JPL DE424

# JPL DE422-DE423-DE424 Ephemerides for the HP-41

Overview

1°)  1018 Coefficients
2°)  Hepax Data File of 1017 Coefficients
3°)  Barycentric Rectangular Equatorial Coordinates

a)  Program#1
b)  Program#2

4°)  Heliocentric Rectangular Equatorial Coordinates
5°)  Geocentric Rectangular Equatorial Coordinates

-The ephemerides of the Jet Propulsion Laboratory employ Chebyshev polynomials
to calculate the coordinates of the major celestial bodies of the Solar system + nutation + libration.
-The same method is used in the French ephemerides "La Connaissance des Temps" and "INPOP10".

-Of course, it would be "difficult" to transfer all the files of the JPL  DE422/LE422 ephemerides or even a single file ( about 30 Megabytes ) into an HP-41.
-However, the coefficients are grouped in sets of 1018 numbers which are valid over time-spans of 32 days.
-Though there are only 319 registers in main memory and 600 registers in extended memory,
you can create a large HEPAX data file if you have an HEPAX module or a CLONIX or NOVRAM ... or an emulator like V41.

-To download the DE422-DE423-DE424 files, go to  ftp://ssd.jpl.nasa.gov/pub/eph/planets/ascii

-DE422 covers JED 625648.5, (-3000 DEC 07) to JED 2816816.5, (3000 JAN 30).

-The proper interval  [625648.5 + 32.k , 625648.5 + 32.(k+1) ]  may be found as follows:

-If JED is the Julian Ephemeris Day number,  k = INT [( JED - 625648.5 )/32 ]
-Then, calculate 625648.5 + 32.k

-For instance, with 3000/01/24 , it yields k = 68473  whence 625648.5 + 32.k = 2816784.5 is the beginning of the time span.

-The number 0.2816784500000000D+07 is in the last set of the last file, namely ascp2999.422 ( just after 1143 1018 )

-DE421, DE423 & DE424 files are built similarly.

1°)  1018 Coefficients

-All the examples below use DE424 for the date 2012/08/29 at 16h41m37s
-Compute the beginning of the time-span as described above, you find 2456144.5

0.2456144500000000E+07 is located in the file ascp2000.424

-Then, copy and paste the 1018 coefficients ( ignore the 0.0000000000000000D+00 at the end ) in a text file
and replace all the "D" by "E" ( CTRL+H ,  D ,  E replace all ) because the powers of 10 are denoted E in HP calculators instead of D.

-Add " at the beginning of the characters and another " at the end.
-You'll get the following coefficients:

