hp41programs

OUTERPLANETS

OUTER PLANETS 2016-2023 for the HP41


 Overview
 

-Just a few programs to compute the heliocentric ecliptic coordinates of the outer planets, Jupiter, Saturn, Uranus & Neptune
  for a time-span of 2800 days, from  2016/01/01 0h TT to 2023/09/01 0h TT

-The longitudes & latitudes are referred to the mean ecliptic of the date,
-The distances are true distances.

-The precision is about 0°000003 for the longitudes & latitudes and of the order of E-7 AU for the radius vector.

-These coordinates are calculated by polynomials fitted to the JPL ephemerides DE431

-All these routines are put together in a module which may be downloaded here:  http://www.hp41.org
 

Notes:

-Always execute "TT" first to initialize R00, with at least SIZE 001

    YYYY.MNDD  ENTER^
       HH.MNSS     XEQ "TT"

-You will get a  DATA ERROR  message if the date is outside the interval    [ 2016/01/01 0h TT ; 2023/09/01 0h TT ]

-Then,  XEQ "HJUP" , "HSAT" , "HURA" , "HNEP"
 

Data Register   Only 1 data register is used: R00 but the alpha "register" is cleared.

  R00 = ( Nb of days since 2019/11/01 )  /  1400   Terrestrial Time ( TT )
 

Program Listing1
 

-All the GTO 10 are three-byte GTO
 
 
 

