INPOP10

INPOP Ephemerides for the HP-41

Overview

1°) Chebyshev Coefficients for a given Date
2°) Data File of 326 Numbers
3°) Barycentric Rectangular Equatorial Coordinates ( geocentric for the Moon )

a) Program#1
b) Program#2

4°) Data File of 236 Numbers
5°) Barycentric Rectangular Equatorial Coordinates ( geocentric for the Moon )

a) Program#1
b) Program#2

6°) 11 Data Files
7°) Barycentric Rectangular Equatorial Coordinates ( geocentric for the Moon )

    a) Program#1
    b) Program#2
    c) Clenshaw's Algorithm

8°) Heliocentric & Geocentric Coordinates

-The following programs employ the French Ephemerides INPOP10b to calculate the positions of the Sun, the Moon and the Planets.
-Like the JPL ephemerides DE4xx / LE4xx, the Chebyshev polynomials are used.
-But the Chebyshev coefficients are given in a specific ascii file for each celestial body.

-There are also ascii files to compute the libration and the difference TDB-TT, but these files are not taken into account here.

1°) Chebyshev Coefficients for a given Date

-The example in all this page is 2012/08/29 16h41m37s TDB i-e JD = 2456169.1955671296....

-We find in the corresponding files ( that you can download freely from http://www.imcce.fr/inpop ) the constants hereunder:

JD1 ( Julian Day #1 ) = Julian date of earliest data. JD2 ( Julian Day #2 ) = Julian date of latest data in record.

   Coefficients for the X-coordinate
   Coefficients for the Y-coordinate
   Coefficients for the Z-coordinate

-For the date & time above, we have, in the TDB scale:

MERCURY

2456169.00 2456177.00

-0.29315336986928027D+08 -0.16463182989792382D+08 +0.97934050942325476D+06 +0.66013163246360753D+05 -0.67986581286844003D+04 +0.68940455919888478D+02 +0.32022176274639641D+02 -0.25048941405745393D+01 -0.38259830872659564D-01 +0.19753710185559541D-01 -0.11176948424546607D-02 -0.66018663346767426D-04 +0.13069790884275886D-04 -0.44187771250454941D-06

2456169.00 2456177.00

+0.31459263881170556D+08 -0.89596151400935594D+07 -0.10970662686767015D+07 +0.79439637257014314D+05 +0.14713336028492513D+04 -0.43880252850673111D+03 +0.19448002386958230D+02 +0.13568626766922571D+01 -0.21669374234822192D+00 +0.56873053823932023D-02 +0.11455261258890683D-02 -0.12392245910384438D-03 +0.60856228091460466D-07 +0.94079963545144347D-06

2456169.00 2456177.00

+0.19839355285150681D+08 -0.30787747770392252D+07 -0.68756968627975089D+06 +0.35591101521921257D+05 +0.14908329783656864D+04 -0.24154807804805009D+03 +0.70687720670573340D+01 +0.98451468469055281D+00 -0.11178719885083153D+00 +0.99002776439137950D-03 +0.72779888183982630D-03 -0.59352764351801440D-04 -0.13213986324942311D-05 +0.54782347796255205D-06

VENUS

2456169.00 2456185.00

+0.78664473103925988D+08 -0.16263781665477723D+08 -0.99631691229176230D+06 +0.33291356865364694D+05 +0.10789879273390341D+04 -0.18943669843560819D+02 -0.51217193886317491D+00 +0.32589786819049288D-02 +0.16446840663526027D-03 +0.12612637383350744D-05

2456169.00 2456185.00

+0.67077255118295603D+08 +0.15750128725996293D+08 -0.85047418465314514D+06 -0.33601995254308393D+05 +0.85080814707811737D+03 +0.22637749269697199D+02 -0.29030559829637398D+00 -0.85426882973739082D-02 +0.24949206999275035D-05 +0.25613048306449545D-05

2456169.00 2456185.00

+0.25183865533687569D+08 +0.81159179529736061D+07 -0.31960530611994863D+06 -0.17225172471078215D+05 +0.31452453187836903D+03 +0.11384115554037475D+02 -0.98206732080659123D-01 -0.40497163842831340D-02 -0.93030000889979658D-05 +0.10739681813607775D-05

EARTH

2456169.00 2456173.00

+0.13994933701800579D+09 +0.18194949565184098D+07 -0.40153146657095858D+05 -0.90829179491372471D+02 -0.19250090778335505D+00 +0.85259705781936639D-02 +0.30067071401044636D-02 -0.13147490888798044D-03 -0.87635773527173745D-05 +0.71739928885553924D-06 +0.28312206268310546D-07 -0.55456791428735875D-08 +0.22952322888474274D-08

2456169.00 2456173.00

-0.51494769242682450D+08 +0.43675319837104334D+07 +0.14643798068799459D+05 -0.18963343617653737D+03 -0.22319400278445389D+00 -0.53503358364105226D-01 +0.12651983576153604D-02 +0.15131152419955131D-03 -0.90022749118208329D-05 -0.50571893990628118D-06 +0.47683715820312503D-07 +0.32550759269715538D-08 +0.90778298457216833D-09

2456169.00 2456173.00

-0.22328845150488295D+08 +0.18933746262047905D+07 +0.63714130122176439D+04 -0.82589903397250424D+02 -0.19872030223270962D+00 -0.19718686491250990D-01 +0.73462174517573522D-03 +0.46802101991847825D-04 -0.41598696629941262D-05 -0.13556937641167059D-06 +0.20489096641540527D-07 +0.20638983212488291D-08 +0.11280369388828533D-08

MARS

2456153.00 2456185.00

-0.84522331819430307D+08 +0.32237677992814425D+08 +0.46770014088665741D+06 -0.26595737788769391D+05 -0.50571713775675744D+03 +0.15637737178598830D+01 +0.25159178342778532D+00 +0.59161623161532130D-02 +0.84140338003635406D-05 -0.30535448715326722D-05 -0.43695688000496946D-07

2456153.00 2456185.00

-0.18984178630630970D+09 -0.84835594997411948D+07 +0.10557242570063577D+07 +0.15155568398922069D+05 -0.36096977708116174D+03 -0.11450579017532347D+02 -0.11821060023912006D+00 +0.30489848596983024D-02 +0.14821253716945648D-03 +0.26076428173330826D-05 -0.46238318676185954D-07

2456153.00 2456185.00

-0.84797112293665886D+08 -0.47616194947781470D+07 +0.47159831292199041D+06 +0.76696853631582217D+04 -0.15190933302417397D+03 -0.52942797743102075D+01 -0.61019930752019939D-01 +0.12383495420742337D-02 +0.67962333559989929D-04 +0.12743976211896523D-05 -0.30744579439711906D-07

JUPITER

2456153.00 2456185.00

+0.34494863937185967D+09 -0.16262803278299069D+08 -0.51492858784948548D+05 +0.42711828402470820D+03 +0.42701618979108802D+00 -0.46816170215606689D-02 +0.29878444691292550D-05 +0.29582061159961023D-06

2456153.00 2456185.00

+0.61657436011927211D+09 +0.82711204868866391D+07 -0.92000207881153910D+05 -0.16538494675315775D+03 +0.13738433508864296D+01 +0.28008222579956055D-03 -0.12947713630336888D-04 +0.26882291923085623D-06