"0.2456144500000000E+07    0.2456176500000000E+07    0.5230245473150194E+08
0.7901492226564614E+05   -0.1253294853219849E+07   -0.3929302599214054E+05
0.1256355766691711E+04    0.1940197919027183E+03    0.1167052680462684E+02
0.2065008146200180E+00   -0.3272521939226505E-01   -0.3947617171021128E-02
-0.2086431979165916E-03    0.1019820542182935E-06    0.1089476955742306E-05
0.1046718674115404E-06   -0.8152214345563528E+07    0.1509424594495380E+08
0.1758707704804942E+06   -0.5379259586190485E+05   -0.2944236986123869E+04
-0.5847305464042022E+02    0.5890235944207363E+01    0.7474749829985006E+00
0.4055698625743757E-01    0.2353551734644063E-03   -0.1748759408854725E-03
-0.1772545177479823E-04   -0.7940454768970553E-06    0.1664943126263065E-07
-0.9784945727409156E+07    0.8055304594945066E+07    0.2238865396201792E+06
-0.2466122525935694E+05   -0.1703016755264991E+04   -0.5135083870223900E+02
0.1936491762513139E+01    0.3778784294483858E+00    0.2505754337355946E-01
0.5349926159803693E-03   -0.7178223210653387E-04   -0.9478929513526365E-05
-0.5369446559593277E-06   -0.2101044855771036E-08    0.4143555023160009E+08
-0.1110390047265020E+08   -0.1431086493732200E+07    0.2484649499359562E+05
0.7111006099102816E+04    0.2657233738466311E+03   -0.2195131396171676E+02
-0.3015796351751162E+01   -0.5719722962186264E-01    0.1685587203154621E-01
0.1580851261858007E-02   -0.1397394164116458E-04   -0.1309205319240619E-04
-0.8426874486866549E-06    0.2083341751680847E+08    0.1312335580571453E+08
-0.7415835453275503E+06   -0.9353219190399429E+05   -0.5256229229757961E+03
0.3987168560964299E+03    0.2728702202033360E+02   -0.6462643393134071E+00
-0.2201514493756180E+00   -0.1053576150233291E-01    0.8501324519225264E-03
0.1383359216066291E-03    0.3355354985121538E-05   -0.8400707905035988E-06
0.6826163170963192E+07    0.8161915361850729E+07   -0.2477682452069556E+06
-0.5253928141795718E+05   -0.1018033984647505E+04    0.1854377294830799E+03
0.1685210101709352E+02   -0.3255009045575431E-01   -0.1116707563253968E+00
-0.7375614511299600E-02    0.2902255233344634E-03    0.7534550412097491E-04
0.3149527841386331E-05   -0.3614226063451145E-06    0.1016133593724436E+08
-0.1933193090454715E+08   -0.4338835656203635E+06    0.1298001295083053E+06
0.2466757983579047E+04   -0.7335534457956543E+03   -0.1691573090996875E+02
0.5239074521076544E+01    0.1393400283469209E+00   -0.4278555512499855E-01
-0.1264754510534333E-02    0.3777922913382803E-03    0.1215537492709974E-04
-0.3529586970814489E-05    0.3798237434344045E+08    0.3303775902659188E+07
-0.1588664612880898E+07   -0.2327701403005185E+05    0.8542395613528426E+04
0.1429952356643542E+03   -0.5467006188086856E+02   -0.1109462552208411E+01
0.4218382630101629E+00    0.9786879151494902E-02   -0.3598895896128450E-02
-0.9290699011142592E-04    0.3261472945826400E-04    0.9296337430298500E-06
0.1923012448501853E+08    0.3769537730552072E+07   -0.8036521529211394E+06
-0.2589161659485363E+05    0.4307446248807610E+04    0.1524389816732625E+03
-0.2744997423076702E+02   -0.1135832929931110E+01    0.2108919059578845E+00
0.9663907840137093E-02   -0.1791338097534510E-02   -0.8879799311911166E-04
0.1616207150474463E-04    0.8624617411367403E-06   -0.2725383722886182E+08
-0.1693325941889565E+08    0.9272409498662842E+06    0.7279133150645504E+05
-0.6849298416801041E+04    0.1782392265641202E+02    0.3626274622785575E+02
-0.2379700246293420E+01   -0.8536801037678199E-01    0.2223239196523264E-01
-0.8792869505721620E-03   -0.1072975683466105E-03    0.1424844934133163E-04
-0.1547402430823969E-06    0.3251523340691639E+08   -0.8398205357430432E+07
-0.1155451715610103E+07    0.7766282840021038E+05    0.2034224827791911E+04
-0.4655550573594914E+03    0.1668182364494722E+02    0.1797127816584979E+01
-0.2256227170979757E+00    0.2408637162692061E-02    0.1478992068085484E-02
-0.1195553602016797E-03   -0.3175431787623599E-05    0.1173902640207963E-05
0.2018965141372477E+08   -0.2730143205254263E+07   -0.7133565828200192E+06
0.3393921588061675E+05    0.1796769717339646E+04   -0.2505391409666771E+03
0.5151474823180727E+01    0.1206716584763627E+01   -0.1116728115794770E+00
-0.1018363517991746E-02    0.8812131229071319E-03   -0.5273993583510374E-04
-0.3172779637750576E-05    0.6428442300453826E-06    0.1066655035346825E+09
-0.1442480412884796E+07   -0.1332720244379613E+07    0.2210302714558303E+04
0.1359291282707593E+04    0.6142206370989874E+00   -0.5121809940143853E+00
-0.2358389112358182E-02    0.7205238376208542E-04   -0.1056269182197196E-05
0.7638223704939518E+07    0.2176930061231765E+08   -0.9897054188852310E+05
-0.4503197497463441E+05    0.6110011093409234E+02    0.2690600318032329E+02
0.4228385781945723E-01   -0.6401897163277009E-02   -0.7184918540889604E-04
-0.1170563405827426E-05   -0.3332309029292385E+07    0.9886218874810327E+07
0.3980518268058248E+05   -0.2040103114652278E+05   -0.5852531694554706E+02
0.1206665428624310E+02    0.5145596535538682E-01   -0.2720572792051886E-02
-0.3823586413246579E-04   -0.9338043468616418E-06    0.9346158188037571E+08
-0.1163191879755292E+08   -0.1177512819377141E+07    0.2337162733859971E+05
0.1244690002790107E+04   -0.1219157375663270E+02   -0.5410473125995183E+00
0.7066535663017169E-03    0.1339738415101251E-03    0.1809116547364218E-05
0.4871256690050923E+08    0.1887355528540559E+08   -0.6157293168195649E+06
-0.3975963416906721E+05    0.5936010341684791E+03    0.2553449113839567E+02
-0.1648548932752315E+00   -0.8215404015693354E-02   -0.3800215468927150E-04
0.1624152723205545E-05    0.1598437526833040E+08    0.9228130826543039E+07
-0.2025208221113571E+06   -0.1936794974421764E+05    0.1883140901336847E+03
0.1226019787661502E+02   -0.3994106889391728E-01   -0.3740368207886280E-02
-0.2560838425974195E-04    0.6083029212672995E-06    0.1160685119984808E+09
0.1274368468090214E+08   -0.5315497532414097E+06   -0.1004371824405775E+05
0.1835411470974306E+03    0.2338323132100544E+01   -0.1372448438849866E-01
-0.5105541302655089E-03   -0.1284271476441609E-04    0.7544160437216364E-05
0.1503503701728379E-05    0.1086411025085318E-06   -0.7307399932786421E-07
-0.8838225604496841E+08    0.1446687145835585E+08    0.4022555919170267E+06
-0.1071593903624332E+05   -0.1578208572544338E+03    0.1890512076361849E+01
0.2264230799286477E-01    0.1579922390552478E-03    0.3718595839285788E-04
-0.1650008951171597E-06   -0.7507081242654544E-06   -0.2653520842972867E-06
-0.1309213627259336E-07   -0.3831937879362880E+08    0.6271458770786908E+07
0.1743852342376558E+06   -0.4645513414146452E+04   -0.6841865011948430E+02
0.8192320547341652E+00    0.9760362455759853E-02    0.9296476270676721E-04
0.2011421678933751E-04   -0.6823839451633849E-06   -0.4965330980816178E-06
-0.1362641254157875E-06   -0.3074731758253035E-08    0.1369593216888312E+09
0.8062533159892526E+07   -0.6329776009969632E+06   -0.6753684890528764E+04
0.2264091030170763E+03    0.1927331368259285E+01   -0.2217370401814369E-01
-0.6430931162278507E-03    0.7208342974068097E-04    0.1298487506614021E-04
-0.4000646670922585E-05   -0.3467616350466972E-06    0.1701672694346923E-06
-0.5666595475709766E+08    0.1713069866760813E+08    0.2598618662326685E+06
-0.1290741365975196E+05   -0.1142564289673975E+03    0.2463235501158048E+01
0.2343833778264532E-01    0.2323177605255429E-03    0.1828775481292037E-04
-0.1356364211248604E-04   -0.1022608656049648E-06    0.5606976100108009E-06
-0.1858269316794339E-07   -0.2457016929007053E+08    0.7426278942007105E+07
0.1126553614920699E+06   -0.5595569731693330E+04   -0.4953332537295758E+02
0.1067488156617393E+01    0.1022720937142542E-01    0.1337005833790341E-03
0.2094266288035116E-05   -0.7470981597153799E-05    0.3182991780318106E-06
0.2946686559782523E-06   -0.2459285856093012E-07   -0.1013288840410297E+09
0.3115834135923591E+08    0.5490324692549594E+06   -0.2443593191571185E+05
-0.5100542878571828E+03    0.9880791110344474E-01    0.2081820458066916E+00
0.5725368367054519E-02    0.3601238482507161E-04   -0.2606496344690010E-05
-0.1128349831615686E-06   -0.1847739544515020E+09   -0.1067263958302755E+08
0.1005163269457298E+07    0.1656423729283635E+05   -0.3022707915659633E+03
-0.1063531754012847E+02   -0.1364869103049377E+00    0.1892395151994203E-02
0.1250518214864762E-03    0.1966130962582513E-05    0.5763796127204672E-07
-0.8201884925671093E+08   -0.5736536026177466E+07    0.4462109230709131E+06
0.8257474777154273E+04   -0.1248687390377110E+03   -0.4880763231410534E+01
-0.6822374423572357E-01    0.7123248163631127E-03    0.5626653575263284E-04
0.1008032862076482E-05    0.3811760828309085E-07    0.3535582742417382E+09
-0.1615193812587457E+08   -0.5285132780744183E+05    0.4252505278583753E+03
0.4519317516898796E+00   -0.4698434992370511E-02    0.3184318723738612E-05
-0.3616685346220436E-06    0.6121287731141032E+09    0.8466049042940572E+07
-0.9146374387687014E+05   -0.1712202247364587E+03    0.1372125899310289E+01
0.3675792002590621E-03   -0.1422206100023062E-04   -0.1339889170553424E-06
0.2537546969927654E+09    0.4022016895982264E+07   -0.3791713448537706E+05
-0.8374306985732909E+02    0.5771399711421581E+00    0.2716358549106815E-03
-0.6211670567735649E-05   -0.8533213907030610E-09   -0.1262183251776217E+10
0.5970448493360388E+07    0.2573896413876962E+05   -0.2595390210821129E+02
-0.3253102621684434E-01    0.3981043804188231E-04    0.1204432260775522E-06
-0.6958796499463700E+09   -0.1061484961830910E+08    0.1419047114198518E+05
0.3293784891885253E+02   -0.3350913564797257E-01   -0.1051890876816737E-04
0.7907440407300758E-07   -0.2330949437747856E+09   -0.4641469263102078E+07
0.4752912635801525E+04    0.1472274193189846E+02   -0.1243728578158865E-01
-0.6011814214413740E-05    0.2244011510517281E-07    0.2984989687389182E+10
-0.1042963120726354E+07   -0.7007945091025635E+04    0.2813973699372320E+00
0.1156749601257825E-02   -0.2038325683576532E-07    0.2998234096982999E+09
0.8169719094471670E+07   -0.7032088599393169E+03   -0.3212406055733868E+01
0.1104915464655303E-04    0.3080599298033161E-06    0.8909557353640683E+08
0.3592874805532602E+07   -0.2089007387988221E+03   -0.1410838367004682E+01
-0.1167564206465967E-04    0.1303058908843467E-06    0.3944277604040891E+10
0.3531671078068776E+07   -0.2771291970198418E+04   -0.4333670604353987E+00
0.1537694014815202E-03    0.4357260381869015E-08   -0.1943603584728840E+10
0.6187815965364382E+07    0.1365901147378689E+04   -0.7159858404575268E+00
-0.8355637649275957E-04    0.2099417624889305E-07   -0.8937265919280205E+09
0.2444779634176255E+07    0.6280693592443588E+03   -0.2822790914271991E+00
-0.3805787662066297E-04    0.1639966740711643E-07    0.7011934688971796E+09
0.7575833756670580E+07   -0.3951555867333577E+03   -0.6559991841760345E+00
0.1714111646198903E-03    0.1489490682186768E-07   -0.4497681687835693E+10
0.4861562019817765E+06    0.2534040975565886E+04   -0.4013879756182998E+00
-0.1126511737270427E-03    0.5212762524215709E-07   -0.1614854693306324E+10
-0.2130856643026206E+07    0.9098180910841293E+03    0.7234188227139654E-01
-0.8598510559675119E-04    0.9505325287100872E-08    0.3661000735927133E+06
-0.3129081751004732E+05   -0.1827726006793254E+05    0.4225071023261218E+03
0.5949508291677557E+02   -0.2455775610931454E+01    0.7500342203147499E-01
0.6235186052311870E-02   -0.8556814175270958E-03    0.2305615452298887E-04
0.1533945458663011E-05   -0.2485733569316785E-06    0.1098599887114775E-07
0.7305545163125948E+05    0.1537052404406675E+06   -0.3708051225561290E+04
-0.1215917203742875E+04    0.3150288767422156E+02    0.1251813445674948E+01
-0.1390222819741968E+00    0.1042104867673766E-01    0.7961184133391296E-04
-0.4400530815264024E-04    0.2801029818003587E-05   -0.2173383833911711E-07
-0.1398485439080749E-07    0.5867500918584621E+05    0.5652868902806630E+05
-0.2968626570078590E+04   -0.4309342761014242E+03    0.1721127609436052E+02
0.2679704616495535E+00   -0.4729671061737215E-01    0.4544827756708215E-02
-0.4223128574500831E-04   -0.1497242979257932E-04    0.1210067471570651E-05
-0.2951763596678010E-07   -0.4451237498240675E-08    0.1827857685183025E+06
-0.1440362800705809E+06   -0.8747402520985414E+04    0.1093994156080625E+04
0.3015058572691945E+02   -0.8134396029379486E+00   -0.8399309918105531E-03
-0.7898071360237379E-02   -0.1522638480878511E-03    0.1164379371962721E-04
0.3475066870195882E-06    0.8286788475490251E-07    0.8234673642973141E-10
0.3114439996564811E+06    0.7543896483897664E+05   -0.1478014855563583E+05
-0.6008638354289375E+03    0.4438674773513370E+02    0.8489530232561495E+00
0.6432140516689813E-01    0.2034584337840075E-02   -0.4053916255654879E-03
-0.7886306428497389E-05   -0.4414311155701982E-06    0.7835283749215584E-08
0.5573013036222024E-08    0.1350445984807707E+06    0.1697246155661187E+05
-0.6407541221662508E+04   -0.1376607664226572E+03    0.1954288552302902E+02
0.2499259232314668E+00    0.2466790512121111E-01    0.1237821860498681E-03
-0.1681249088612827E-03   -0.2010332624169791E-05   -0.1413461197830954E-06
0.9889566117980956E-08    0.2142485140836702E-08   -0.1289626963209099E+06
-0.1549363201208462E+06    0.6520331615803590E+04    0.1367176349596608E+04
-0.4605281519856153E+01   -0.3411976045467562E+01   -0.1770164935005849E+00
0.1298079012784104E-02    0.9418948214188950E-03    0.3528181856948960E-04
-0.2248438242588989E-05   -0.2920862824578919E-06   -0.4242266450419010E-08
0.3309510799578793E+06   -0.5775956759576136E+05   -0.1691637484386475E+05
0.3181987419817834E+03    0.7259815943882516E+02    0.1331594991353595E+01
-0.1000631437230280E+00   -0.1357358054380692E-01   -0.2514210799436452E-03
0.4717740174828264E-04    0.3335016298767340E-05   -0.3969424782391840E-07
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0.1906622447515008E-03   -0.3104756786553820E-04   -0.3318831517879336E-05
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0.1742042774069454E-09   -0.1825510291096042E-10   -0.4123673454224310E-11
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0.5119765154824824E-11   -0.2035962363209002E-04   -0.1493954859174803E-06
0.2566863948543266E-06    0.6190972671188500E-07   -0.2643546953450523E-07
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0.1432594592982743E-03   -0.6535966946992410E-04   -0.3834239823955287E-05
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0.3622826783517814E+04    0.9192314862359342E+00   -0.3812125676835298E-04
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0.1158040859031368E-05   -0.7182925247432473E-07   -0.3084996506966047E-07
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0.2211867031993893E-05   -0.3485353632320250E-06   -0.8243648951182942E-07
0.5338461689500014E-09    0.1707772483619627E-08    0.1436917994309938E-09
0.3624665728918126E+04    0.9199675876992941E+00    0.2503790519381089E-03
0.1776225520785399E-04   -0.6434229862593272E-05   -0.1052976385275265E-05
0.6246575601935069E-07    0.2798541264651049E-07    0.1180540107373283E-08
-0.4648015695716446E-09    0.5649942577240461E-01   -0.1150075191650946E-02
0.1680329148217113E-03    0.4550374616333872E-04   -0.8843933704147856E-05
-0.8509316882963572E-06    0.2790642046107786E-06    0.1229367156332337E-07
-0.5724118657951199E-08   -0.1182609493862763E-09    0.4226035336446058E+00
0.2988754995404324E-03    0.1049813732627915E-03   -0.1724887104733408E-04
-0.2660836574271362E-05    0.6795089061536113E-06    0.4307858999117768E-07
-0.1715100405810751E-07   -0.5481318055369453E-09    0.2794837550513186E-09
0.3626506921561757E+04    0.9208606631756032E+00   -0.1504655256801448E-03
-0.3979575957717319E-04    0.8023817780326130E-05    0.7634508846915149E-06
-0.2546077181084635E-06   -0.1138837095720773E-07    0.5244296231338590E-08
0.1139763276067164E-09    0.5585788247358223E-01    0.4474495417557853E-03
0.1268441292586789E-03   -0.1402627969086186E-04    0.2001122520961554E-05
-0.3022359554039851E-06   -0.1123847558288252E-06    0.1771948966202929E-07
0.8834941904432827E-09   -0.4133417797868971E-09    0.4234041170366454E+00
0.3678578699893051E-03   -0.5119094118297494E-04   -0.2699140220643110E-05
0.1150465179379818E-06   -0.2736213253618040E-06    0.3649992653707743E-07
0.5358554956120766E-08   -0.1186363970052293E-08    0.1091326626563041E-10
0.3628347196037978E+04    0.9194765363571894E+00   -0.1048472512633549E-03
0.1197706558170332E-04   -0.2020321069328077E-05    0.2859416354846712E-06
0.1040846834595151E-06   -0.1635135035390533E-07   -0.8171530799563627E-09
0.3813432517082373E-09"