 01 LBL "TT"
 02 HR
 03 24
 04 /
 05 X<>Y
 06 ENTER
 07 INT
 08 ST- Y
 09 X<>Y
 10  E2
 11 *
 12 ENTER
 13 INT
 14 STO 00
 15 -
 16  E2
 17 *
 18 X<> 00
 19 1
 20 E^X
 21 -
 22 12
 23 /
 24 +
 25 INT
 26 ST- 00
 27 LASTX
 28 367
 29 *
 30 INT
 31 ST+ 00
 32 SIGN
 33 %
 34 INT
 35 .75
 36 ST* Z
 37 *
 38 X<>Y
 39 ST- 00
 40 CLX
 41 RCL 00
 42 INT
 43 X<>Y
 44 -
 45 INT
 46 737678
 47 -
 48 +
 49 1400
 50 /
 51 STO 00
 52 ABS
 53 1
 54 X<>Y
 55 X>Y?
 56 ACOS
 57 RCL 00
 58 RTN
 59 LBL "HJUP"
 60 RCL 00 
 61 4
 62 *
 63 2
 64 X<Y?
 65 GTO 04
 66 RDN
 67 X>0?
 68 GTO 03
 69 2
 70 CHS
 71 X<Y?
 72 GTO 02
 73 CLX
 74 3
 75 +
 76 1141
 77 RCL Y
 78 3284
 79 *
 80 +
 81 *
 82 CHS
 83 13451
 84 +
 85 *
 86 4297
 87 +
 88 *
 89 23307
 90 -
 91 *
 92 6747
 93 -
 94 *
 95 21670
 96 +
 97 *
 98 5762
 99 +
100 *
101 11443
102 -
103 *
104 2437
105 -
106 *
107 97955
108 +
109 *
110 51202
111 -
112 *
113 26436310
114 +
115 *
116 189728480
117 +
118 STO M           
119 CLX
120 49
121 *
122 18
123 +
124 *
125 CHS
126 112
127 +
128 *
129 3
130 -
131 *
132 1402
133 +
134 *
135 241
136 +
137 *
138 138575
139 -
140 *
141 9692
142 +
143 *
144 1302960
145 +
146 STO N
147 CLX
148 12923
149 *
150 30260
151 -
152 *
153 50253
154 -
155 *
156 116632
157 +
158 *
159 83194
160 +
161 *
162 181842
163 -
164 *
165 77457
166 -
167 *
168 142123
169 +
170 *
171 44707
172 +
173 *
174 7277
175 -
176 *
177 49451
178 -
179 *
180 2965171
181 -
182 *
183 1077371
184 +
185 *
186 545554436
187 GTO 10
188 LBL 02
189 SIGN
190 -
191 111
192 RCL Y 
193 3272
194 *
195 -
196 *
197 13608
198 +
199 *
200 201
201 -
202 *
203 24057
204 -
205 *
206 38
207 +
208 *
209 23081
210 +
211 *
212 28
213 -
214 *
215 13491
216 -
217 *
218 5621
219 -
220 *
221 81763
222 +
223 *
224 491921
225 +
226 *
227 27348661
228 +
229 *
230 243148440
231 +
232 STO M
233 CLX
234 172
235 *
236 8
237 +
238 *
239 424
240 -
241 *
242 32
243 -
244 *
245 476
246 +
247 *
248 2313
249 +
250 *
251 13943
252 +
253 *
254 99279
255 -
256 *
257 493132
258 -
259 *
260 793791
261 +
262 STO N           
263 CLX
264 30113
265 *
266 1583
267 +
268 *
269 CHS
270 117781
271 +
272 *
273 5049
274 +
275 *
276 187758
277 -
278 *
279 5853
280 -
281 *
282 152655
283 +
284 *
285 1324
286 +
287 *
288 18330
289 -
290 *
291 348064
292 +
293 *
294 2018618
295 -
296 *
297 9700339
298 -
299 *
300 536300717
301 GTO 10
302 LBL 03
303 1
304 -
305 887
306 RCL Y
307 1695
308 *
309 -
310 *
311 8411
312 +
313 *
314 3332
315 -
316 *
317 17159
318 -
319 *
320 5350
321 +
322 *
323 18031
324 +
325 *
326 4597
327 -
328 *
329 10638
330 -
331 *
332 16088
333 -
334 *
335 16546
336 -
337 *
338 724404
339 +
340 *
341 29977071
342 +
343 *
344 300311805
345 +
346 STO M 
347 CLX
348 150
349 *
350 55
351 +
352 *
353 363
354 -
355 *
356 209
357 -
358 *
359 302
360 -
361 *
362 1173
363 +
364 *
365 32501
366 +
367 *
368 44388
369 +
370 *
371 641952
372 -
373 *
374 437538
375 -
376 STO N           
377 CLX
378 12833
379 *
380 23224
381 +
382 *
383 CHS
384 46062
385 +
386 *
387 95085
388 +
389 *
390 70725
391 -
392 *
393 155620
394 -
395 *
396 63183
397 +
398 *
399 124573
400 +
401 *
402 46740
403 -
404 *
405 52025
406 -
407 *
408 592504
409 +
410 *
411 955958
412 +
413 *
414 12353089
415 -
416 *
417 512236615
418 GTO 10
419 LBL 04
420 CLX
421 3
422 -
423 1055
424 RCL Y
425 678
426 *
427 +
428 *
429 CHS
430 3706
431 +
432 *
433 6247
434 +
435 *
436 8838
437 -
438 *
439 13922
440 -
441 *
442 11513
443 +
444 *
445 14788
446 +
447 *
448 8116
449 -
450 *
451 3924
452 -
453 *
454 3468
455 -
456 *
457 150204
458 -
459 *
460 165894
461 +
462 *
463 32038426
464 +
465 *
466 2706248
467 +
468 STO M 
469 CLX
470 7
471 *
472 167
473 +
474 *
475 353
476 -
477 *
478 7001
479 -
480 *
481 7824