2456153.00 2456185.00

+0.25586985129875845D+09 +0.39411648466497753D+07 -0.38180158090569857D+05 -0.81287343504534988D+02 +0.57848208080693742D+00 +0.23411214351654053D-03 -0.55839893605068355D-05 +0.82638222978606241D-07

SATURN

2456153.00 2456185.00

-0.12589969804793978D+10 +0.60250555881640008D+07 +0.25656016408884636D+05 -0.26091706789991974D+02 -0.32318383455276489D-01 +0.39586280213747601D-04 -0.14316174201667309D-06

2456153.00 2456185.00

-0.70151070696737397D+09 -0.10584583622590527D+08 +0.14295233363278850D+05 +0.32795317709571542D+02 -0.33564344048500061D-01 -0.10505670946373188D-04 +0.14092074707150459D-06

2456153.00 2456185.00

-0.23555800950844052D+09 -0.46313195842606947D+07 +0.47997570216998720D+04 +0.14669815857262556D+02 -0.12469083070755005D-01 -0.59867382424084607D-05 -0.44965418055653572D-08

URANUS

2456153.00 2456185.00

+0.29844306253814359D+10 -0.10578598666025975D+07 -0.70070440413590486D+04 +0.28631464640299481D+00 +0.11568502797874520D-02 +0.17801034522967207D-07

2456153.00 2456185.00

+0.30416411644151908D+09 +0.81682147366144164D+07 -0.71345117492477095D+03 -0.32123588124910989D+01 +0.12586514155069986D-04 +0.32741162512037488D-06

2456153.00 2456185.00

+0.91005867922737196D+08 +0.35924279427734483D+07 -0.21340204341134006D+03 -0.14108885402480762D+01 -0.10933274299734168D-04 +0.15719302205575838D-06

NEPTUNE

2456153.00 2456185.00

+0.39461517846225348D+10 +0.35257790407171724D+07 -0.27726735504026419D+04 -0.43271374702453613D+00 +0.15508683605326546D-03 +0.42935910945137340D-06

2456153.00 2456185.00

-0.19403155528979404D+10 +0.61907166574255098D+07 +0.13636191657213105D+04 -0.71634089946746826D+00 -0.83508862492938832D-04 -0.34499680623412132D-06

2456153.00 2456185.00

-0.89242513523491347D+09 +0.24461173395014242D+07 +0.62716806971311519D+03 -0.28244119882583618D+00 -0.38417974590427344D-04 -0.43500525255997978D-07

PLUTO

2456153.00 2456185.00

+0.70521664500415242D+09 +0.75749968357384838D+07 -0.39723892320745574D+03 -0.65525954961776733D+00 +0.17123970772243210D-03 -0.63776193807522460D-07

2456153.00 2456185.00

-0.44974451175417824D+10 +0.49147782427988190D+06 +0.25327369069405177D+04 -0.40186929702758789D+00 -0.11056142830057070D-03 +0.85691256875482702D-06

2456153.00 2456185.00

-0.16159925232548270D+10 -0.21289386711855391D+07 +0.91003840069202442D+03 +0.71972052256266281D-01 -0.85952161397371033D-04 +0.12505592571364508D-06

MOON

2456169.00 2456173.00

+0.33556904722635489D+06 +0.74197720621400513D+05 -0.18109224790720833D+05 -0.48338213519564391D+03 +0.90567100254557630D+02 -0.55366993848874702D+00 -0.24795138176960044D+00 +0.10819729358699027D-01 +0.72144437306794439D-03 -0.58587893525884731D-04 -0.24973778636194766D-05 +0.33636592704640511D-06 +0.64630294497092650D-08

2456169.00 2456173.00

-0.14137101919242449D+06 +0.14361224970360560D+06 +0.77421789623283767D+04 -0.13613681570455030D+04 -0.15887487733404202D+02 +0.46084360801847648D+01 -0.10362942910054790D+00 -0.12451898315208237D-01 +0.74068787508441375D-03 +0.41322680664683920D-04 -0.40485506701770643D-05 -0.13863012972682188D-06 +0.24800410809070071D-07

2456169.00 2456173.00

-0.26859677107778265D+05 +0.60814163120020603D+05 +0.14614689828688038D+04 -0.55884126894143685D+03 +0.15031750050645436D+01 +0.17117697163543197D+01 -0.60240352001099763D-01 -0.38513654043244865D-02 +0.34216660052815864D-03 +0.10899753854288665D-04 -0.17498468878329732D-05 -0.25049415528480990D-07 +0.99905895412808800D-08

SUN

2456169.00 2456185.00

-0.29679665346556518D+06 +0.68992426438827461D+04 +0.13937490815254240D+02 -0.14502888565091926D+00 +0.94310869972105138D-02 -0.11645078150632141D-02 -0.43779188366174216D-04 +0.30695233390345058D-04 -0.39159531297627836D-05 -0.89881849972524960D-07 +0.98907025124491183D-07

2456169.00 2456185.00

-0.30422657092360721D+06 -0.27781546046598733D+04 +0.22921659539994550D+02 +0.42247233378477411D-01 +0.13890369373257272D-02 +0.92303741724564161D-03 -0.20226195636958256D-03 +0.11925225696786511D-04 +0.23768188839312643D-05 -0.63105068443818848D-06 +0.48248874620036552D-07

2456169.00 2456185.00

-0.13630479264692534D+06 -0.13672004988200645D+04 +0.96366419825635337D+01 +0.18917873923655796D-01 -0.26396620160085149D-03 +0.62068370757140123D-03 -0.10349973362450982D-03 +0.31858047813540080D-05 +0.16756257537053898D-05 -0.32781703111714128D-06 +0.15528367354045134D-07

-Among these numbers, JD1 & JD2 are repeated several time.
-We are going to save only JD1 once

2°) Data File of 326 Numbers

Note: Skip to paragraph 4 if you don't want to store 326 numbers...

Planet Nb Coeff DT Pointer

Mercury        14           8          0 ->42
Venus            10         16         43->73
Earth             13           4         74->113
Mars             11          32       114->147
Jupiter            8           32       148->172
Saturn            7           32       173->194
Uranus           6           32       195->213
Neptune         6          32        214->232
Pluto              6          32        233->251
Moon           13          4         252->291
Sun              11          16        292->325

-Create a data file of 326 numbers ( for instance 326 alpha DATA alpha XEQ CRFLD ) and store all these numbers ( assign SAVEX to a key ... )

( 2456169 SAVEX -.2931533699 E8 SAVEX ..................................... .1552836735 E-7 SAVEX )

MERCURY pointer 0 to 42

2456169.00 Initial Julian Day

-0.29315336986928027D+08 Chebyshev coefficients for coordinate X
-0.16463182989792382D+08
+0.97934050942325476D+06
+0.66013163246360753D+05
-0.67986581286844003D+04
+0.68940455919888478D+02
+0.32022176274639641D+02
-0.25048941405745393D+01
-0.38259830872659564D-01
+0.19753710185559541D-01
-0.11176948424546607D-02
-0.66018663346767426D-04
+0.13069790884275886D-04
-0.44187771250454941D-06