-The 2 first numbers are the Julian date of earliest data in record and the Julian date of latest data in record.
-The meaning of the other coefficients are given at the bottom of the HEADER files:

Mer  Ven  EMB  Mar  Jup   Sat    Ura   Nep   Plu  Moon  Sun   Nut   Libr    ( EMB = Earth-Moon barycenter )

3    171   231   309   342   366   387   405   423   441   753   819   899
14    10     13     11      8       7       6       6       6      13     11     10     10
4      2       2       1       1       1       1       1       1       8       2       4       4

-The 1st row is the position of the first coefficient corresponding to a specific item.
-The 2nd row = the number of coefficients in the Chebyshev polynomial per component.
-The 3rd row = the number of complete sets of coefficients in each data record for the ith item.
-It is also the number by which 32 days must be divided to get the interval of time DT in the Chebyshev representation.

-For example, the coefficients of the Moon starts at the 441st position.
-13 coefficients are used for each cartesian coordinate X , Y , Z.
-For the Moon, DT = 32/8 = 4 days in the formula   x = -1 + 2(t-t0)/DT      ( -1 <= x <= +1 )

y = a0 + a1.T1(x) + ....... + an.Tn(x)    where  y(t) is a coordinate at a given instant t belonging to the interval  [ t0 , t0 + DT ]

( -1 <= x <= +1 )    cf "Orthogonal Polynomials for the HP-41" §5-b)

-So, there are 13x3x8 = 312 coefficients ( from the 441st one to the 752nd one ) to calculate the coordinates of the Moon for each time-span of 32 days.

2°)  Hepax Data File of 1017 Coefficients

-The second coefficient above  (   0.2456176500000000E+07  )  may be deleted since it's simply 32 + the 1st coefficient.
-Now, you have to transfer these 1017 numbers into your HP-41: it's the difficult part of the job !

-You can of course type the 1017 coefficients and 1017 times HSAVEX, but it is particularly awkward, with many risks of errors !

-I don't know if there is an easy way to do that but here is a method to transfer them into V41, provided you have an HP-48 ( or HP-49/50 )

1°) Transfer the text file of the paragraph above ( after deleting the 2nd coefficient ) to your HP-48 ( ascii mode )
2°) Press OBJ->  to put these 1017 numbers in the stack
3°) Create a list of 1017 numbers ( 1017 ->LIST ) and store it in a variable, say  'L'
( at this step, it's much easier to use an HP-48 program but let's continue... )

4°) Execute the following routine

<<  9  SCI  """"  1  1017
FOR k  L  k  DUP  1  DISP  GET  +
"
Z
"  +
NEXT  STD
>>                                        ( 77 bytes / # 61260d  with an HP-48 )

5°) You get a long alpha string ( 17436 characters ). Transfer it to your PC ( ascii mode )
6°)  Replace all the "Z" by "XROM 07,33"  ( CTRL+H   Z   XROM 07,33   replace all )
7°)  Split the obtained text file in several parts and add several global LBLs and ENDs so that each program does not exceed 2237 bytes.

-An example is given below with 11 LBLs ( LBL "DAT1"  LBL "DAT2" ..............  LBL "DAT11" )

8°)  Create an HEPAX DATA file of 1017 numbers in V41, for instance   alpha  DE424  alpha  1017  XEQ "HCRFLD"
9°)  Use HP41UC to create 11 .raw files from the 11 .txt files.
10°)  Transfer them and execute them successively.

-All the 1017 numbers will be - at last - in your V41.

Notes:

- XROM 07,33 corresponds to  HSAVEX
-If it is difficult to transfer the long alpha string of 17436 characters from your HP-48 to your PC ( step 5°) ), split it in several parts.

LBL "DAT1"
2.456144500E6
XROM 07,33
5.230245473E7
XROM 07,33
7.901492227E4
XROM 07,33
-1.253294853E6
XROM 07,33
-3.929302599E4
XROM 07,33
1.256355767E3
XROM 07,33
1.940197919E2
XROM 07,33
1.167052680E1
XROM 07,33
2.065008146E-1
XROM 07,33
-3.272521939E-2
XROM 07,33
-3.947617171E-3
XROM 07,33
-2.086431979E-4
XROM 07,33
1.019820542E-7
XROM 07,33
1.089476956E-6
XROM 07,33
1.046718674E-7
XROM 07,33
-8.152214346E6
XROM 07,33
1.509424595E7
XROM 07,33
1.758707705E5
XROM 07,33
-5.379259586E4
XROM 07,33
-2.944236986E3
XROM 07,33
-5.847305464E1
XROM 07,33
5.890235944E0
XROM 07,33
7.474749830E-1
XROM 07,33
4.055698626E-2
XROM 07,33
2.353551735E-4
XROM 07,33
-1.748759409E-4
XROM 07,33
-1.772545177E-5
XROM 07,33
-7.940454769E-7
XROM 07,33
1.664943126E-8
XROM 07,33
-9.784945727E6
XROM 07,33
8.055304595E6
XROM 07,33
2.238865396E5
XROM 07,33
-2.466122526E4
XROM 07,33
-1.703016755E3
XROM 07,33
-5.135083870E1
XROM 07,33
1.936491763E0
XROM 07,33
3.778784294E-1
XROM 07,33
2.505754337E-2
XROM 07,33
5.349926160E-4
XROM 07,33
-7.178223211E-5
XROM 07,33
-9.478929514E-6
XROM 07,33
-5.369446560E-7
XROM 07,33
-2.101044856E-9
XROM 07,33
4.143555023E7
XROM 07,33
-1.110390047E7
XROM 07,33
-1.431086494E6
XROM 07,33
2.484649499E4
XROM 07,33
7.111006099E3
XROM 07,33
2.657233738E2
XROM 07,33
-2.195131396E1
XROM 07,33
-3.015796352E0
XROM 07,33
-5.719722962E-2
XROM 07,33
1.685587203E-2
XROM 07,33
1.580851262E-3
XROM 07,33
-1.397394164E-5
XROM 07,33
-1.309205319E-5
XROM 07,33
-8.426874487E-7
XROM 07,33
2.083341752E7
XROM 07,33
1.312335581E7
XROM 07,33
-7.415835453E5
XROM 07,33
-9.353219190E4
XROM 07,33
-5.256229230E2
XROM 07,33
3.987168561E2
XROM 07,33
2.728702202E1
XROM 07,33
-6.462643393E-1
XROM 07,33
-2.201514494E-1
XROM 07,33
-1.053576150E-2
XROM 07,33
8.501324519E-4
XROM 07,33
1.383359216E-4
XROM 07,33
3.355354985E-6
XROM 07,33
-8.400707905E-7
XROM 07,33
6.826163171E6
XROM 07,33
8.161915362E6
XROM 07,33
-2.477682452E5
XROM 07,33
-5.253928142E4
XROM 07,33
-1.018033985E3
XROM 07,33
1.854377295E2
XROM 07,33
1.685210102E1
XROM 07,33
-3.255009046E-2
XROM 07,33
-1.116707563E-1
XROM 07,33
-7.375614511E-3
XROM 07,33
2.902255233E-4
XROM 07,33
7.534550412E-5
XROM 07,33
3.149527841E-6
XROM 07,33
-3.614226063E-7
XROM 07,33
1.016133594E7
XROM 07,33
-1.933193090E7
XROM 07,33
-4.338835656E5
XROM 07,33
1.298001295E5
XROM 07,33
2.466757984E3
XROM 07,33
-7.335534458E2
XROM 07,33
-1.691573091E1
XROM 07,33
5.239074521E0
XROM 07,33
1.393400283E-1
XROM 07,33
-4.278555513E-2
XROM 07,33
-1.264754511E-3
XROM 07,33
3.777922913E-4
XROM 07,33
1.215537493E-5
XROM 07,33
-3.529586971E-6
XROM 07,33
3.798237434E7
XROM 07,33
3.303775903E6
XROM 07,33
-1.588664613E6
XROM 07,33
-2.327701403E4
XROM 07,33
8.542395614E3
XROM 07,33
1.429952357E2
XROM 07,33
-5.467006188E1
XROM 07,33
END