482 +
483 *
484 200983
485 +
486 *
487 101322
488 -
489 *
490 1290090
491 -
492 STO N           
493 CLX
494 7941
495 *
496 19631
497 +
498 *
499 CHS
500 39509
501 +
502 *
503 80839
504 +
505 *
506 81105
507 -
508 *
509 130413
510 -
511 *
512 85778
513 +
514 *
515 100647
516 +
517 *
518 50560
519 -
520 *
521 128385
522 -
523 *
524 152139
525 +
526 *
527 3502011
528 +
529 *
530 2566270
531 -
532 *
533 495566212
534 LBL 10
535 XEQ 10
536 RTN
537 LBL "HSAT"
538 RCL 00
539 4
540 *
541 2
542 X<Y?
543 GTO 04
544 RDN
545 X>0?
546 GTO 03
547 2
548 CHS
549 X<Y?
550 GTO 02
551 CLX
552 3
553 +
554 1351
555 RCL Y
556 1704
557 *
558 +
559 *
560 6511
561 -
562 *
563 4686
564 -
565 *
566 9921
567 +
568 *
569 6363
570 +
571 *
572 7401
573 -
574 *
575 4239
576 -
577 *
578 2651
579 +
580 *
581 7944
582 +
583 *
584 27753
585 -
586 *
587 10567390
588 +
589 *
590 259034324
591 +
592 STO M
593 CLX
594 25
595 *
596 2021
597 +
598 *
599 23077
600 -
601 *
602 376468
603 -
604 *
605 1417485
606 +
607 STO N           
608 CLX
609 28919
610 *
611 30316
612 -
613 *
614 123195
615 -
616 *
617 125147
618 +
619 *
620 225530
621 +
622 *
623 215895
624 -
625 *
626 232795
627 -
628 *
629 195648
630 +
631 *
632 146529
633 +
634 *
635 93553
636 -
637 *
638 53014
639 -
640 *
641 5597
642 +
643 *
644 931144
645 -
646 *
647 2684417
648 +
649 *
650 1004681974
651 GTO 10
652 LBL 02
653 SIGN
654 -
655 1804
656 RCL Y
657 1287
658 *
659 +
660 *
661 4907
662 -
663 *
664 6195
665 -
666 *
667 7598
668 +
669 *
670 8215
671 +
672 *
673 6019
674 -
675 *
676 5170
677 -
678 *
679 2539
680 +
681 *
682 8277
683 +
684 *
685 12165
686 +
687 *
688 10537513
689 +
690 *
691 280112839
692 +
693 STO M
694 CLX
695 23
696 *
697 2187
698 +
699 *
700 10463
701 -
702 *
703 443867
704 -
705 *
706 588744
707 +
708 STO N
709 CLX
710 23618
711 *
712 26953
713 -
714 *
715 110689
716 -
717 *
718 106309
719 +
720 *
721 225063
722 +
723 *
724 176904
725 -
726 *
727 255362
728 -
729 *
730 159665
731 +
732 *
733 169774
734 +
735 *
736 82092
737 -
738 *
739 61263
740 -
741 *
742 20825
743 +
744 *
745 976560
746 -
747 *
748 1199618
749 -
750 *
751 1006200509
752 GTO 10
753 LBL 03
754 1
755 -
756 530
757 CHS
758 RCL Y           
759 2032
760 *
761 +
762 *
763 6871
764 -
765 *
766 1743
767 +
768 *
769 8805
770 +
771 *
772 2260
773 -
774 *
775 5176
776 -
777 *
778 1361
779 +
780 *
781 8490
782 +
783 *
784 54513
785 +
786 *
787 10671412
788 +
789 *
790 301293810
791 +
792 STO M
793 CLX
794 34
795 *
796 2406
797 +
798 *
799 3259
800 +
801 *
802 458704
803 -
804 *
805 322967
806 -
807 STO N
808 CLX
809 14434
810 *
811 31826
812 +
813 *
814 CHS
815 53662
816 +
817 *
818 125368
819 +
820 *
821 85808
822 -
823 *
824 195862
825 -
826 *
827 78990
828 +
829 *
830 148574
831 +
832 *
833 46345
834 -
835 *
836 46233
837 -
838 *
839 42008
840 +
841 *
842 935642
843 -
844 *
845 5109594
846 -
847 *
848 999870426
849 GTO 10
850 LBL 04
851 CLX
852 3
853 -
854 249
855 RCL Y
856 2178
857 *
858 +
859 *
860 7212
861 -
862 *
863 595
864 -
865 *
866 8883
867 +
868 *
869 355
870 +
871 *
872 4699
873 -
874 *
875 106
876 -
877 *
878 6292
879 +
880 *
881 93216
882 +
883 *
884 10971960
885 +
886 *
887 322911612
888 +
889 STO M           
890 CLX
891 29
892 *
893 2691
894 +
895 *
896 18578
897 +
898 *
899 415625
900 -
901 *
902 1207514
903 -
904 STO N
905 CLX
906 33322
907 *
908 6121
909 +
910 *
911 CHS
912 130112
913 +
914 *
915 18284
916 +
917 *
918 199059
919 -
920 *
921 18381
922 -
923 *
924 143969
925 +
926 *
927 4749
928 +
929 *
930 43206
931 -
932 *
933 57837
934 +
935 *
936 669065
937 -
938 *
939 8395154
940 -
941 *
942 986185075
943 LBL 10
944 +
945  E8
946 /
947 RCL N
948 RCL M
949  E6
950 ST/ Z
951 /
952 CLA
953 RTN
954 GTO "HURA"
955 END