+0.31459263881170556D+08 Chebyshev coefficients for coordinate Y
-0.89596151400935594D+07
-0.10970662686767015D+07
+0.79439637257014314D+05
+0.14713336028492513D+04
-0.43880252850673111D+03
+0.19448002386958230D+02
+0.13568626766922571D+01
-0.21669374234822192D+00
+0.56873053823932023D-02
+0.11455261258890683D-02
-0.12392245910384438D-03
+0.60856228091460466D-07
+0.94079963545144347D-06

+0.19839355285150681D+08 Chebyshev coefficients for coordinate Z
-0.30787747770392252D+07
-0.68756968627975089D+06
+0.35591101521921257D+05
+0.14908329783656864D+04
-0.24154807804805009D+03
+0.70687720670573340D+01
+0.98451468469055281D+00
-0.11178719885083153D+00
+0.99002776439137950D-03
+0.72779888183982630D-03
-0.59352764351801440D-04
-0.13213986324942311D-05
+0.54782347796255205D-06

VENUS pointer 43 to 73

2456169.00 Initial Julian Day

+0.78664473103925988D+08 Chebyshev coefficients for coordinate X
-0.16263781665477723D+08
-0.99631691229176230D+06
+0.33291356865364694D+05
+0.10789879273390341D+04
-0.18943669843560819D+02
-0.51217193886317491D+00
+0.32589786819049288D-02
+0.16446840663526027D-03
+0.12612637383350744D-05

+0.67077255118295603D+08 Chebyshev coefficients for coordinate Y
+0.15750128725996293D+08
-0.85047418465314514D+06
-0.33601995254308393D+05
+0.85080814707811737D+03
+0.22637749269697199D+02
-0.29030559829637398D+00
-0.85426882973739082D-02
+0.24949206999275035D-05
+0.25613048306449545D-05

+0.25183865533687569D+08 Chebyshev coefficients for coordinate Z
+0.81159179529736061D+07
-0.31960530611994863D+06
-0.17225172471078215D+05
+0.31452453187836903D+03
+0.11384115554037475D+02
-0.98206732080659123D-01
-0.40497163842831340D-02
-0.93030000889979658D-05
+0.10739681813607775D-05

EARTH pointer 74 to 113

2456169.00 Initial Julian Day

+0.13994933701800579D+09 Chebyshev coefficients for coordinate X
+0.18194949565184098D+07
-0.40153146657095858D+05
-0.90829179491372471D+02
-0.19250090778335505D+00
+0.85259705781936639D-02
+0.30067071401044636D-02
-0.13147490888798044D-03
-0.87635773527173745D-05
+0.71739928885553924D-06
+0.28312206268310546D-07
-0.55456791428735875D-08
+0.22952322888474274D-08

-0.51494769242682450D+08 Chebyshev coefficients for coordinate Y
+0.43675319837104334D+07
+0.14643798068799459D+05
-0.18963343617653737D+03
-0.22319400278445389D+00
-0.53503358364105226D-01
+0.12651983576153604D-02
+0.15131152419955131D-03
-0.90022749118208329D-05
-0.50571893990628118D-06
+0.47683715820312503D-07
+0.32550759269715538D-08
+0.90778298457216833D-09

-0.22328845150488295D+08 Chebyshev coefficients for coordinate Z
+0.18933746262047905D+07
+0.63714130122176439D+04
-0.82589903397250424D+02
-0.19872030223270962D+00
-0.19718686491250990D-01
+0.73462174517573522D-03
+0.46802101991847825D-04
-0.41598696629941262D-05
-0.13556937641167059D-06
+0.20489096641540527D-07
+0.20638983212488291D-08
+0.11280369388828533D-08

MARS pointer 114 to 147

2456153.00 Initial Julian Day

-0.84522331819430307D+08 Chebyshev coefficients for coordinate X
+0.32237677992814425D+08
+0.46770014088665741D+06
-0.26595737788769391D+05
-0.50571713775675744D+03
+0.15637737178598830D+01
+0.25159178342778532D+00
+0.59161623161532130D-02
+0.84140338003635406D-05
-0.30535448715326722D-05
-0.43695688000496946D-07

-0.18984178630630970D+09 Chebyshev coefficients for coordinate Y
-0.84835594997411948D+07
+0.10557242570063577D+07
+0.15155568398922069D+05
-0.36096977708116174D+03
-0.11450579017532347D+02
-0.11821060023912006D+00
+0.30489848596983024D-02
+0.14821253716945648D-03
+0.26076428173330826D-05
-0.46238318676185954D-07

-0.84797112293665886D+08 Chebyshev coefficients for coordinate Z
-0.47616194947781470D+07
+0.47159831292199041D+06
+0.76696853631582217D+04
-0.15190933302417397D+03
-0.52942797743102075D+01
-0.61019930752019939D-01
+0.12383495420742337D-02
+0.67962333559989929D-04
+0.12743976211896523D-05
-0.30744579439711906D-07

JUPITER pointer 148 to 172

2456153.00 Initial Julian Day

+0.34494863937185967D+09 Chebyshev coefficients for coordinate X
-0.16262803278299069D+08
-0.51492858784948548D+05
+0.42711828402470820D+03
+0.42701618979108802D+00
-0.46816170215606689D-02
+0.29878444691292550D-05
+0.29582061159961023D-06

+0.61657436011927211D+09 Chebyshev coefficients for coordinate Y
+0.82711204868866391D+07
-0.92000207881153910D+05
-0.16538494675315775D+03
+0.13738433508864296D+01
+0.28008222579956055D-03
-0.12947713630336888D-04
+0.26882291923085623D-06

+0.25586985129875845D+09 Chebyshev coefficients for coordinate Z
+0.39411648466497753D+07
-0.38180158090569857D+05
-0.81287343504534988D+02
+0.57848208080693742D+00
+0.23411214351654053D-03
-0.55839893605068355D-05
+0.82638222978606241D-07

SATURN pointer 173 to 194

2456153.00 Initial Julian Day

-0.12589969804793978D+10 Chebyshev coefficients for coordinate X
+0.60250555881640008D+07
+0.25656016408884636D+05
-0.26091706789991974D+02
-0.32318383455276489D-01
+0.39586280213747601D-04
-0.14316174201667309D-06

-0.70151070696737397D+09 Chebyshev coefficients for coordinate Y
-0.10584583622590527D+08
+0.14295233363278850D+05
+0.32795317709571542D+02
-0.33564344048500061D-01
-0.10505670946373188D-04
+0.14092074707150459D-06

-0.23555800950844052D+09 Chebyshev coefficients for coordinate Z
-0.46313195842606947D+07
+0.47997570216998720D+04
+0.14669815857262556D+02
-0.12469083070755005D-01
-0.59867382424084607D-05
-0.44965418055653572D-08

URANUS pointer 195 to 213

2456153.00 Initial Julian Day

+0.29844306253814359D+10 Chebyshev coefficients for coordinate X
-0.10578598666025975D+07
-0.70070440413590486D+04
+0.28631464640299481D+00
+0.11568502797874520D-02
+0.17801034522967207D-07

+0.30416411644151908D+09 Chebyshev coefficients for coordinate Y
+0.81682147366144164D+07
-0.71345117492477095D+03
-0.32123588124910989D+01
+0.12586514155069986D-04
+0.32741162512037488D-06

+0.91005867922737196D+08 Chebyshev coefficients for coordinate Z
+0.35924279427734483D+07
-0.21340204341134006D+03
-0.14108885402480762D+01
-0.10933274299734168D-04
+0.15719302205575838D-06