LBL "DAT2"
-1.109462552E0
XROM 07,33
4.218382630E-1
XROM 07,33
9.786879151E-3
XROM 07,33
-3.598895896E-3
XROM 07,33
-9.290699011E-5
XROM 07,33
3.261472946E-5
XROM 07,33
9.296337430E-7
XROM 07,33
1.923012449E7
XROM 07,33
3.769537731E6
XROM 07,33
-8.036521529E5
XROM 07,33
-2.589161659E4
XROM 07,33
4.307446249E3
XROM 07,33
1.524389817E2
XROM 07,33
-2.744997423E1
XROM 07,33
-1.135832930E0
XROM 07,33
2.108919060E-1
XROM 07,33
9.663907840E-3
XROM 07,33
-1.791338098E-3
XROM 07,33
-8.879799312E-5
XROM 07,33
1.616207150E-5
XROM 07,33
8.624617411E-7
XROM 07,33
-2.725383723E7
XROM 07,33
-1.693325942E7
XROM 07,33
9.272409499E5
XROM 07,33
7.279133151E4
XROM 07,33
-6.849298417E3
XROM 07,33
1.782392266E1
XROM 07,33
3.626274623E1
XROM 07,33
-2.379700246E0
XROM 07,33
-8.536801038E-2
XROM 07,33
2.223239197E-2
XROM 07,33
-8.792869506E-4
XROM 07,33
-1.072975683E-4
XROM 07,33
1.424844934E-5
XROM 07,33
-1.547402431E-7
XROM 07,33
3.251523341E7
XROM 07,33
-8.398205357E6
XROM 07,33
-1.155451716E6
XROM 07,33
7.766282840E4
XROM 07,33
2.034224828E3
XROM 07,33
-4.655550574E2
XROM 07,33
1.668182364E1
XROM 07,33
1.797127817E0
XROM 07,33
-2.256227171E-1
XROM 07,33
2.408637163E-3
XROM 07,33
1.478992068E-3
XROM 07,33
-1.195553602E-4
XROM 07,33
-3.175431788E-6
XROM 07,33
1.173902640E-6
XROM 07,33
2.018965141E7
XROM 07,33
-2.730143205E6
XROM 07,33
-7.133565828E5
XROM 07,33
3.393921588E4
XROM 07,33
1.796769717E3
XROM 07,33
-2.505391410E2
XROM 07,33
5.151474823E0
XROM 07,33
1.206716585E0
XROM 07,33
-1.116728116E-1
XROM 07,33
-1.018363518E-3
XROM 07,33
8.812131229E-4
XROM 07,33
-5.273993584E-5
XROM 07,33
-3.172779638E-6
XROM 07,33
6.428442300E-7
XROM 07,33
1.066655035E8
XROM 07,33
-1.442480413E6
XROM 07,33
-1.332720244E6
XROM 07,33
2.210302715E3
XROM 07,33
1.359291283E3
XROM 07,33
6.142206371E-1
XROM 07,33
-5.121809940E-1
XROM 07,33
-2.358389112E-3
XROM 07,33
7.205238376E-5
XROM 07,33
-1.056269182E-6
XROM 07,33
7.638223705E6
XROM 07,33
2.176930061E7
XROM 07,33
-9.897054189E4
XROM 07,33
-4.503197497E4
XROM 07,33
6.110011093E1
XROM 07,33
2.690600318E1
XROM 07,33
4.228385782E-2
XROM 07,33
-6.401897163E-3
XROM 07,33
-7.184918541E-5
XROM 07,33
-1.170563406E-6
XROM 07,33
-3.332309029E6
XROM 07,33
9.886218875E6
XROM 07,33
3.980518268E4
XROM 07,33
-2.040103115E4
XROM 07,33
-5.852531695E1
XROM 07,33
1.206665429E1
XROM 07,33
5.145596536E-2
XROM 07,33
-2.720572792E-3
XROM 07,33
-3.823586413E-5
XROM 07,33
-9.338043469E-7
XROM 07,33
9.346158188E7
XROM 07,33
-1.163191880E7
XROM 07,33
-1.177512819E6
XROM 07,33
END

LBL "DAT3"
2.337162734E4
XROM 07,33
1.244690003E3
XROM 07,33
-1.219157376E1
XROM 07,33
-5.410473126E-1
XROM 07,33
7.066535663E-4
XROM 07,33
1.339738415E-4
XROM 07,33
1.809116547E-6
XROM 07,33
4.871256690E7
XROM 07,33
1.887355529E7
XROM 07,33
-6.157293168E5
XROM 07,33
-3.975963417E4
XROM 07,33
5.936010342E2
XROM 07,33
2.553449114E1
XROM 07,33
-1.648548933E-1
XROM 07,33
-8.215404016E-3
XROM 07,33
-3.800215469E-5
XROM 07,33
1.624152723E-6
XROM 07,33
1.598437527E7
XROM 07,33
9.228130827E6
XROM 07,33
-2.025208221E5
XROM 07,33
-1.936794974E4
XROM 07,33
1.883140901E2
XROM 07,33
1.226019788E1
XROM 07,33
-3.994106889E-2
XROM 07,33
-3.740368208E-3
XROM 07,33
-2.560838426E-5
XROM 07,33
6.083029213E-7
XROM 07,33
1.160685120E8
XROM 07,33
1.274368468E7
XROM 07,33
-5.315497532E5
XROM 07,33
-1.004371824E4
XROM 07,33
1.835411471E2
XROM 07,33
2.338323132E0
XROM 07,33
-1.372448439E-2
XROM 07,33
-5.105541303E-4
XROM 07,33
-1.284271476E-5
XROM 07,33
7.544160437E-6
XROM 07,33
1.503503702E-6
XROM 07,33
1.086411025E-7
XROM 07,33
-7.307399933E-8
XROM 07,33
-8.838225605E7
XROM 07,33
1.446687146E7
XROM 07,33
4.022555919E5
XROM 07,33
-1.071593904E4
XROM 07,33
-1.578208573E2
XROM 07,33
1.890512076E0
XROM 07,33
2.264230799E-2
XROM 07,33
1.579922391E-4
XROM 07,33
3.718595839E-5
XROM 07,33
-1.650008951E-7
XROM 07,33
-7.507081243E-7
XROM 07,33
-2.653520843E-7
XROM 07,33
-1.309213627E-8
XROM 07,33
-3.831937879E7
XROM 07,33
6.271458771E6
XROM 07,33
1.743852342E5
XROM 07,33
-4.645513414E3
XROM 07,33
-6.841865012E1
XROM 07,33
8.192320547E-1
XROM 07,33
9.760362456E-3
XROM 07,33
9.296476271E-5
XROM 07,33
2.011421679E-5
XROM 07,33
-6.823839452E-7
XROM 07,33
-4.965330981E-7
XROM 07,33
-1.362641254E-7
XROM 07,33
-3.074731758E-9
XROM 07,33
1.369593217E8
XROM 07,33
8.062533160E6
XROM 07,33
-6.329776010E5
XROM 07,33
-6.753684891E3
XROM 07,33
2.264091030E2
XROM 07,33
1.927331368E0
XROM 07,33
-2.217370402E-2
XROM 07,33
-6.430931162E-4
XROM 07,33
7.208342974E-5
XROM 07,33
1.298487507E-5
XROM 07,33
-4.000646671E-6
XROM 07,33
-3.467616350E-7
XROM 07,33
1.701672694E-7
XROM 07,33
-5.666595476E7
XROM 07,33
1.713069867E7
XROM 07,33
2.598618662E5
XROM 07,33
-1.290741366E4
XROM 07,33
-1.142564290E2
XROM 07,33
2.463235501E0
XROM 07,33
2.343833778E-2
XROM 07,33
2.323177605E-4
XROM 07,33
1.828775481E-5
XROM 07,33
-1.356364211E-5
XROM 07,33
-1.022608656E-7
XROM 07,33
5.606976100E-7
XROM 07,33
-1.858269317E-8
XROM 07,33
-2.457016929E7
XROM 07,33
7.426278942E6
XROM 07,33
1.126553615E5
XROM 07,33
-5.595569732E3
XROM 07,33
END

LBL "DAT4"
-4.953332537E1
XROM 07,33
1.067488157E0
XROM 07,33
1.022720937E-2
XROM 07,33
1.337005834E-4
XROM 07,33
2.094266288E-6
XROM 07,33
-7.470981597E-6
XROM 07,33
3.182991780E-7
XROM 07,33
2.946686560E-7
XROM 07,33
-2.459285856E-8
XROM 07,33
-1.013288840E8
XROM 07,33
3.115834136E7
XROM 07,33
5.490324693E5
XROM 07,33
-2.443593192E4
XROM 07,33
-5.100542879E2
XROM 07,33
9.880791110E-2
XROM 07,33
2.081820458E-1
XROM 07,33
5.725368367E-3
XROM 07,33
3.601238483E-5
XROM 07,33
-2.606496345E-6
XROM 07,33
-1.128349832E-7
XROM 07,33
-1.847739545E8
XROM 07,33
-1.067263958E7
XROM 07,33
1.005163269E6
XROM 07,33
1.656423729E4
XROM 07,33
-3.022707916E2
XROM 07,33
-1.063531754E1
XROM 07,33
-1.364869103E-1
XROM 07,33
1.892395152E-3
XROM 07,33
1.250518215E-4
XROM 07,33
1.966130963E-6
XROM 07,33
5.763796127E-8
XROM 07,33
-8.201884926E7
XROM 07,33
-5.736536026E6
XROM 07,33
4.462109231E5
XROM 07,33
8.257474777E3
XROM 07,33
-1.248687390E2
XROM 07,33
-4.880763231E0
XROM 07,33
-6.822374424E-2
XROM 07,33
7.123248164E-4
XROM 07,33
5.626653575E-5
XROM 07,33
1.008032862E-6
XROM 07,33
3.811760828E-8
XROM 07,33
3.535582742E8
XROM 07,33
-1.615193813E7
XROM 07,33
-5.285132781E4
XROM 07,33
4.252505279E2
XROM 07,33
4.519317517E-1
XROM 07,33
-4.698434992E-3
XROM 07,33
3.184318724E-6
XROM 07,33
-3.616685346E-7
XROM 07,33
6.121287731E8
XROM 07,33
8.466049043E6
XROM 07,33
-9.146374388E4
XROM 07,33
-1.712202247E2
XROM 07,33
1.372125899E0
XROM 07,33
3.675792003E-4
XROM 07,33
-1.422206100E-5
XROM 07,33
-1.339889171E-7
XROM 07,33
2.537546970E8
XROM 07,33
4.022016896E6
XROM 07,33
-3.791713449E4
XROM 07,33
-8.374306986E1
XROM 07,33
5.771399711E-1
XROM 07,33
2.716358549E-4
XROM 07,33
-6.211670568E-6
XROM 07,33
-8.533213907E-10
XROM 07,33
-1.262183252E9
XROM 07,33
5.970448493E6
XROM 07,33
2.573896414E4
XROM 07,33
-2.595390211E1
XROM 07,33
-3.253102622E-2
XROM 07,33
3.981043804E-5
XROM 07,33
1.204432261E-7
XROM 07,33
-6.958796499E8
XROM 07,33
-1.061484962E7
XROM 07,33
1.419047114E4
XROM 07,33
3.293784892E1
XROM 07,33
-3.350913565E-2
XROM 07,33
-1.051890877E-5
XROM 07,33
7.907440407E-8
XROM 07,33
-2.330949438E8
XROM 07,33
-4.641469263E6
XROM 07,33
4.752912636E3
XROM 07,33
1.472274193E1
XROM 07,33
-1.243728578E-2
XROM 07,33
-6.011814214E-6
XROM 07,33
2.244011511E-8
XROM 07,33
2.984989687E9
XROM 07,33
-1.042963121E6
XROM 07,33
-7.007945091E3
XROM 07,33
2.813973699E-1
XROM 07,33
1.156749601E-3
XROM 07,33
-2.038325684E-8
XROM 07,33
2.998234097E8
XROM 07,33
8.169719094E6
XROM 07,33
-7.032088599E2
XROM 07,33
END