 
            ( 2182 bytes / SIZE 001 )
 
 

      STACK        INPUTS      OUTPUTS
           Y  YYYY.MNDD             /
           X      HH.MNSS             T

  Where   T  is between  -1 & +1  ( otherwise, DATA ERROR is displayed )

Example:    Calculate the mean heliocentric ecliptic coordinates of the outer planets on 2016/07/04 at 16h48m  TT

       2016.0704  ENTER^
           16.48      XEQ "TT"  >>>>   X = -0.8673571429 = R00

-Then, the ecliptic heliocentric coordinates are returned in the stack:
 
 

      STACK        INPUTS      OUTPUTS
           Z              /       R  ( AU )
           Y              /       B ( deg )
           X              /       L ( deg )

               L =  heliocentric longitude
   Where  B = heliocentric latitude
               R = radius vector

    •  Jupiter

-After executing "TT"  XEQ "HJUP"  ( or simply R/S )   >>>>   L = 177°297209                    ---Execution time = 11s---
                                                                                     RDN    B =  1°267918
                                                                                     RDN    R =  5.4440047  AU

    •  Saturn
 

   XEQ "HSAT"  ( or simply R/S )   >>>>   L = 254°066891                    ---Execution time = 10s---
                                                       RDN    B =  1°588917
                                                       RDN    R = 10.0321597  AU
 

Program Listing2
 

-All the GTO 10 are three-byte GTO
 
 