NEPTUNE pointer 214 to 232

2456153.00 Initial Julian Day

+0.39461517846225348D+10 Chebyshev coefficients for coordinate X
+0.35257790407171724D+07
-0.27726735504026419D+04
-0.43271374702453613D+00
+0.15508683605326546D-03
+0.42935910945137340D-06

-0.19403155528979404D+10 Chebyshev coefficients for coordinate Y
+0.61907166574255098D+07
+0.13636191657213105D+04
-0.71634089946746826D+00
-0.83508862492938832D-04
-0.34499680623412132D-06

-0.89242513523491347D+09 Chebyshev coefficients for coordinate Z
+0.24461173395014242D+07
+0.62716806971311519D+03
-0.28244119882583618D+00
-0.38417974590427344D-04
-0.43500525255997978D-07

PLUTO pointer 233 to 251

2456153.00 Initial Julian Day

+0.70521664500415242D+09 Chebyshev coefficients for coordinate X
+0.75749968357384838D+07
-0.39723892320745574D+03
-0.65525954961776733D+00
+0.17123970772243210D-03
-0.63776193807522460D-07

-0.44974451175417824D+10 Chebyshev coefficients for coordinate Y
+0.49147782427988190D+06
+0.25327369069405177D+04
-0.40186929702758789D+00
-0.11056142830057070D-03
+0.85691256875482702D-06

-0.16159925232548270D+10 Chebyshev coefficients for coordinate Z
-0.21289386711855391D+07
+0.91003840069202442D+03
+0.71972052256266281D-01
-0.85952161397371033D-04
+0.12505592571364508D-06

MOON pointer 252 to 291

2456169.00 Initial Julian Day

+0.33556904722635489D+06 Chebyshev coefficients for coordinate X
+0.74197720621400513D+05
-0.18109224790720833D+05
-0.48338213519564391D+03
+0.90567100254557630D+02
-0.55366993848874702D+00
-0.24795138176960044D+00
+0.10819729358699027D-01
+0.72144437306794439D-03
-0.58587893525884731D-04
-0.24973778636194766D-05
+0.33636592704640511D-06
+0.64630294497092650D-08

-0.14137101919242449D+06 Chebyshev coefficients for coordinate Y
+0.14361224970360560D+06
+0.77421789623283767D+04
-0.13613681570455030D+04
-0.15887487733404202D+02
+0.46084360801847648D+01
-0.10362942910054790D+00
-0.12451898315208237D-01
+0.74068787508441375D-03
+0.41322680664683920D-04
-0.40485506701770643D-05
-0.13863012972682188D-06
+0.24800410809070071D-07

-0.26859677107778265D+05 Chebyshev coefficients for coordinate Z
+0.60814163120020603D+05
+0.14614689828688038D+04
-0.55884126894143685D+03
+0.15031750050645436D+01
+0.17117697163543197D+01
-0.60240352001099763D-01
-0.38513654043244865D-02
+0.34216660052815864D-03
+0.10899753854288665D-04
-0.17498468878329732D-05
-0.25049415528480990D-07
+0.99905895412808800D-08

SUN pointer 292 to 325

2456169.00

-0.29679665346556518D+06 Chebyshev coefficients for coordinate X
+0.68992426438827461D+04
+0.13937490815254240D+02
-0.14502888565091926D+00
+0.94310869972105138D-02
-0.11645078150632141D-02
-0.43779188366174216D-04
+0.30695233390345058D-04
-0.39159531297627836D-05
-0.89881849972524960D-07
+0.98907025124491183D-07

-0.30422657092360721D+06 Chebyshev coefficients for coordinate Y
-0.27781546046598733D+04
+0.22921659539994550D+02
+0.42247233378477411D-01
+0.13890369373257272D-02
+0.92303741724564161D-03
-0.20226195636958256D-03
+0.11925225696786511D-04
+0.23768188839312643D-05
-0.63105068443818848D-06
+0.48248874620036552D-07

-0.13630479264692534D+06 Chebyshev coefficients for coordinate Z
-0.13672004988200645D+04
+0.96366419825635337D+01
+0.18917873923655796D-01
-0.26396620160085149D-03
+0.62068370757140123D-03
-0.10349973362450982D-03
+0.31858047813540080D-05
+0.16756257537053898D-05
-0.32781703111714128D-06
+0.15528367354045134D-07

3°) Barycentric Rectangular Equatorial Coordinates ( Geocentric for the Moon )

a) Program#1

-Now we have our DATA file of 326 numbers, so we can use the "INPOP" programs listed hereunder.

Data Registers: R00 & R34 to R41: temp R39 = ( number of Chebyshev coefficients per coordinate ) - 2 , R40 = DT/2

                               R01 = X_Mercury     R04 = X_Venus        R07 = X_EMB        R10 = X_Mars        R13 = X_Jupiter        R16 = X_Saturn
                               R02 = Y_Mercury     R05 = Y_Venus        R08 = Y_EMB        R11 = Y_Mars        R14 = Y_Jupiter        R17 = Y_Saturn
                               R03 = Z_Mercury      R06 = Z_Venus        R09 = Z_EMB         R12 = Z_Mars        R15 = Z_Jupiter        R18 = Z_Saturn

                                R19 = X_Uranus      R22 = X_Neptune      R25 = X_Pluto      R28 = X_Moon      R31 = X_Sun
                                R20 = Y_Uranus      R23 = Y_Neptune      R26 = Y_Pluto      R29 = Y_Moon      R32 = Y_Sun
                                R21 = Z_Uranus      R24 = Z_Neptune       R27 = Z_Pluto      R30 = Z_Moon       R33 = Z_Sun

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

01 LBL "INPOP"
02 HR
03 24
04 /
05 STO 36
06 X<>Y
07 XEQ "J2"
08 2451544.5
09 +
10 STO 37
11 149597870.7
12 STO 41
13 "DATA"
14 CLX
15 SEEKPTA
16 SIGN
17 STO 35
18 12
19 STO 39
20 4

21 STO 40
22 XEQ 01
23 8
24 STO 39
25 STO 40
26 XEQ 01
27 11
28 STO 39
29 2
30 STO 40
31 XEQ 01
32 9
33 STO 39
34 16
35 STO 40
36 XEQ 01
37 6
38 STO 39
39 XEQ 01
40 DSE 39

41 XEQ 01
42 DSE 39
43 XEQ 01
44 XEQ 01
45 XEQ 01
46 11
47 STO 39
48 2
49 STO 40
50 XEQ 01
51 9
52 STO 39
53 8
54 STO 40
55 LBL 01
56 RCL 37
57 GETX
58 -
59 RCL 36
60 +

61 RCL 40
62 ST- Y
63 /
64 STO 00
65 ACOS
66 3 E-3
67 ST+ 35
68 LBL 02
69 GETX
70 RCL 00
71 GETX
72 *
73 +
74 STO 38
75 RCL 39
76 STO 34
77 SIGN
78 RCL 00
79 LBL 03
80 RCL 00

81 ST+ X
82 RCL Y
83 *
84 R^
85 -
86 GETX
87 RCL Y
88 *
89 ST+ 38
90 RDN
91 DSE 34
92 GTO 03
93 RCL 38
94 RCL 41
95 /
96 STO IND 35
97 ISG 35
98 GTO 02
99 END