LBL "DAT5"
-3.212406056E0
XROM 07,33
1.104915465E-5
XROM 07,33
3.080599298E-7
XROM 07,33
8.909557354E7
XROM 07,33
3.592874806E6
XROM 07,33
-2.089007388E2
XROM 07,33
-1.410838367E0
XROM 07,33
-1.167564206E-5
XROM 07,33
1.303058909E-7
XROM 07,33
3.944277604E9
XROM 07,33
3.531671078E6
XROM 07,33
-2.771291970E3
XROM 07,33
-4.333670604E-1
XROM 07,33
1.537694015E-4
XROM 07,33
4.357260382E-9
XROM 07,33
-1.943603585E9
XROM 07,33
6.187815965E6
XROM 07,33
1.365901147E3
XROM 07,33
-7.159858405E-1
XROM 07,33
-8.355637649E-5
XROM 07,33
2.099417625E-8
XROM 07,33
-8.937265919E8
XROM 07,33
2.444779634E6
XROM 07,33
6.280693592E2
XROM 07,33
-2.822790914E-1
XROM 07,33
-3.805787662E-5
XROM 07,33
1.639966741E-8
XROM 07,33
7.011934689E8
XROM 07,33
7.575833757E6
XROM 07,33
-3.951555867E2
XROM 07,33
-6.559991842E-1
XROM 07,33
1.714111646E-4
XROM 07,33
1.489490682E-8
XROM 07,33
-4.497681688E9
XROM 07,33
4.861562020E5
XROM 07,33
2.534040976E3
XROM 07,33
-4.013879756E-1
XROM 07,33
-1.126511737E-4
XROM 07,33
5.212762524E-8
XROM 07,33
-1.614854693E9
XROM 07,33
-2.130856643E6
XROM 07,33
9.098180911E2
XROM 07,33
7.234188227E-2
XROM 07,33
-8.598510560E-5
XROM 07,33
9.505325287E-9
XROM 07,33
3.661000736E5
XROM 07,33
-3.129081751E4
XROM 07,33
-1.827726007E4
XROM 07,33
4.225071023E2
XROM 07,33
5.949508292E1
XROM 07,33
-2.455775611E0
XROM 07,33
7.500342203E-2
XROM 07,33
6.235186052E-3
XROM 07,33
-8.556814175E-4
XROM 07,33
2.305615452E-5
XROM 07,33
1.533945459E-6
XROM 07,33
-2.485733569E-7
XROM 07,33
1.098599887E-8
XROM 07,33
7.305545163E4
XROM 07,33
1.537052404E5
XROM 07,33
-3.708051226E3
XROM 07,33
-1.215917204E3
XROM 07,33
3.150288767E1
XROM 07,33
1.251813446E0
XROM 07,33
-1.390222820E-1
XROM 07,33
1.042104868E-2
XROM 07,33
7.961184133E-5
XROM 07,33
-4.400530815E-5
XROM 07,33
2.801029818E-6
XROM 07,33
-2.173383834E-8
XROM 07,33
-1.398485439E-8
XROM 07,33
5.867500919E4
XROM 07,33
5.652868903E4
XROM 07,33
-2.968626570E3
XROM 07,33
-4.309342761E2
XROM 07,33
1.721127609E1
XROM 07,33
2.679704617E-1
XROM 07,33
-4.729671062E-2
XROM 07,33
4.544827757E-3
XROM 07,33
-4.223128575E-5
XROM 07,33
-1.497242979E-5
XROM 07,33
1.210067472E-6
XROM 07,33
-2.951763597E-8
XROM 07,33
-4.451237498E-9
XROM 07,33
1.827857685E5
XROM 07,33
-1.440362801E5
XROM 07,33
-8.747402521E3
XROM 07,33
1.093994156E3
XROM 07,33
3.015058573E1
XROM 07,33
-8.134396029E-1
XROM 07,33
-8.399309918E-4
XROM 07,33
-7.898071360E-3
XROM 07,33
-1.522638481E-4
XROM 07,33
1.164379372E-5
XROM 07,33
3.475066870E-7
XROM 07,33
8.286788475E-8
XROM 07,33
END

LBL "DAT6"
8.234673643E-11
XROM 07,33
3.114439997E5
XROM 07,33
7.543896484E4
XROM 07,33
-1.478014856E4
XROM 07,33
-6.008638354E2
XROM 07,33
4.438674774E1
XROM 07,33
8.489530233E-1
XROM 07,33
6.432140517E-2
XROM 07,33
2.034584338E-3
XROM 07,33
-4.053916256E-4
XROM 07,33
-7.886306429E-6
XROM 07,33
-4.414311156E-7
XROM 07,33
7.835283749E-9
XROM 07,33
5.573013036E-9
XROM 07,33
1.350445985E5
XROM 07,33
1.697246156E4
XROM 07,33
-6.407541222E3
XROM 07,33
-1.376607664E2
XROM 07,33
1.954288552E1
XROM 07,33
2.499259232E-1
XROM 07,33
2.466790512E-2
XROM 07,33
1.237821861E-4
XROM 07,33
-1.681249089E-4
XROM 07,33
-2.010332624E-6
XROM 07,33
-1.413461198E-7
XROM 07,33
9.889566118E-9
XROM 07,33
2.142485141E-9
XROM 07,33
-1.289626963E5
XROM 07,33
-1.549363201E5
XROM 07,33
6.520331616E3
XROM 07,33
1.367176350E3
XROM 07,33
-4.605281520E0
XROM 07,33
-3.411976045E0
XROM 07,33
-1.770164935E-1
XROM 07,33
1.298079013E-3
XROM 07,33
9.418948214E-4
XROM 07,33
3.528181857E-5
XROM 07,33
-2.248438243E-6
XROM 07,33
-2.920862825E-7
XROM 07,33
-4.242266450E-9
XROM 07,33
3.309510800E5
XROM 07,33
-5.775956760E4
XROM 07,33
-1.691637484E4
XROM 07,33
3.181987420E2
XROM 07,33
7.259815944E1
XROM 07,33
1.331594991E0
XROM 07,33
-1.000631437E-1
XROM 07,33
-1.357358054E-2
XROM 07,33
-2.514210799E-4
XROM 07,33
4.717740175E-5
XROM 07,33
3.335016299E-6
XROM 07,33
-3.969424782E-8
XROM 07,33
-1.979076376E-8
XROM 07,33
1.166076668E5
XROM 07,33
-3.503276264E4
XROM 07,33
-5.939257942E3
XROM 07,33
2.365609809E2
XROM 07,33
2.733468231E1
XROM 07,33
2.219374713E-1
XROM 07,33
-5.283522133E-2
XROM 07,33
-5.081544027E-3
XROM 07,33
-1.765045116E-5
XROM 07,33
2.098029601E-5
XROM 07,33
1.087976604E-6
XROM 07,33
-3.948904524E-8
XROM 07,33
-7.926987142E-9
XROM 07,33
-3.397693564E5
XROM 07,33
-4.475624788E4
XROM 07,33
1.967818854E4
XROM 07,33
5.950063584E2
XROM 07,33
-9.376329246E1
XROM 07,33
-3.768029507E0
XROM 07,33
2.402154732E-1
XROM 07,33
1.833470249E-2
XROM 07,33
-8.317833875E-4
XROM 07,33
-8.831683109E-5
XROM 07,33
4.494200228E-6
XROM 07,33
5.219570771E-7
XROM 07,33
-2.469327256E-8
XROM 07,33
1.065535339E5
XROM 07,33
-1.575119020E5
XROM 07,33
-6.007951064E3
XROM 07,33
1.443040320E3
XROM 07,33
4.851889772E1
XROM 07,33
-4.456315417E0
XROM 07,33
-2.570269925E-1
XROM 07,33
1.173410626E-2
XROM 07,33
1.192541321E-3
XROM 07,33
-5.362693078E-5
XROM 07,33
-6.326062787E-6
XROM 07,33
3.007512430E-7
XROM 07,33
4.008977121E-8
XROM 07,33
1.307804966E4
XROM 07,33
-6.407574937E4
XROM 07,33
-6.652719680E2
XROM 07,33
6.014373495E2
XROM 07,33
END