 01 LBL "HURA"
 02 RCL 00
 03 4
 04 *
 05 2
 06 X<Y?
 07 GTO 04
 08 RDN
 09 X>0?
 10 GTO 03
 11 2
 12 CHS
 13 X<Y?
 14 GTO 02
 15 CLX
 16 3
 17 +
 18 99
 19 RCL Y            
 20 1179
 21 *
 22 +
 23 *
 24 CHS
 25 3995
 26 +
 27 *
 28 370
 29 +
 30 *
 31 5177
 32 -
 33 *
 34 579
 35 -
 36 *
 37 3126
 38 +
 39 *
 40 451
 41 +
 42 *
 43 441
 44 -
 45 *
 46 6148
 47 +
 48 *
 49 3802970
 50 +
 51 *
 52 23173870
 53 +
 54 STO M
 55 CLX
 56 17
 57 *
 58 CHS
 59 1351
 60 +
 61 *
 62 32288
 63 +
 64 *
 65 599224
 66 -
 67 STO N
 68 CLX
 69 44102
 70 *
 71 6032
 72 +
 73 *
 74 CHS
 75 192060
 76 +
 77 *
 78 22146
 79 +
 80 *
 81 359530
 82 -
 83 *
 84 35322
 85 -
 86 *
 87 374420
 88 +
 89 *
 90 34759
 91 +
 92 *
 93 228176
 94 -
 95 *
 96 24610
 97 -
 98 *
 99 75903
100 +
101 *
102 14191
103 +
104 *
105 151578
106 -
107 *
108 3466752
109 -
110 *
111 1994201755
112 GTO 10
113 LBL 02
114 SIGN
115 -
116 646
117 RCL Y           
118 977
119 *
120 +
121 *
122 CHS
123 3356
124 +
125 *
126 1900
127 +
128 *
129 4463
130 -
131 *
132 2052
133 -
134 *
135 2842
136 +
137 *
138 964
139 +
140 *
141 462
142 -
143 *
144 8526
145 +
146 *
147 3832988
148 +
149 *
150 30808047
151 +
152 STO M
153 CLX
154 17
155 *
156 CHS
157 1247
158 +
159 *
160 37483
161 +
162 *
163 529384
164 -
165 STO N
166 CLX
167 39869
168 *
169 18524
170 +
171 *
172 CHS
173 170160
174 +
175 *
176 82278
177 +
178 *
179 312907
180 -
181 *
182 151590
183 -
184 *
185 323220
186 +
187 *
188 146476
189 +
190 *
191 200122
192 -
193 *
194 76420
195 -
196 *
197 70860
198 +
199 *
200 19761
201 +
202 *
203 140809
204 -
205 *
206 3998186
207 -
208 *
209 1986732394
210 GTO 10
211 LBL 03
212 1
213 -
214 975
215 RCL Y
216 398
217 *
218 +
219 *
220 CHS
221 1436
222 +
223 *
224 2787
225 +
226 *
227 2064
228 -
229 *
230 2820
231 -
232 *
233 1492
234 +
235 *
236 1121
237 +
238 *
239 268
240 -
241 *
242 10653
243 +
244 *
245 3872211
246 +
247 *
248 38511671
249 +
250 STO M           
251 CLX
252 19
253 *
254 CHS
255 1139
256 +
257 *
258 42259
259 +
260 *
261 449571
262 -
263 STO N
264 CLX
265 24530
266 *
267 CHS
268 14217
269 +
270 *
271 114381
272 +
273 *
274 55530
275 -
276 *
277 217116
278 -
279 *
280 89745
281 +
282 *
283 209356
284 +
285 *
286 76926
287 -
288 *
289 102297
290 -
291 *
292 36157
293 +
294 *
295 17426
296 +
297 *
298 148049
299 -
300 *
301 4525662
302 -
303 *
304 1978218675
305 GTO 10
306 LBL 04
307 CLX
308 3
309 -
310 328
311 RCL Y
312 1071
313 *
314 +
315 *
316 4116
317 -
318 *
319 1011
320 -
321 *
322 6184
323 +
324 *
325 1094
326 +
327 *
328 4386
329 -
330 *
331 410
332 -
333 *
334 1313
335 +
336 *
337 13
338 -
339 *
340 11576
341 +
342 *
343 3917669
344 +
345 *
346 46300862
347 +
348 STO M
349 CLX
350 28
351 *
352 CHS
353 1001
354 +
355 *
356 46560
357 +
358 *
359 360662
360 -
361 STO N           
362 CLX
363 25125
364 *
365 10512
366 +
367 *
368 CHS
369 118614
370 +
371 *
372 38949
373 +
374 *
375 225173
376 -
377 *
378 54577
379 -
380 *
381 213115
382 +
383 *
384 32861
385 +
386 *
387 97969
388 -
389 *
390 4243
391 -
392 *
393 14038
394 +
395 *
396 166996
397 -
398 *
399 5137063
400 -
401 *
402 1968574799