( 203 bytes / SIZE 042 )

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 "INPOP" gives in 3mn18s

• Mercury

      R01 = -0.086268056 AU
      R02 = 0.261011681 AU
      R03 = 0.148335924 AU

• Venus

      R04 = 0.625711278 AU
      R05 = 0.340718753 AU
      R06 = 0.113580260 AU

• Earth

      R07 = 0.924361847 AU
      R08 = -0.370499848 AU
      R09 = -0.160651074 AU

• Mars

     R10 = -0.565485208 AU
     R11 = -1.276768212 AU
     R12 = -0.570377128 AU

• Jupiter

    R13 = 2.304854478 AU
    R14 = 4.122835672 AU
    R15 = 1.710961493 AU

• Saturn

    R16 = -8.415554159 AU
    R17 = -4.690269793 AU
    R18 = -1.575018519 AU

• Uranus

    R19 = 19.94964692 AU
    R20 = 2.033883690 AU
    R21 = 0.608631600 AU

• Neptune

    R22 = 26.37870201 AU
    R23 = -12.96971165 AU
    R24 = -5.965297896 AU

• Pluto

    R25 = 4.714703676 AU
    R26 = -30.06354049 AU
    R27 = -10.80242284 AU

• Moon

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

• Sun

   R31 = -0.002028869 AU
   R32 = -0.002015374 AU
   R33 = -0.000902167 AU

Notes:

-Line 65 ACOS is only useful to produce a DATAERROR message if an x-value is outside the intervall [-1,+1]
-Otherwise, this instruction may be deleted: it will save 6 seconds.

-There is also an inpop ascii file that contains the Chebyshev coefficients for the Earth-Moon barycenter.
-In this case, replace line 29 by 8 ( instead of 2 ), because DT = 16 days for EMB instead of 4 days for the Earth.
-The coefficients for EMB are to be updated every 16 days only.

-If you have an HP-41 CX and if you can use an M-Code routine CdT ( cf "Ephemerides & Chebyshev Polynomials for the HP-41 )
the following variant will return the results much faster:

b) Program#2

-This variant uses the same DATA file of 326 numbers in extended memory.

Data Registers: R00 & R34 to R54: temp R39 = number of Chebyshev coefficients per coordinate , R40 = DT/2

Flags: /
Subroutine: "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 "INPOP"
02 HR
03 24
04 /
05 STO 36
06 X<>Y
07 XEQ "J2"
08 2451544.5
09 +
10 STO 37
11 149597870.7
12 STO 38
13 "DATA"
14 CLX
15 SEEKPTA
16 SIGN
17 STO 35

18 41.04
19 STO 34
20 14
21 STO 39
22 4
23 STO 40
24 XEQ 01
25 10
26 STO 39
27 8
28 STO 40
29 XEQ 01
30 13
31 STO 39
32 2
33 STO 40
34 XEQ 01

35 11
36 STO 39
37 16
38 STO 40
39 XEQ 01
40 8
41 STO 39
42 XEQ 01
43 DSE 39
44 XEQ 01
45 DSE 39
46 XEQ 01
47 XEQ 01
48 XEQ 01
49 13
50 STO 39
51 2

52 STO 40
53 XEQ 01
54 11
55 STO 39
56 8
57 STO 40
58 LBL 01
59 RCL 37
60 GETX
61 -
62 RCL 36
63 +
64 RCL 40
65 ST- Y
66 /
67 STO 00
68 ACOS

69 3 E-3
70 ST+ 35
71 LBL 02
72 RCL 34
73 RCL 39
74 E3
75 /
76 +
77 GETRX
78 RCL 00
79 CdT
80 RCL 38
81 /
82 STO IND 35
83 ISG 35
84 GTO 02
85 END

( 189 bytes / SIZE 055 )

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

where the time is expressed in TDB ---Execution time = 1mn38s---

Example:

-The same example gives the same results, though the last decimal may vary according to the version of "CdT" that you employ.

Notes:

-Line 68 ACOS is only useful to produce a DATAERROR message if an x-value is outside the intervall [-1,+1]
-Otherwise, this instruction may be deleted: it will save 6 seconds.

-If you are using the inpop ascii file that contains the Chebyshev coefficients for the Earth-Moon barycenter,
replace line 32 by 8 ( instead of 2 ), because DT = 16 days for EMB instead of 4 days for the Earth.

4°) Data File of 236 Numbers

-Since the HP-41 works with 10 digits only, we can save many keystrokes and registers if we neglect the smallest coefficients:
-Instead of 326 numbers, we can get the same results with a data file of 236 numbers

Planet Nb Coeff DT Pointer

Mercury        11           8          0 ->33
Venus             8          16        34->58
Earth              8           4          59->83
Mars              8          32         84->108
Jupiter            5          32        109->124
Saturn            5          32        125->140
Uranus           4          32        141->153
Neptune         4          32        154->166
Pluto              4          32        167->179
Moon           10          4         180->210
Sun                8          16        211->235

-Create a data file of 236 numbers ( for instance 236 alpha DATA alpha XEQ CRFLD ) and store all these numbers ( assign SAVEX to a key ... )

( 2456169 SAVEX -.2931533699 E8 SAVEX ..................................... .3185804781 E-5 SAVEX )

MERCURY pointer 0 to 33

2456169.00 Initial Julian Day

VENUS pointer 34 to 58

2456169.00 Initial Julian Day

EARTH pointer 59 to 83

2456169.00 Initial Julian Day

MARS pointer 84 to 108

2456153.00 Initial Julian Day

JUPITER pointer 109 to 124

2456153.00 Initial Julian Day

+0.34494863937185967D+09 Chebyshev coefficients for coordinate X
-0.16262803278299069D+08
-0.51492858784948548D+05
+0.42711828402470820D+03
+0.42701618979108802D+00

+0.61657436011927211D+09 Chebyshev coefficients for coordinate Y
+0.82711204868866391D+07
-0.92000207881153910D+05
-0.16538494675315775D+03
+0.13738433508864296D+01

+0.25586985129875845D+09 Chebyshev coefficients for coordinate Z
+0.39411648466497753D+07
-0.38180158090569857D+05
-0.81287343504534988D+02
+0.57848208080693742D+00

SATURN pointer 125 to 140

2456153.00 Initial Julian Day

-0.12589969804793978D+10 Chebyshev coefficients for coordinate X
+0.60250555881640008D+07
+0.25656016408884636D+05
-0.26091706789991974D+02
-0.32318383455276489D-01

-0.70151070696737397D+09 Chebyshev coefficients for coordinate Y
-0.10584583622590527D+08
+0.14295233363278850D+05
+0.32795317709571542D+02
-0.33564344048500061D-01

-0.23555800950844052D+09 Chebyshev coefficients for coordinate Z
-0.46313195842606947D+07
+0.47997570216998720D+04
+0.14669815857262556D+02
-0.12469083070755005D-01

URANUS pointer 141 to 153

2456153.00 Initial Julian Day

+0.29844306253814359D+10 Chebyshev coefficients for coordinate X
-0.10578598666025975D+07
-0.70070440413590486D+04
+0.28631464640299481D+00

+0.30416411644151908D+09 Chebyshev coefficients for coordinate Y
+0.81682147366144164D+07
-0.71345117492477095D+03
-0.32123588124910989D+01