LBL "DAT7"
1.068344070E1
XROM 07,33
-2.016423391E0
XROM 07,33
-7.806664014E-2
XROM 07,33
6.015284466E-3
XROM 07,33
3.865728896E-4
XROM 07,33
-2.788573669E-5
XROM 07,33
-2.045701126E-6
XROM 07,33
1.585466575E-7
XROM 07,33
1.328123016E-8
XROM 07,33
-2.693913571E5
XROM 07,33
1.126016633E5
XROM 07,33
1.664362044E4
XROM 07,33
-1.094944835E3
XROM 07,33
-9.152236807E1
XROM 07,33
3.968147441E0
XROM 07,33
2.506300762E-1
XROM 07,33
-1.207861326E-2
XROM 07,33
-1.127047764E-4
XROM 07,33
4.528875193E-5
XROM 07,33
-4.246442619E-6
XROM 07,33
-1.662531921E-7
XROM 07,33
3.434751410E-8
XROM 07,33
-1.977586703E5
XROM 07,33
-1.313050636E5
XROM 07,33
1.236130892E4
XROM 07,33
1.328063130E3
XROM 07,33
-6.421216290E1
XROM 07,33
-4.926667708E0
XROM 07,33
1.958843659E-1
XROM 07,33
9.276879722E-3
XROM 07,33
-6.746231240E-4
XROM 07,33
2.572817451E-5
XROM 07,33
2.782770783E-6
XROM 07,33
-3.861253573E-7
XROM 07,33
-8.305946196E-9
XROM 07,33
-9.772138328E4
XROM 07,33
-4.101205227E4
XROM 07,33
6.103163643E3
XROM 07,33
4.162512755E2
XROM 07,33
-3.216129692E1
XROM 07,33
-1.547907892E0
XROM 07,33
9.582197306E-2
XROM 07,33
2.525642333E-3
XROM 07,33
-2.679030026E-4
XROM 07,33
1.364080449E-5
XROM 07,33
7.131691777E-7
XROM 07,33
-1.615157969E-7
XROM 07,33
-3.202197009E-10
XROM 07,33
3.474746029E4
XROM 07,33
1.758855971E5
XROM 07,33
-1.916757091E3
XROM 07,33
-1.711751444E3
XROM 07,33
2.084317280E1
XROM 07,33
5.957029020E0
XROM 07,33
-9.128823581E-2
XROM 07,33
-1.385515939E-2
XROM 07,33
-1.163175353E-4
XROM 07,33
2.791370006E-5
XROM 07,33
4.042379345E-6
XROM 07,33
-6.812556683E-8
XROM 07,33
-2.933411580E-8
XROM 07,33
-3.270449498E5
XROM 07,33
8.341931851E3
XROM 07,33
1.987260041E4
XROM 07,33
-1.753585221E2
XROM 07,33
-1.033191201E2
XROM 07,33
1.336494600E0
XROM 07,33
2.802010427E-1
XROM 07,33
-2.542514371E-3
XROM 07,33
-5.825463323E-4
XROM 07,33
-3.260546819E-5
XROM 07,33
1.120295568E-6
XROM 07,33
3.493355341E-7
XROM 07,33
-2.410441591E-9
XROM 07,33
-1.222751710E5
XROM 07,33
1.757258055E4
XROM 07,33
7.429706516E3
XROM 07,33
-2.089958558E2
XROM 07,33
-3.767554838E1
XROM 07,33
1.008118917E0
XROM 07,33
9.917990773E-2
XROM 07,33
-2.128109017E-3
XROM 07,33
-2.310455519E-4
XROM 07,33
-1.012476349E-5
XROM 07,33
7.593610759E-7
XROM 07,33
1.276869935E-7
XROM 07,33
-3.345213256E-9
XROM 07,33
3.152422328E5
XROM 07,33
9.171778643E4
XROM 07,33
-1.724806348E4
XROM 07,33
-6.644355659E2
XROM 07,33
9.094974146E1
XROM 07,33
2.378186047E-1
XROM 07,33
-2.799963781E-1
XROM 07,33
7.471032414E-3
XROM 07,33
9.487453248E-4
XROM 07,33
END

LBL "DAT8"
-4.178158931E-5
XROM 07,33
-4.188671257E-6
XROM 07,33
2.642687802E-7
XROM 07,33
1.951138502E-8
XROM 07,33
-1.752270579E5
XROM 07,33
1.349080762E5
XROM 07,33
9.742576531E3
XROM 07,33
-1.317651683E3
XROM 07,33
-2.768856258E1
XROM 07,33
4.846955970E0
XROM 07,33
-5.560377954E-2
XROM 07,33
-1.497044100E-2
XROM 07,33
5.142804373E-4
XROM 07,33
5.885764050E-5
XROM 07,33
-2.893149826E-6
XROM 07,33
-2.779473350E-7
XROM 07,33
2.028980644E-8
XROM 07,33
-4.142891149E4
XROM 07,33
5.893715595E4
XROM 07,33
2.295206291E3
XROM 07,33
-5.572855139E2
XROM 07,33
-2.966674541E0
XROM 07,33
1.868844118E0
XROM 07,33
-4.458368858E-2
XROM 07,33
-5.089049113E-3
XROM 07,33
2.746911015E-4
XROM 07,33
1.897358935E-5
XROM 07,33
-1.449110368E-6
XROM 07,33
-8.413351318E-8
XROM 07,33
9.351401382E-9
XROM 07,33
3.519679081E5
XROM 07,33
-5.491021229E4
XROM 07,33
-1.722469890E4
XROM 07,33
5.726673430E2
XROM 07,33
5.521248146E1
XROM 07,33
-2.427208689E0
XROM 07,33
4.978600986E-2
XROM 07,33
6.935024600E-3
XROM 07,33
-6.277092137E-4
XROM 07,33
-7.357594182E-7
XROM 07,33
2.037783167E-6
XROM 07,33
-1.318453073E-7
XROM 07,33
-2.477771839E-9
XROM 07,33
1.213852071E5
XROM 07,33
1.484508548E5
XROM 07,33
-6.037829769E3
XROM 07,33
-1.151820264E3
XROM 07,33
3.608797607E1
XROM 07,33
1.260808129E0
XROM 07,33
-1.313020953E-1
XROM 07,33
7.444166424E-3
XROM 07,33
2.592370959E-4
XROM 07,33
-3.586742734E-5
XROM 07,33
9.392319144E-7
XROM 07,33
8.969526932E-8
XROM 07,33
-1.040117280E-8
XROM 07,33
7.460045850E4
XROM 07,33
5.205174128E4
XROM 07,33
-3.712487600E3
XROM 07,33
-3.907478941E2
XROM 07,33
1.836619557E1
XROM 07,33
2.762059431E-1
XROM 07,33
-4.612969106E-2
XROM 07,33
3.412619755E-3
XROM 07,33
4.683764150E-5
XROM 07,33
-1.373559060E-5
XROM 07,33
5.273013431E-7
XROM 07,33
2.332675049E-8
XROM 07,33
-4.171248708E-9
XROM 07,33
-3.176405807E5
XROM 07,33
6.707269327E3
XROM 07,33
1.693806818E1
XROM 07,33
-3.899370186E-3
XROM 07,33
-1.450307973E-2
XROM 07,33
-1.614010466E-3
XROM 07,33
-4.835416567E-5
XROM 07,33
2.418337051E-5
XROM 07,33
4.863780720E-6
XROM 07,33
2.242296206E-7
XROM 07,33
-7.510513523E-8
XROM 07,33
-2.953008795E5
XROM 07,33
-3.045245628E3
XROM 07,33
1.980075005E1
XROM 07,33
2.635639020E-1
XROM 07,33
7.033533837E-3
XROM 07,33
-6.713845148E-4
XROM 07,33
-2.071144423E-4
XROM 07,33
-1.983905766E-5
XROM 07,33
1.257097753E-6
XROM 07,33
6.456368999E-7
XROM 07,33
7.524371512E-8
XROM 07,33
-1.319436126E5
XROM 07,33
-1.477754563E3
XROM 07,33
7.979908620E0
XROM 07,33
1.256607048E-1
XROM 07,33
5.039612813E-3
XROM 07,33
END

LBL "DAT9"
-1.859670728E-4
XROM 07,33
-1.055529451E-4
XROM 07,33
-1.310591260E-5
XROM 07,33
1.672332811E-7
XROM 07,33
3.216374994E-7
XROM 07,33
4.797806143E-8
XROM 07,33
-3.040942806E5
XROM 07,33
6.837515659E3
XROM 07,33
1.516344241E1
XROM 07,33
-2.362884208E-1
XROM 07,33
6.061032969E-3
XROM 07,33
2.588093321E-3
XROM 07,33
-3.811045372E-4
XROM 07,33
-4.237151422E-5
XROM 07,33
1.349848668E-5
XROM 07,33
3.751265496E-7
XROM 07,33
-4.288461373E-7
XROM 07,33
-3.012232412E5
XROM 07,33
-2.874795184E3
XROM 07,33
2.251763517E1
XROM 07,33
1.066263893E-1
XROM 07,33
-1.818741501E-2
XROM 07,33
1.801142923E-3
XROM 07,33
2.828936105E-4
XROM 07,33
-6.634250684E-5
XROM 07,33
-3.592993482E-6
XROM 07,33
2.133898102E-6
XROM 07,33
-3.273297243E-8
XROM 07,33
-1.348303274E5
XROM 07,33
-1.407733386E3
XROM 07,33
9.411347768E0
XROM 07,33
6.331681841E-2
XROM 07,33
-1.044395994E-2
XROM 07,33
7.004308598E-4
XROM 07,33
1.906622448E-4
XROM 07,33
-3.104756787E-5
XROM 07,33
-3.318831518E-6
XROM 07,33
1.100995507E-6
XROM 07,33
2.697895979E-8
XROM 07,33
7.954125449E-5
XROM 07,33
-5.582213453E-7
XROM 07,33
5.146002724E-7
XROM 07,33
1.216449209E-8
XROM 07,33
-3.096015700E-8
XROM 07,33
1.053675568E-9
XROM 07,33
1.469115639E-10
XROM 07,33
-3.792849515E-11
XROM 07,33
1.166601455E-11
XROM 07,33
-1.453914749E-12
XROM 07,33
-2.105130989E-5
XROM 07,33
-2.468082377E-7
XROM 07,33
-9.647721406E-9
XROM 07,33
6.815204344E-8
XROM 07,33
-1.702301631E-9
XROM 07,33
-1.657999832E-9
XROM 07,33
1.742042774E-10
XROM 07,33
-1.825510291E-11
XROM 07,33
-4.123673454E-12
XROM 07,33
3.284085817E-13
XROM 07,33
7.926888646E-5
XROM 07,33
-8.016983650E-7
XROM 07,33
-6.153752816E-7
XROM 07,33
2.448937254E-8
XROM 07,33
5.374376440E-8
XROM 07,33
2.893192299E-9
XROM 07,33
-1.861519622E-9
XROM 07,33
-2.774020318E-10
XROM 07,33
3.435660453E-11
XROM 07,33
1.035620948E-11
XROM 07,33
-2.056501557E-5
XROM 07,33
6.902714541E-7
XROM 07,33
-7.532593127E-8
XROM 07,33
-9.225484637E-8
XROM 07,33
-1.773233397E-10
XROM 07,33
4.819201506E-9
XROM 07,33
4.207501483E-10
XROM 07,33
-1.385544478E-10
XROM 07,33
-2.336121921E-11
XROM 07,33
3.262568004E-12
XROM 07,33
7.791076792E-5
XROM 07,33
5.551550266E-7
XROM 07,33
3.982484981E-7
XROM 07,33
-2.289140267E-7
XROM 07,33
-4.032773929E-8
XROM 07,33
1.353615419E-8
XROM 07,33
1.563881943E-9
XROM 07,33
-4.096474232E-10
XROM 07,33
-3.500726134E-11
XROM 07,33
5.119765155E-12
XROM 07,33
-2.035962363E-5
XROM 07,33
-1.493954859E-7
XROM 07,33
2.566863949E-7
XROM 07,33
6.190972671E-8
XROM 07,33
-2.643546953E-8
XROM 07,33
-3.468396505E-9
XROM 07,33
1.129731914E-9
XROM 07,33
END