403 LBL 10
404 XEQ 10
405 RTN
406 LBL "HNEP"
407 RCL 00
408 4
409 *
410 2
411 X<Y?
412 GTO 04
413 RDN
414 X>0?
415 GTO 03
416 2
417 CHS
418 X<Y?
419 GTO 02
420 CLX
421 3
422 +
423 546
424 RCL Y
425 561
426 *
427 +
428 *
429 CHS
430 1872
431 +
432 *
433 1639
434 +
435 *
436 2341
437 -
438 *
439 1836
440 -
441 *
442 1302
443 +
444 *
445 928
446 +
447 *
448 177
449 -
450 *
451 959
452 +
453 *
454 2118896
455 +
456 *
457 341255481
458 +
459 STO M
460 CLX
461 13
462 *
463 562
464 +
465 *
466 56810
467 -
468 *
469 865332
470 -
471 STO N           
472 CLX
473 28276
474 *
475 34605
476 +
477 *
478 CHS
479 125459
480 +
481 *
482 139302
483 +
484 *
485 239244
486 -
487 *
488 235484
489 -
490 *
491 251164
492 +
493 *
494 214452
495 +
496 *
497 149405
498 -
499 *
500 110571
501 -
502 *
503 44504
504 +
505 *
506 26781
507 +
508 *
509 46025
510 +
511 *
512 717370
513 -
514 *
515 2995197991
516 GTO 10
517 LBL 02
518 SIGN
519 -
520 120
521 RCL Y
522 752
523 *
524 -
525 *
526 2227
527 +
528 *
529 318
530 -
531 *
532 2437
533 -
534 *
535 308
536 +
537 *
538 1172
539 +
540 *
541 92
542 -
543 *
544 1405
545 +
546 *
547 2124629
548 +
549 *
550 345498646
551 +
552 STO M
553 CLX
554 14
555 *
556 644
557 +
558 *
559 54400
560 -
561 *
562 976596
563 -
564 STO N
565 CLX
566 40741
567 *
568 CHS
569 8491
570 +
571 *
572 170118
573 +
574 *
575 31517
576 -
577 *
578 297426
579 -
580 *
581 47895
582 +
583 *
584 276875
585 +
586 *
587 38028
588 -
589 *
590 142294
591 -
592 *
593 16160
594 +
595 *
596 29989
597 +
598 *
599 15736
600 +
601 *
602 569421
603 -
604 *
605 2993939103
606 GTO 10
607 LBL 03
608 1
609 -
610 645
611 CHS
612 RCL Y           
613 370
614 *
615 +
616 *
617 1179
618 -
619 *
620 1901
621 +
622 *
623 1358
624 +
625 *
626 2049
627 -
628 *
629 609
630 -
631 *
632 945
633 +
634 *
635 63
636 -
637 *
638 1291
639 +
640 *
641 2131132
642 +
643 *
644 349754475
645 +
646 STO M
647 CLX
648 14
649 *
650 727
651 +
652 *
653 51657
654 -
655 *
656 1082709
657 -
658 STO N
659 CLX
660 30802
661 *
662 16672
663 +
664 *
665 CHS
666 132617
667 +
668 *
669 64349
670 +
671 *
672 238521
673 -
674 *
675 95202
676 -
677 *
678 226471
679 +
680 *
681 63124
682 +
683 *
684 116464
685 -
686 *
687 14141
688 -
689 *
690 21836
691 +
692 *
693 29540
694 -
695 *
696 585725
697 -
698 *
699 2992822440
700 GTO 10
701 LBL 04
702 CLX
703 3
704 -
705 284
706 CHS
707 RCL Y
708 745
709 *
710 +
711 *
712 2412
713 -
714 *
715 823
716 +
717 *
718 2873
719 +
720 *
721 855
722 -
723 *
724 1427
725 -
726 *
727 374
728 +
729 *
730 6
731 +
732 *
733 365
734 +
735 *
736 2135131
737 +
738 *
739 354021419
740 +
741 STO M           
742 CLX
743 12
744 *
745 806
746 +
747 *
748 48586
749 -
750 *
751 1183004
752 -
753 STO N
754 CLX
755 11741
756 *
757 36352
758 +
759 *
760 CHS
761 52717
762 +
763 *
764 138397
765 +
766 *
767 97958
768 -
769 *
770 204817
771 -
772 *
773 94237
774 +
775 *
776 141008
777 +
778 *
779 47290
780 -
781 *
782 38244
783 -
784 *
785 12273
786 +
787 *
788 50581
789 -
790 *
791 764539
792 -
793 *
794 2991492060
795 LBL 10
796 +
797  E8
798 /
799 RCL N
800 RCL M
801  E6
802 ST/ Z
803 /
804 CLA
805 END