+0.91005867922737196D+08 Chebyshev coefficients for coordinate Z
+0.35924279427734483D+07
-0.21340204341134006D+03
-0.14108885402480762D+01

NEPTUNE pointer 154 to 166

2456153.00 Initial Julian Day

+0.39461517846225348D+10 Chebyshev coefficients for coordinate X
+0.35257790407171724D+07
-0.27726735504026419D+04
-0.43271374702453613D+00

-0.19403155528979404D+10 Chebyshev coefficients for coordinate Y
+0.61907166574255098D+07
+0.13636191657213105D+04
-0.71634089946746826D+00

-0.89242513523491347D+09 Chebyshev coefficients for coordinate Z
+0.24461173395014242D+07
+0.62716806971311519D+03
-0.28244119882583618D+00

PLUTO pointer 167 to 179

2456153.00 Initial Julian Day

+0.70521664500415242D+09 Chebyshev coefficients for coordinate X
+0.75749968357384838D+07
-0.39723892320745574D+03
-0.65525954961776733D+00

-0.44974451175417824D+10 Chebyshev coefficients for coordinate Y
+0.49147782427988190D+06
+0.25327369069405177D+04
-0.40186929702758789D+00

-0.16159925232548270D+10 Chebyshev coefficients for coordinate Z
-0.21289386711855391D+07
+0.91003840069202442D+03
+0.71972052256266281D-01

MOON pointer 180 to 210

2456169.00 Initial Julian Day

SUN pointer 211 to 235

2456169.00

5°) Barycentric Rectangular Equatorial Coordinates ( Geocentric for the Moon )

a) Program#1

-With a DATA file of 236 numbers instead of 326, the program will run faster, without significant changes in the outputs.

Data Registers: R00 & R34 to R41: temp R39 = ( number of Chebyshev coefficients per coordinate ) - 2 , R40 = DT/2

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

01 LBL "INPOP"
02 HR
03 24
04 /
05 STO 36
06 X<>Y
07 XEQ "J2"
08 2451544.5
09 +
10 STO 37
11 149597870.7
12 STO 41
13 "DATA"
14 CLX
15 SEEKPTA
16 SIGN
17 STO 35
18 9
19 STO 39

20 4
21 STO 40
22 XEQ 01
23 6
24 STO 39
25 8
26 STO 40
27 XEQ 01
28 2
29 STO 40
30 XEQ 01
31 16
32 STO 40
33 XEQ 01
34 3
35 STO 39
36 XEQ 01
37 XEQ 01
38 DSE 39

39 XEQ 01
40 XEQ 01
41 XEQ 01
42 8
43 STO 39
44 2
45 STO 40
46 XEQ 01
47 6
48 STO 39
49 8
50 STO 40
51 LBL 01
52 RCL 37
53 GETX
54 -
55 RCL 36
56 +
57 RCL 40

58 ST- Y
59 /
60 STO 00
61 ACOS
62 3 E-3
63 ST+ 35
64 LBL 02
65 GETX
66 RCL 00
67 GETX
68 *
69 +
70 STO 38
71 RCL 39
72 STO 34
73 SIGN
74 RCL 00
75 LBL 03
76 RCL 00

77 ST+ X
78 RCL Y
79 *
80 R^
81 -
82 GETX
83 RCL Y
84 *
85 ST+ 38
86 RDN
87 DSE 34
88 GTO 03
89 RCL 38
90 RCL 41
91 /
92 STO IND 35
93 ISG 35
94 GTO 02
95 END

( 193 bytes / SIZE 042 )

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

where the time is expressed in TDB

Example: The same one: 2012/08/29 16h41m37s TDB

2012.0829 ENTER^
16.4137 XEQ "INPOP" gives in 2mn13s

• Mercury

      R01 = -0.086268056 AU
      R02 = 0.261011681 AU
      R03 = 0.148335924 AU

• Venus

      R04 = 0.625711278 AU
      R05 = 0.340718753 AU
      R06 = 0.113580260 AU

• Earth

      R07 = 0.924361847 AU
      R08 = -0.370499848 AU
      R09 = -0.160651074 AU

• Mars

     R10 = -0.565485208 AU
     R11 = -1.276768212 AU
     R12 = -0.570377128 AU

• Jupiter

    R13 = 2.304854478 AU
    R14 = 4.122835672 AU
    R15 = 1.710961493 AU

• Saturn

    R16 = -8.415554159 AU
    R17 = -4.690269793 AU
    R18 = -1.575018519 AU

• Uranus

    R19 = 19.94964692 AU
    R20 = 2.033883690 AU
    R21 = 0.608631600 AU

• Neptune

    R22 = 26.37870201 AU
    R23 = -12.96971165 AU
    R24 = -5.965297896 AU

• Pluto

    R25 = 4.714703676 AU
    R26 = -30.06354049 AU
    R27 = -10.80242284 AU

• Moon

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

• Sun

   R31 = -0.002028869 AU
   R32 = -0.002015374 AU
   R33 = -0.000902167 AU

Notes:

-Line 60 ACOS is only useful to produce a DATAERROR message if an x-value is outside the intervall [-1,+1]
-Otherwise, this instruction may be deleted: it will save 6 seconds.

-If you employ the inpop ascii file that contains the Chebyshev coefficients for the Earth-Moon barycenter,
replace line 28 by 8 ( instead of 2 ), because DT = 16 days for EMB instead of 4 days for the Earth.

b) Program#2

-This variant uses the same DATA file of 236 numbers in extended memory.

Data Registers: R00 & R34 to R51: temp R39 = number of Chebyshev coefficients per coordinate , R40 = DT/2

Flags: /
Subroutine: "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 "INPOP"
02 HR
03 24
04 /
05 STO 36
06 X<>Y
07 XEQ "J2"
08 2451544.5
09 +
10 STO 37
11 149597870.7
12 STO 38
13 "DATA"
14 CLX
15 SEEKPTA
16 SIGN

17 STO 35
18 41.04
19 STO 34
20 11
21 STO 39
22 4
23 STO 40
24 XEQ 01
25 8
26 STO 39
27 STO 40
28 XEQ 01
29 2
30 STO 40
31 XEQ 01
32 16

33 STO 40
34 XEQ 01
35 5
36 STO 39
37 XEQ 01
38 XEQ 01
39 DSE 39
40 XEQ 01
41 XEQ 01
42 XEQ 01
43 10
44 STO 39
45 2
46 STO 40
47 XEQ 01
48 8

49 STO 39
50 STO 40
51 LBL 01
52 RCL 37
53 GETX
54 -
55 RCL 36
56 +
57 RCL 40
58 ST- Y
59 /
60 STO 00
61 ACOS
62 3 E-3
63 ST+ 35
64 LBL 02

65 RCL 34
66 RCL 39
67 E3
68 /
69 +
70 GETRX
71 RCL 00
72 CdT
73 RCL 38
74 /
75 STO IND 35
76 ISG 35
77 GTO 02
78 END

( 175 bytes / SIZE 052 )

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

where the time is expressed in TDB ---Execution time = 78s---

Example:

-The same example gives the same results, though the last decimal may vary according to the version of "CdT" that you employ.

Notes:

-Line 61 ACOS is only useful to produce a DATAERROR message if an x-value is outside the intervall [-1,+1]
-Otherwise, this instruction may be deleted: it will save 6 seconds.