LBL "DAT10"
1.067788849E-10
XROM 07,33
-2.782600149E-11
XROM 07,33
-2.503608101E-12
XROM 07,33
7.674916117E-5
XROM 07,33
-2.095575399E-6
XROM 07,33
-3.155140491E-8
XROM 07,33
1.977568766E-7
XROM 07,33
-1.451743862E-8
XROM 07,33
-7.527990723E-9
XROM 07,33
1.282040059E-9
XROM 07,33
8.450788416E-11
XROM 07,33
-4.504473538E-11
XROM 07,33
1.140738646E-12
XROM 07,33
-1.985794350E-5
XROM 07,33
1.018040721E-7
XROM 07,33
-2.642701755E-7
XROM 07,33
1.482218707E-8
XROM 07,33
1.812988529E-8
XROM 07,33
-2.045392074E-9
XROM 07,33
-3.564480340E-10
XROM 07,33
9.735731119E-11
XROM 07,33
-4.400123586E-12
XROM 07,33
-2.181112126E-12
XROM 07,33
5.727693776E-2
XROM 07,33
7.292755049E-4
XROM 07,33
4.718860196E-5
XROM 07,33
-1.258282858E-5
XROM 07,33
-1.805969988E-6
XROM 07,33
-4.841567953E-7
XROM 07,33
4.471146359E-8
XROM 07,33
6.510993372E-9
XROM 07,33
-5.937190091E-10
XROM 07,33
1.046635431E-10
XROM 07,33
4.230440926E-1
XROM 07,33
1.432594593E-4
XROM 07,33
-6.535966947E-5
XROM 07,33
-3.834239824E-6
XROM 07,33
-4.550180490E-7
XROM 07,33
1.202884816E-7
XROM 07,33
3.165808554E-8
XROM 07,33
-2.413739444E-9
XROM 07,33
1.665788473E-12
XROM 07,33
1.405145097E-11
XROM 07,33
3.622826784E3
XROM 07,33
9.192314862E-1
XROM 07,33
-3.812125677E-5
XROM 07,33
9.723932805E-6
XROM 07,33
1.584397111E-6
XROM 07,33
4.575221871E-7
XROM 07,33
-4.116476296E-8
XROM 07,33
-5.839042545E-9
XROM 07,33
5.531002486E-10
XROM 07,33
-9.870787443E-11
XROM 07,33
5.818120867E-2
XROM 07,33
-1.186263725E-4
XROM 07,33
-2.870169872E-4
XROM 07,33
-1.964200791E-5
XROM 07,33
7.320350464E-6
XROM 07,33
1.158040859E-6
XROM 07,33
-7.182925247E-8
XROM 07,33
-3.084996507E-8
XROM 07,33
-1.237526481E-9
XROM 07,33
5.163108845E-10
XROM 07,33
4.227846223E-1
XROM 07,33
-3.677685285E-4
XROM 07,33
-1.602341956E-5
XROM 07,33
2.099378912E-5
XROM 07,33
2.211867032E-6
XROM 07,33
-3.485353632E-7
XROM 07,33
-8.243648951E-8
XROM 07,33
5.338461690E-10
XROM 07,33
1.707772484E-9
XROM 07,33
1.436917994E-10
XROM 07,33
3.624665729E3
XROM 07,33
9.199675877E-1
XROM 07,33
2.503790519E-4
XROM 07,33
1.776225521E-5
XROM 07,33
-6.434229863E-6
XROM 07,33
-1.052976385E-6
XROM 07,33
6.246575602E-8
XROM 07,33
2.798541265E-8
XROM 07,33
1.180540107E-9
XROM 07,33
-4.648015696E-10
XROM 07,33
5.649942577E-2
XROM 07,33
-1.150075192E-3
XROM 07,33
1.680329148E-4
XROM 07,33
4.550374616E-5
XROM 07,33
-8.843933704E-6
XROM 07,33
-8.509316883E-7
XROM 07,33
2.790642046E-7
XROM 07,33
1.229367156E-8
XROM 07,33
-5.724118658E-9
XROM 07,33
-1.182609494E-10
XROM 07,33
4.226035336E-1
XROM 07,33
2.988754995E-4
XROM 07,33
1.049813733E-4
XROM 07,33
END

LBL "DAT11"
-1.724887105E-5
XROM 07,33
-2.660836574E-6
XROM 07,33
6.795089062E-7
XROM 07,33
4.307858999E-8
XROM 07,33
-1.715100406E-8
XROM 07,33
-5.481318055E-10
XROM 07,33
2.794837551E-10
XROM 07,33
3.626506922E3
XROM 07,33
9.208606632E-1
XROM 07,33
-1.504655257E-4
XROM 07,33
-3.979575958E-5
XROM 07,33
8.023817780E-6
XROM 07,33
7.634508847E-7
XROM 07,33
-2.546077181E-7
XROM 07,33
-1.138837096E-8
XROM 07,33
5.244296231E-9
XROM 07,33
1.139763276E-10
XROM 07,33
5.585788247E-2
XROM 07,33
4.474495418E-4
XROM 07,33
1.268441293E-4
XROM 07,33
-1.402627969E-5
XROM 07,33
2.001122521E-6
XROM 07,33
-3.022359554E-7
XROM 07,33
-1.123847558E-7
XROM 07,33
1.771948966E-8
XROM 07,33
8.834941904E-10
XROM 07,33
-4.133417798E-10
XROM 07,33
4.234041170E-1
XROM 07,33
3.678578700E-4
XROM 07,33
-5.119094118E-5
XROM 07,33
-2.699140221E-6
XROM 07,33
1.150465179E-7
XROM 07,33
-2.736213254E-7
XROM 07,33
3.649992654E-8
XROM 07,33
5.358554956E-9
XROM 07,33
-1.186363970E-9
XROM 07,33
1.091326627E-11
XROM 07,33
3.628347196E3
XROM 07,33
9.194765364E-1
XROM 07,33
-1.048472513E-4
XROM 07,33
1.197706558E-5
XROM 07,33
-2.020321069E-6
XROM 07,33
2.859416355E-7
XROM 07,33
1.040846835E-7
XROM 07,33
-1.635135035E-8
XROM 07,33
-8.171530800E-10
XROM 07,33
3.813432517E-10
XROM 07,33
END

3°)  Barycentric Rectangular Equatorial Coordinates

a)  Program#1

-Given a date and a time in TDB = Temps Dynamique Barycentrique = Barycentric Dynamical Time,
"JPL" computes the barycentric coordinates of the major planets & the Sun,  the geocentric coordinates of the Moon,
referred to the International Celestial Reference Frame ( ICRF ), and the nutations & librations in registers R01 thru R38.
-For the planets, the coordinates are actually those of the barycenter of the planetary system.

-In the JPL files, the coefficients are given in kilometers for the coordinates X , Y , Z and in radians for the angles,
but the routine below gives the coordinates in Astronomical Units and the angles in degrees.

Data Registers:   R00 & R39 to R49: temp                      R41 = Number of Chebyshev coefficients / coordinate     R42 = DT

R01 = XMercury     R04 = XVenus        R07 = XEMB        R10 = XMars        R13 = XJupiter        R16 = XSaturn
R02 = YMercury     R05 = YVenus        R08 = YEMB        R11 = YMars        R14 = YJupiter        R17 = YSaturn
R03 = ZMercury      R06 = ZVenus        R09 = ZEMB         R12 = ZMars        R15 = ZJupiter        R18 = ZSaturn

R19 = XUranus      R22 = XNeptune      R25 = XPluto      R28 = XMoon      R31 = XSun      R34 = Dy = Nutation in Longitude
R20 = YUranus      R23 = YNeptune      R26 = YPluto      R29 = YMoon      R32 = YSun      R35 = De  = Nutation in Obliquity
R21 = ZUranus      R24 = ZNeptune       R27 = ZPluto      R30 = ZMoon       R33 = ZSun

R36 = f
R37 = q               are the 3 Euler angles.
R38 = y

Flags:  /
Subroutine:  "J0" or "J1" or J2"  ( cf "Julian & Gregorian Calendars for the HP-41" )

HGETX = XROM 07,19
HSEKPT = XROM 07,35
HSEKPTA = XROM 07,36

 01  LBL "JPL"   02  HR   03  24   04  /   05  STO 43   06  X<>Y   07  XEQ "J2"   08  "DE424"   09  0   10  HSEKPTA   11  CLX   12  HGETX   13  -   14  2451544.5   15  +   16  STO 44   17  +   18  STO 45   19  16   20  -   21  ABS   22  16   23  X

( 307 bytes / SIZE 050 )

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

where the time is expressed in TDB

Example:      2012/08/29  16h41m37s   TDB

2012.0829    ENTER^
16.4137    XEQ "JPL"   gives in  3mn40s

•  Mercury

R01 = -0.086268056  AU
R02 =  0.261011681  AU
R03 =  0.148335932  AU

•  Venus

R04 =  0.625711277  AU
R05 =  0.340718754  AU
R06 =  0.113580262  AU

•  Earth-Moon Barycenter

R07 =  0.924382748  AU
R08 = -0.370521433  AU
R09 = -0.160657623  AU

•  Mars

R10 = -0.565485209  AU
R11 = -1.276768211  AU
R12 = -0.570377126  AU

•  Jupiter

R13 =  2.304854616  AU
R14 =  4.122835712  AU
R15 =  1.710961220  AU

•  Saturn

R16 = -8.415554159  AU
R17 = -4.690269792  AU
R18 = -1.575018518  AU

•  Uranus

R19 =  19.94965382  AU
R20 =  2.033877358  AU
R21 =  0.608620231  AU

•  Neptune

R22 =  26.37870504  AU
R23 = -12.96971155  AU
R24 = -5.965313363  AU

•  Pluto

R25 =  4.714712105  AU
R26 = -30.06338587  AU
R27 = -10.80238054  AU

•  Moon

R28 =  0.001720256  AU
R29 = -0.001776480  AU
R30 = -0.000539310  AU

•  Sun

R31 = -0.002028870  AU
R32 = -0.002015372  AU
R33 = -0.000902165  AU

•  Nutation

R34 =  0°004498581 = Delta Psi = nutation in longitude
R35 = -0°001148788 = Delta Epsilon = nutation in obliquity