 
            ( 1834 bytes / SIZE 001 )
 
 

      STACK        INPUTS      OUTPUTS
           Z              /       R  ( AU )
           Y              /       B ( deg )
           X              /       L ( deg )

               L =  heliocentric longitude
   Where  B = heliocentric latitude
               R = radius vector
 

    •  Uranus
 

   XEQ "HURA"  ( or simply R/S )   >>>>   L = 21°390015                    ---Execution time = 12s---
                                                       RDN    B =  -0°614081
                                                       RDN    R = 19.9579666  AU
 

Note:

-When you press R/S after executing "HSAT", the HP41 actually executes a GTO "HURA"
-So, it could give wrong results if there is another LBL "HURA" in your calculator...
 

    •  Neptune
 

   XEQ "HNEP"  ( or simply R/S )   >>>>   L = 340°261050                    ---Execution time = 11s---
                                                       RDN    B = -0°838541
                                                       RDN    R = 29.9554483  AU
 

Polynomial Approximations
 

-Here are the polynomials that are used to approximate the ecliptic coordinates, with R00 = T  ( -1 <= T <= +1 )

-They are displayed as lists  { a0  a1  ................  an }  meaning that  p(x) = a0 + a1 x + ................ + an xn

Units:

  0°000001                for the longitude & latitude
  0.00000001  AU     for the radius vector

-The interval [-1,+1]  is actually divided in 4 intervalls of 700 days, corresponding to T between -1 , -0.5 , 0 , +0.5 , +1
-A linear transformation is performed to get x between -1 and +1 in each case.
 

JUPITER

JUP1    x = 4 T + 3

L { 189728480. 26436310. -51202. 97955. -2437. -11443. 5762. 21670. -6747. -23307. 4297. 13451. -1141. -3284. }
B { 1302960. 9692. -138575. 241. 1402. -3. 112. -18. -49. }
R { 545554436. 1077371. -2965171. -49451. -7277. 44707. 142123. -77457. -181842. 83194. 116632. -50253. -30260. 12923. }

JUP2    x = 4 T + 1

L { 243148440. 27348661. 491921. 81763. -5621. -13491. -28. 23081. 38. -24057. -201. 13608. 111. -3272. }
B { 793791. -493132. -99279. 13943. 2313. 476. -32. -424. 8. 172. }
R { 536300717. -9700339. -2018618. 348064. -18330. 1324. 152655. -5853. -187758. 5049. 117781. -1583. -30113. }

JUP3    x = 4 T - 1

L { 300311805. 29977071. 724404. -16546. -16088. -10638. -4597. 18031. 5350. -17159. -3332. 8411. 887. -1695. }
B { -437538. -641952. 44388. 32501. 1173. -302. -209. -363. 55. 150. }
R { 512236615. -12353089. 955958. 592504. -52025. -46740. 124573. 63183. -155620. -70725. 95085. 46062. -23224. -12833. }

JUP4    x = 4 T - 3

L { 2706248. 32038426. 165894. -150204. -3468. -3924. -8116. 14788. 11513. -13922. -8838. 6247. 3706. -1055. -678. }
B { -1290090. -101322. 200983. 7824. -7001. -353. 167. 7. }
R { 495566212. -2566270. 3502011. 152139. -128385. -50560. 100647. 85778. -130413. -81105. 80839. 39509. -19631. -7941. }
 

SATURN

SAT1    x = 4 T + 3

L { 259034324. 10567390. -27753. 7944. 2651. -4239. -7401. 6363. 9921. -4686. -6511. 1351. 1704. }
B { 1417485. -376468. -23077. 2021. 25. }
R { 1004681974. 2684417. -931144. 5597. -53014. -93553. 146529. 195648. -232795. -215895. 225530. 125147. -123195. -30316. 28919. }

SAT2    x = 4 T + 1

L { 280112839. 10537513. 12165. 8277. 2539. -5170. -6019. 8215. 7598. -6195. -4907. 1804. 1287. }
B { 588744. -443867. -10463. 2187. 23. }
R { 1006200509. -1199618. -976560. 20825. -61263. -82092. 169774. 159665. -255362. -176904. 225063. 106309. -110689. -26953. 23618. }