-If you are using the inpop ascii file that contains the Chebyshev coefficients for the Earth-Moon barycenter,
replace line 29 by 8 ( instead of 2 ), because DT = 16 days for EMB instead of 4 days for the Earth.

-Line 72 CdT may of course be replaced by XEQ "CdT"

6°) 11 Data Files

-Instead of a single file, we can of course create several data files, i-e one for each celestial body.
-It will cost more bytes, but it will be easier to update.

-Namely, "ME" "VE" "EAR" "MA" JU" "SA" "UR" "NE" "PL" "MO" "SUN"

-For the 2 following programs, the 1st number of each data file must be the initial Julian day number + n / 1000
where n is the number of Chebyshev coefficients per coordinate.
-This "trick" simplifies "INPOP" and it gives more flexibility to the program.

-For instance, in the simplified version of paragraph 4 and for Saturn, the "SA" file must contain:

2456153.005 Initial Julian Day + 5 / 1000 because there are 5 Chebyshev coefficients for each coordinate.

-0.12589969804793978D+10 Chebyshev coefficients for coordinate X
+0.60250555881640008D+07
+0.25656016408884636D+05
-0.26091706789991974D+02
-0.32318383455276489D-01

-0.70151070696737397D+09 Chebyshev coefficients for coordinate Y
-0.10584583622590527D+08
+0.14295233363278850D+05
+0.32795317709571542D+02
-0.33564344048500061D-01

-0.23555800950844052D+09 Chebyshev coefficients for coordinate Z
-0.46313195842606947D+07
+0.47997570216998720D+04
+0.14669815857262556D+02
-0.12469083070755005D-01

7°) Barycentric Rectangular Equatorial Coordinates ( Geocentric for the Moon )

a) Program#1

-First create the 11 data files as suggested above.

Data Registers: R00 & R34 to R41: temp R39 = ( number of Chebyshev coefficients per coordinate ) - 2 , R40 = DT/2

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

01 LBL "INPOP"
02 HR
03 24
04 /
05 STO 36
06 X<>Y
07 XEQ "J2"
08 2451544.5
09 +
10 STO 37
11 149597870.7
12 STO 41
13 1
14 STO 35
15 4
16 STO 40
17 "ME"
18 XEQ 01
19 8
20 STO 40
21 "VE"

22 XEQ 01
23 2
24 STO 40
25 "EAR"
26 XEQ 01
27 16
28 STO 40
29 "MA"
30 XEQ 01
31 "JU"
32 XEQ 01
33 "SA"
34 XEQ 01
35 "UR"
36 XEQ 01
37 "NE"
38 XEQ 01
39 "PL"
40 XEQ 01
41 2
42 STO 40

43 "MO"
44 XEQ 01
45 8
46 STO 40
47 "SUN"
48 LBL 01
49 CLX
50 SEEKPTA
51 GETX
52 ENTER^
53 FRC
54 E3
55 *
56 2
57 -
58 STO 39
59 RCL 37
60 RCL Z
61 INT
62 -
63 RCL 36

64 +
65 RCL 40
66 ST- Y
67 /
68 STO 00
69 ACOS
70 3 E-3
71 ST+ 35
72 LBL 02
73 GETX
74 RCL 00
75 GETX
76 *
77 +
78 STO 38
79 RCL 39
80 STO 34
81 SIGN
82 RCL 00
83 LBL 03
84 RCL 00

85 ST+ X
86 RCL Y
87 *
88 R^
89 -
90 GETX
91 RCL Y
92 *
93 ST+ 38
94 RDN
95 DSE 34
96 GTO 03
97 RCL 38
98 RCL 41
99 /
100 STO IND 35
101 ISG 35
102 GTO 02
103 END

( 218 bytes / SIZE 042 )

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

where the time is expressed in TDB ---Execution time = 2m45s---

Example:

-The same example gives the same results.

Notes:

-Line 69 ACOS is only useful to produce a DATAERROR message if an x-value is outside the intervall [-1,+1]
-Otherwise, this instruction may be deleted: it will save 6 seconds.

-If you are using the inpop ascii file that contains the Chebyshev coefficients for the Earth-Moon barycenter,
replace line 23 by 8 ( instead of 2 ), and line 25 by "EMB"

b) Program#2

-The same method is used hereunder - 11 DATA files - but the M-Code routine ( or focal program ) CdT is called.

Data Registers: R00 & R34 to R41: temp R39 = number of Chebyshev coefficients per coordinate / 1000 , R40 = DT/2

Flags: /
Subroutine: "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 "INPOP"
02 HR
03 24
04 /
05 STO 36
06 X<>Y
07 XEQ "J2"
08 2451544.5
09 +
10 STO 37
11 149597870.7
12 STO 38
13 1
14 STO 35
15 41.04
16 STO 34

17 "ME"
18 XEQ 01
19 8
20 STO 40
21 "VE"
22 XEQ 01
23 2
24 STO 40
25 "EAR"
26 XEQ 01
27 16
28 STO 40
29 "MA"
30 XEQ 01
31 "JU"
32 XEQ 01

33 "SA"
34 XEQ 01
35 "UR"
36 XEQ 01
37 "NE"
38 XEQ 01
39 "PL"
40 XEQ 01
41 2
42 STO 40
43 "MO"
44 XEQ 01
45 8
46 STO 40
47 "SUN"
48 LBL 01

49 CLX
50 SEEKPTA
51 GETX
52 FRC
53 STO 39
54 RCL 37
55 LASTX
56 INT
57 -
58 RCL 36
59 +
60 RCL 40
61 ST- Y
62 /
63 STO 00
64 ACOS

65 3 E-3
66 ST+ 35
67 LBL 02
68 RCL 34
69 RCL 39
70 +
71 GETRX
72 RCL 00
73 CdT
74 RCL 00
75 RCL 38
76 /
77 STO IND 35
78 ISG 35
79 GTO 02
80 END

( 189 bytes / SIZE 052 )

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

where the time is expressed in TDB ---Execution time = 85s---

Example:

-The same example gives the same results again.

Notes:

-Line 73 may be replaced by XEQ "CdT"
-Line 64 ACOS is only useful to produce a DATAERROR message if an x-value is outside the intervall [-1,+1]
-Otherwise, this instruction may be deleted: it will save 6 seconds.

-If you are using the inpop ascii file that contains the Chebyshev coefficients for the Earth-Moon barycenter,
replace line 23 by 8 ( instead of 2 ), and line 25 by "EMB"

c) Clenshaw's Algorithm

-All the programs listed in paragraphs 3-a) , 5-a) , 7-a) may be modified to use Clenshaw's algorithm.
-Simply store the Chebyshev coefficients in the opposite order after the initial Julian day number

   a_n a_n-1 ..... a₀   ( X-coordinate )
   b_n b_n-1 ..... b₀   ( Y-coordinate )
   c_n c_n-1 ..... c₀   ( Z-coordinate )

and change the listing like the following one.