•  Libration

R36 = 3°181619738  = phi
R37 = 24°24073041  = theta         the 3 Euler angles
R38 = 207845°4579  = psi

Notes:

-Line 08  "DE424"  is the name of the HEPAX data file created in paragraph 2.
-You can replace line 08 by ARCL 01 , add  ASTO 01 after line 01 and place the name of the data file in the alpha register before executing "JPL"

-Lines 53-56-59-61-63-69 may be replaced with  HRCLPT ( saves 6 bytes but slightly slower )

-If the date is outside the domain of validity, you'll get the "DATAERROR" message ( line 24 )
-Line 25 is the astronomical unit in km, 1AU = 149597870.691 km  rounded to 1 decimal.

b)  Program#2

-This variant employs an M-Code routine "CdT" among those that are listed in "Ephemerides & Chebyshev Polynomials for the "HP-41"

Data Registers:   R00 & R39 to R61: temp                      R41 = number of Chebyshev coefficients / coordinate       R42 = DT

R01 = XMercury     R04 = XVenus        R07 = XEMB        R10 = XMars        R13 = XJupiter        R16 = XSaturn
R02 = YMercury     R05 = YVenus        R08 = YEMB        R11 = YMars        R14 = YJupiter        R17 = YSaturn
R03 = ZMercury      R06 = ZVenus        R09 = ZEMB         R12 = ZMars        R15 = ZJupiter        R18 = ZSaturn

R19 = XUranus      R22 = XNeptune      R25 = XPluto      R28 = XMoon      R31 = XSun      R34 = Dy = Nutation in Longitude
R20 = YUranus      R23 = YNeptune      R26 = YPluto      R29 = YMoon      R32 = YSun      R35 = De  = Nutation in Obliquity
R21 = ZUranus      R24 = ZNeptune       R27 = ZPluto      R30 = ZMoon       R33 = ZSun

R36 = f
R37 = q               are the 3 Euler angles.
R38 = y

Flags:  /
Subroutines:  "J0" or "J1" or J2"  ( cf "Julian & Gregorian Calendars for the HP-41" )
"CdT"  M-Code routine or focal program ( cf "Ephemerides & Chebyshev Polynomials for the HP-41" )

 01  LBL "JPL"   02  HR   03  24   04  /   05  STO 43   06  X<>Y   07  XEQ "J2"   08  "DE424"   09  0   10  HSEKPTA   11  CLX   12  HGETX   13  -   14  2451544.5   15  +   16  STO 44   17  +   18  STO 45   19  16   20  -   21  ABS   22  16   23  X

( 284 bytes / SIZE 062 )

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

where the time is expressed in TDB

Example:      2012/08/29  16h41m37s   TDB

2012.0829    ENTER^
16.4137    XEQ "JPL"   gives the same results in  1mn56s

Notes:

-The last decimal may depend on the version of "CdT" that you are using.
-Lines 55-57-61-63-65-71 may be replaced with  HRCLPT ( saves 6 bytes but slightly slower )

-In fact, many coefficients could be deleted since the HP-41 works with 10 digits.
-So, these programs may be simplified and use a smaller data file, especially if you don't want to calculate the libration...

4°)  Heliocentric Rectangular Equatorial Coordinates

-After executing "JPL", "HELIO" replaces the barycentric coordinates by the heliocentric coordinates.
-The coordinates of the Earth-Moon barycenter are replaced with the coordinates of the Earth in registers R07-R08-R09.
-The coordinates of the Moon are unchanged.

Data Registers:    R00 is unused   R34 , R35 , ......  are undisturbed

R01 = XMercury     R04 = XVenus        R07 = XEarth        R10 = XMars        R13 = XJupiter        R16 = XSaturn
R02 = YMercury     R05 = YVenus        R08 = YEarth        R11 = YMars        R14 = YJupiter        R17 = YSaturn
R03 = ZMercury      R06 = ZVenus        R09 = ZEarth         R12 = ZMars        R15 = ZJupiter        R18 = ZSaturn

R19 = XUranus      R22 = XNeptune      R25 = XPluto      R28 = XMoon      R31 = XSun
R20 = YUranus      R23 = YNeptune      R26 = YPluto      R29 = YMoon      R32 = YSun
R21 = ZUranus      R24 = ZNeptune       R27 = ZPluto      R30 = ZMoon       R33 = ZSun

Flags:  /
Subroutines:  /

 01  LBL "HELIO"  02  RCL 33  03  RCL 32                04  RCL 31   05  27  06  SIGN  07  LBL 01 08  R^  09  ST- IND L  10  DSE L   11  R^  12  ST- IND L  13  DSE L                  14  R^ 15  ST- IND L  16  R^  17  DSE L   18  GTO 01  19  CLX  20  STO 31                21  STO 32 22  STO 33  23  RCL 28  24  12.15058563 E-3  25  *  26  ST- 07  27  RCL 29                28  LASTX 29  *  30  ST- 08  31  RCL 30                32  LASTX  33  *  34  ST- 09  35  END

( 78 bytes / SIZE 034 )

 STACK INPUT OUTPUT X / /

Example:       The same one:

-After executing "JPL"

XEQ "HELIO"  gives in 5 seconds

•  Mercury

R01 = -0.084239186  AU
R02 =  0.263027053  AU
R03 =  0.149238098  AU

•  Venus

R04 =  0.627740147  AU
R05 =  0.342734127  AU
R06 =  0.114482428  AU

•  Earth

R07 =  0.926390716  AU
R08 = -0.368484476  AU
R09 = -0.159748904  AU

•  Mars

R10 = -0.563456338  AU
R11 = -1.274752839  AU
R12 = -0.569474960  AU

•  Jupiter

R13 =  2.306883486  AU
R14 =  4.124851084  AU
R15 =  1.711863385  AU

•  Saturn

R16 = -8.413525289  AU
R17 = -4.688254420  AU
R18 = -1.574116353  AU

•  Uranus

R19 =  19.95168269  AU
R20 =  2.035892730  AU
R21 =  0.609522397  AU

•  Neptune

R22 =  26.38073391  AU
R23 = -12.96769618  AU
R24 = -5.964411198  AU

•  Pluto

R25 =  4.716740975  AU
R26 = -30.06137050  AU
R27 = -10.80147837  AU

•  Moon

R28 =  0.001720256  AU
R29 = -0.001776480  AU         ( unchanged )
R30 = -0.000539310  AU

•  Sun

R31 =  0
R32 =  0             The heliocentric coordinates of the Sun are  0 , 0 , 0
R33 =  0

Notes:

-Here, we get the coordinates of the Earth in R07-R08-R09 instead of the Earth-Moon Barycenter.
-Line 24 is µ/(1+µ)  where µ = Moon-Earth mass ratio = 0.0123000383

5°)  Geocentric Rectangular Equatorial Coordinates

-"GEOC" replaces the heliocentric coordinates by the geocentric coordinates, provided you have already executed "JPL" & "HELIO".
-The coordinates of the Moon are unchanged.

Data Registers:    R00 is unused   R34 , R35 , ......  are undisturbed too.

R01 = XMercury     R04 = XVenus        R07 = XEarth        R10 = XMars        R13 = XJupiter        R16 = XSaturn
R02 = YMercury     R05 = YVenus        R08 = YEarth        R11 = YMars        R14 = YJupiter        R17 = YSaturn
R03 = ZMercury      R06 = ZVenus        R09 = ZEarth         R12 = ZMars        R15 = ZJupiter        R18 = ZSaturn

R19 = XUranus      R22 = XNeptune      R25 = XPluto      R28 = XMoon      R31 = XSun
R20 = YUranus      R23 = YNeptune      R26 = YPluto      R29 = YMoon      R32 = YSun
R21 = ZUranus      R24 = ZNeptune       R27 = ZPluto      R30 = ZMoon       R33 = ZSun

Flags:  /
Subroutines:  /

 01  LBL "GEOC"  02  RCL 09  03  CHS  04  STO 33  05  RCL 08  06  CHS  07  STO 32  08  RCL 07  09  CHS  10  STO 31  11  27  12  SIGN  13  LBL 01  14  R^  15  ST+ IND L  16  DSE L  17  R^  18  ST+ IND L  19  DSE L  20  R^  21  ST+ IND L  22  R^  23  DSE L  24  GTO 01  25  END

( 45 bytes / SIZE 034 )

 STACK INPUT OUTPUT X / /

Example:    Again the same one

-After executing "JPL" and "HELIO"

XEQ "GEOC"   returns in 4 seconds

•  Mercury

R01 = -1.010629902  AU
R02 =  0.631511529  AU
R03 =  0.308987002  AU

•  Venus

R04 = -0.298650569  AU
R05 =  0.711218602  AU
R06 =  0.274231332  AU

•  Earth

R07 =  0
R08 =  0             The geocentric coordinates of the Earth are  0 , 0 , 0
R09 =  0

•  Mars

R10 = -1.489847054  AU
R11 = -0.906268364  AU
R12 = -0.409726056  AU

•  Jupiter

R13 =  1.380492770  AU
R14 =  4.493335560  AU
R15 =  1.871612289  AU

•  Saturn

R16 = -9.339916005  AU
R17 = -4.319769945  AU
R18 = -1.414367449  AU

•  Uranus

R19 =  19.02529197  AU
R20 =  2.404377206  AU
R21 =  0.769271301  AU

•  Neptune

R22 =  25.45434319  AU
R23 = -12.59921170  AU
R24 = -5.804662294  AU

•  Pluto

R25 =  3.790350259  AU
R26 = -29.69288602  AU
R27 = -10.64172947  AU

•  Moon

R28 =  0.001720256  AU
R29 = -0.001776480  AU         ( unchanged )
R30 = -0.000539310  AU

•  Sun

R31 = -0.926390716  AU
R32 =  0.368484476  AU
R33 =  0.159748904  AU

Notes:

-Since the HP-41 works with 10 digits, we cannot get the full precision of the JPL ephemerides.
-Other programs must be used to get the spherical coordinates and the equatorial or ecliptic coordinates with respect to the equinox and ecliptic of the date.
-See for instance  "Transformation of Coordinates for the HP-41" and "Precession for the HP-41"

References:

[1]   ftp://ssd.jpl.nasa.gov/pub/eph/planets/ascii
[2]  Taylor, Bell, Hilton, Sinclair - "Computation of the Quantities Describing the Lunar Libration in the Astronomical Almanac"