105 STO 10
106 4
107 RCL 15
108 *
109 STO 05
110 ST+ X
111 STO 04
112 LASTX
113 31
114 *
115 STO 03
116 RTN
117 LBL 14
118 +
119 E3
120 ST/ 03
121 ST/ 04
122 ST/ 05
123 ST/ 11
124 ST/ 12
125 ST/ 13
126 /
127 STO 14
128 E5
129 ST/ 10
130 9
131 STO 15
132 RCL 12
133 RCL 13
134 -
135 360
136 STO 08
137 MOD
138 ENTER
139 ENTER
140 LBL 11
141 SIN
142 RCL 10
143 R-D
144 *
145 +
146 DSE 15
147 GTO 11
148 2
149 /
150 1
151 RCL 10
152 +
153 1
154 LASTX
155 -
156 /
157 SQRT
158 P-R
159 LASTX
160 /
161 R-P
162 RDN
163 ST+ X
164 1
165 R^
166 ST+ X
167 COS
168 RCL 10
169 *
170 -
171 RCL 09
172 *
173 RCL 05
174 +
175 X<> 13
176 +
177 RCL 14
178 -
179 COS
180 RCL 11
181 LASTX
182 SIN
183 P-R
184 X<>Y
185 ASIN
186 RCL 04
187 +
188 STO 12
189 X<> Z
190 R-P
191 CLX
192 RCL 14
193 +
194 RCL 03
195 +
196 RCL 08
197 MOD
198 STO 11
199 RCL 12
200 RCL 11
201 RCL 13
202 XEQ 10
203 RCL 02
204 ST+ Z
205 CLX
206 RCL 01
207 +
208 XEQ 12
209 STO 05
210 CLX
211 RCL 21
212 +
213 STO 03
214 X<>Y
215 STO 04
216 RCL 05
217 X^2
218 RCL 23
219 X^2
220 STO 08
221 -
222 RCL 13
223 X^2
224 +
225 RCL 05
226 ST+ X
227 /
228 RCL 09
229 1
230 RCL 10
231 X^2
232 -
233 *
234 SQRT
235 RCL 13
236 X^2
237 /
238 RCL 08
239 1/X
240 -
241 *
242 RCL 05
243 RCL 08
244 /
245 +
246 176
247 /
248 ST- 03
249 LBL 00
250 RCL 20
251 CHS
252 RCL 04
253 RCL 03
254 XEQ 13
255 RCL 05
256 X<> Z
257 HMS
258 STO 07
259 X<>Y
260 15
261 /
262 24
263 MOD
264 HMS
265 STO 06
266 RCL 19
267 X<>Y
268 HMS-
269 HR
270 15
271 *
272 RCL 17
273 HR
274 RCL 07
275 HR
276 90
277 STO 15
278 ST- Z
279 R^
280 -
281 XEQ 13
282 RCL 15
283 +
284 CHS
285 360
286 MOD
287 HMS
288 STO 08
289 X<>Y
290 HMS
291 STO 15
292 LASTX
293 ENTER
294 COS
295 RCL 05
296 23455
297 *
298 /
299 ASIN
300 -
301 HMS
302 STO 09
303 LASTX
304 17.964
305 RCL Y
306 6.6
307 +
308 /
309 +
310 5.267
311 X<>Y
312 /
313 +
314 TAN
315 61.921
316 *
317 1/X
318 +
319 HMS
320 STO 10
321 RCL 03
322 RCL 22
323 -
324 COS
325 RCL 04
326 COS
327 *
328 ACOS
329 HMS
330 STO 14
331 X<>Y
332 RCL 09
333 RCL 08
334 RTN
335 LBL 13
336 1
337 XEQ 10
338 RDN
339 R-P
340 X<> Z
341 ST- Y
342 X<> Z
343 P-R
344 R^
345 XEQ 12
346 RDN
347 RTN
348 LBL 12
349 R-P
350 X<>Y
351 RDN
352 R-P
353 R^
354 X<>Y
355 RTN
356 LBL 10
357 X<>Y
358 RDN
359 P-R
360 R^
361 X<>Y
362 P-R
363 END

STACK	INPUT	OUTPUTS
T	/	Elg = elongation from the Sun ( ° ' " )
Z	/	h₀ = apparent altitude ( ° ' '' )
Y	YYYY.MNDD	h = true altitude ( ° ' '' )
X	hh.mnss (TT)	Az = Azimuth ( ° ' '' )

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] Aldo Vitagliano Software: excellent "SOLEX" which may be downloaded freely from http://www.solexorb.it/
[5] https://datacenter.iers.org/data/latestVersion/6_BULLETIN_A_V2013_016.txt

hp41programs

Astronomical Ephemeris (7) for the HP-41