-For instance, the routine of §7-a) becomes:

Data Registers: R00 & R34 to R41: temp R39 = ( number of Chebyshev coefficients per coordinate ) - 1 , R40 = DT/2

                               R19 = X_Uranus      R22 = X_Neptune      R25 = X_Pluto      R28 = X_Moon      R31 = X_Sun
                               R20 = Y_Uranus      R23 = Y_Neptune      R26 = Y_Pluto      R29 = Y_Moon      R32 = Y_Sun
                               R21 = Z_Uranus      R24 = Z_Neptune       R27 = Z_Pluto      R30 = Z_Moon       R33 = Z_Sun

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

01 LBL "INPOP"
02 HR
03 24
04 /
05 STO 36
06 X<>Y
07 XEQ "J2"
08 2451544.5
09 +
10 STO 37
11 149597870.7
12 STO 38
13 1
14 STO 35
15 4
16 STO 40
17 "ME"
18 XEQ 01
19 8
20 STO 40

21 "VE"
22 XEQ 01
23 2
24 STO 40
25 "EAR"
26 XEQ 01
27 16
28 STO 40
29 "MA"
30 XEQ 01
31 "JU"
32 XEQ 01
33 "SA"
34 XEQ 01
35 "UR"
36 XEQ 01
37 "NE"
38 XEQ 01
39 "PL"
40 XEQ 01

41 2
42 STO 40
43 "MO"
44 XEQ 01
45 8
46 STO 40
47 "SUN"
48 LBL 01
49 CLX
50 SEEKPTA
51 GETX
52 ENTER^
53 FRC
54 E3
55 *
56 DSE X
57 STO 39
58 RCL 37
59 RCL Z
60 INT

61 -
62 RCL 36
63 +
64 RCL 40
65 ST- Y
66 /
67 STO 00
68 ACOS
69 3 E-3
70 ST+ 35
71 LBL 02
72 RCL 39
73 STO 34
74 CLST
75 LBL 03
76 RCL X
77 RCL00
78 ST+ X
79 *
80 R^

81 -
82 GETX
83 +
84 DSE 34
85 GTO 03
86 RCL 00
87 *
88 X<>Y
89 -
90 GETX
91 +
92 RCL 38
93 /
94 STO IND 35
95 ISG 35
96 GTO 02
97 END

( 208 bytes / SIZE 041 )

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

where the time is expressed in TDB ---Execution time = 2m33s---

Example:

-The same example gives - almost - the same results.

Notes:

-Line 69 ACOS is only useful to produce a DATAERROR message if an x-value is outside the intervall [-1,+1]
-Otherwise, this instruction may be deleted: it will save 6 seconds.

-If you are using the inpop ascii file that contains the Chebyshev coefficients for the Earth-Moon barycenter,
replace line 23 by 8 ( instead of 2 ), and line 25 by "EMB"

8°) Heliocentric & Geocentric Coordinates

-If you have used the coordinates of the Earth-Moon barycentre, simply employ
"HELIO" and "GEOC" which are listed in "JPL DE422-DE423-DE424 Ephemerides for the HP-41"
-Otherwise, if you have obtained directly the barycentric coordinates of the Earth ( like above ), employ the following variant of "HELIO".

-We simply have to subtract the barycentric coordinates of the Sun from all the barycentric coordinates.

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

                               R01 = X_Mercury     R04 = X_Venus        R07 = X_Earth        R10 = X_Mars        R13 = X_Jupiter        R16 = X_Saturn
                               R02 = Y_Mercury     R05 = Y_Venus        R08 = Y_Earth        R11 = Y_Mars        R14 = Y_Jupiter        R17 = Y_Saturn
                               R03 = Z_Mercury      R06 = Z_Venus        R09 = Z_Earth         R12 = Z_Mars        R15 = Z_Jupiter        R18 = Z_Saturn

                               R19 = X_Uranus      R22 = X_Neptune      R25 = X_Pluto        R28 = X_Moon      R31 = X_Sun
                               R20 = Y_Uranus      R23 = Y_Neptune      R26 = Y_Pluto        R29 = Y_Moon      R32 = Y_Sun
                               R21 = Z_Uranus      R24 = Z_Neptune       R27 = Z_Pluto        R30 = Z_Moon       R33 = Z_Sun

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 END

( 47 bytes / SIZE 034 )

STACK	INPUT	OUTPUT
X	/	/

Example: The same one:

-After executing "JPL"

XEQ "HELIO" gives in 4 seconds

• Mercury

      R01 = -0.084239187 AU
      R02 = 0.263027055 AU
      R03 = 0.149238092 AU

• Venus

      R04 = 0.627740147 AU
      R05 = 0.342734127 AU
      R06 = 0.114482427 AU

• Earth

      R07 = 0.926390716 AU
      R08 = -0.368484474 AU
      R09 = -0.159748907 AU

• Mars

     R10 = -0.563456339 AU
     R11 = -1.274752838 AU
     R12 = -0.569474961 AU

• Jupiter

    R13 = 2.306883348 AU
    R14 = 4.124851045 AU
    R15 = 1.711863661 AU

• Saturn

    R16 = -8.413525290 AU
    R17 = -4.688254419 AU
    R18 = -1.574116352 AU

• Uranus

    R19 = 19.95167579 AU
    R20 = 2.035899065 AU
    R21 = 0.609533767 AU

• Neptune

    R22 = 26.38073088 AU
    R23 = -12.96769628 AU
    R24 = -5.964395729 AU

• Pluto

    R25 = 4.716732545 AU
    R26 = -30.06152512 AU
    R27 = -10.80152067 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:

-I've used the results given by the last program ( §7-c) )
-The last decimals may differ slightly with another version.
-After executing "HELIO" , execute "GEOC" that listed in "JPL DE422-DE423-DE424 Ephemerides for the HP-41" to get the geocentric coordinates.
-It yields:

• Mercury

      R01 = -1.010629903 AU
      R02 = 0.631511529 AU
      R03 = 0.308986998 AU

• Venus

      R04 = -0.298650569 AU
      R05 = 0.711218601 AU
      R06 = 0.274231333 AU

• Earth

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

• Mars

     R10 = -1.489847055 AU
     R11 = -0.906268364 AU
     R12 = -0.409726054 AU

• Jupiter

    R13 = 1.380492632 AU
    R14 = 4.493335519 AU
    R15 = 1.871612568 AU

• Saturn

    R16 = -9.339916006 AU
    R17 = -4.319769945 AU
    R18 = -1.414367446 AU

• Uranus

    R19 = 19.02528507 AU
    R20 = 2.404383539 AU
    R21 = 0.769282674 AU

• Neptune

    R22 = 25.45434016 AU
    R23 = -12.59921181 AU
    R24 = -5.804646823 AU

• Pluto

    R25 = 3.790341829 AU
    R26 = -29.69304065 AU
    R27 = -10.64177176 AU

• Moon

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

• Sun

   R31 = -0.926390716 AU
   R32 = 0.368484474 AU
   R33 = 0.159748907 AU

Notes:

-The different versions of "INPOP" allow you to use your HP-41 to compute accurate positions of the Sun, Moon and planets,
even if you don't have any way to transfer data to your calculator and if you don't have an HEPAX , CLONIX or NOVRAM module.
-However, it's still necessary to update the coefficients every 16 days for the Sun & Venus,
every 8 days for Mercury, every 4 days for the Moon & the Earth or every 16 days for the Earth-Moon barycenter and every 32 days for the other planets.
-The JPLDE4xx ephemerides may also be computed with these programs after minor modifications.

Reference:

[1] http://www.imcce.fr/inpop

hp41programs

INPOP Ephemerides for the HP-41