SAT3    x = 4 T - 1

L { 301293810. 10671412. 54513. 8490. 1361. -5176. -2260. 8805. 1743. -6871. -530. 2032. }
B { -322967. -458704. 3259. 2406. 34. }
R { 999870426. -5109594. -935642. 42008. -46233. -46345. 148574. 78990. -195862. -85808. 125368. 53662. -31826. -14434. }

SAT4    x = 4 T - 3

L { 322911612. 10971960. 93216. 6292. -106. -4699. 355. 8883. -595. -7212. 249. 2178. }
B { -1207514. -415625. 18578. 2691. 29. }
R { 986185075. -8395154. -669065. 57837. -43206. 4749. 143969. -18381. -199059. 18284. 130112. -6121. -33322. }
 

URANUS

URA1    x = 4 T + 3

L { 23173870. 3802970. 6148. -441. 451. 3126. -579. -5177. 370. 3995. -99. -1179. }
B { -599224. 32288. 1351. -17. }
R { 1994201755. -3466752. -151578. 14191. 75903. -24610. -228176. 34759. 374420. -35322. -359530. 22146. 192060. -6032. -44102. }

URA2    x = 4 T + 1

L { 30808047. 3832988. 8526. -462. 964. 2842. -2052. -4463. 1900. 3356. -646. -977. }
B { -529384. 37483. 1247. -17. }
R { 1986732394. -3998186. -140809. 19761. 70860. -76420. -200122. 146476. 323220. -151590. -312907. 82278. 170160. -18524. -39869. }

URA3    x = 4 T - 1

L { 38511671. 3872211. 10653. -268. 1121. 1492. -2820. -2064. 2787. 1436. -975. -398. }
B { -449571. 42259. 1139. -19. }
R { 1978218675. -4525662. -148049. 17426. 36157. -102297. -76926. 209356. 89745. -217116. -55530. 114381. 14217. -24530. }

URA4    x = 4 T - 3

L { 46300862. 3917669. 11576. -13. 1313. -410. -4386. 1094. 6184. -1011. -4116. 328. 1071. }
B { -360662. 46560. 1001. -28. }
R { 1968574799. -5137063. -166996. 14038. -4243. -97969. 32861. 213115. -54577. -225173. 38949. 118614. -10512. -25125. }
 

NEPTUNE

NEP1    x = 4 T + 3

L { 341255481. 2118896. 959. -177. 928. 1302. -1836. -2341. 1639. 1872. -546. -561. }
B { -865332. -56810. 562. 13. }
R { 2995197991. -717370. 46025. 26781. 44504. -110571. -149405. 214452. 251164. -235484. -239244. 139302. 125459. -34605. -28276. }

NEP2    x = 4 T + 1

L { 345498646. 2124629. 1405. -92. 1172. 308. -2437. -318. 2227. 120. -752. }
B { -976596. -54400. 644. 14. }
R { 2993939103. -569421. 15736. 29989. 16160. -142294. -38028. 276875. 47895. -297426. -31517. 170118. 8491. -40741. }

NEP3    x = 4 T - 1

L { 349754475. 2131132. 1291. -63. 945. -609. -2049. 1358. 1901. -1179. -645. 370. }
B { -1082709. -51657. 727. 14. }
R { 2992822440. -585725. -29540. 21836. -14141. -116464. 63124. 226471. -95202. -238521. 64349. 132617. -16672. -30802. }

NEP4    x = 4 T - 3

L { 354021419. 2135131. 365. 6. 374. -1427. -855. 2873. 823. -2412. -284. 745. }
B { -1183004. -48586. 806. 12. }
R{ 2991492060. -764539. -50581. 12273. -38244. -47290. 141008. 94237. -204817. -97958. 138397. 52717. -36352. -11741. }
 
 

Reference:

[1]  Aldo Vitagliano SOLEX  http://www.solexorb.it/