Planets & Plutoïds for the HP-41


Overview
 

*******************-LAST UPDATE-**********************
                                                                                                              *
-In this new version, the positions of the Plutinos are fitted to DE431       *
-Rhadamanthus & Typhon have also been added.                                   *
                                                                                                              *
********************************************************
 

-PLANETS is a module that computes the positions of the Sun, the Moon and the major planets.

-It is actually a small improvement of some of the programs in the ASTRO2010 module
-Nutation , aberration & parallax are taken into account

-The position of several transneptunian objects may also be computed:

>>>   Pluto - Xena ( Eris ) - Sedna

-It may be used alone.

-The second mod file PLUTOIDS deals with 14 other transneptunian planets

>>>   Altjira - Chaos - Deucalion - Hauméa - Ixion - Makémaké - Orcus - Quaoar
      - Rhadamanthus - Salacia - Sila-Nunam - Typhon - Varda - Varuna

-These second programs calculate the heliocentric coordinates and then call "Z" ( XROM "Z" in PLANETS ) to get the geocentric & topocentric coordinates.

-For the Sun, the Moon and the major planets, the accuracy is about 0°01 over the time-span [1000-3000] ( at least )
-For Pluto, the same precision is obtained between 1880 & 2100
-For the other Plutinos, between 1900 & 2100.

-So, the accuracy is not so good as in the TRANSNEP module, but the time-span is longer.

-For the Sun, Mercury & Venus, truncated series from the VSOP87/VSOP09 theories are used.
-For Jupiter, Saturn, Uranus & Neptune, the perturbations come from the theory TOP2010.
-They are expressed as functions of a unique variable µ with µ = 20°599908944 T
-The perturbations of Mars are expressed with µ too.

-For Jupiter and Saturn, these series converge more rapidly than the usual perturbations expressed with the mean mean longitudes.

-The heliocentric spherical coordinates of most of the Plutinos are obtained by polynomials fitted to the JPL DE431 ephemerides.
-However, there is an uncertainty on the orbital elements of the asteroids. I've used "Solex" with the default option
 which calculates the average of the Astorb database and the AstDys database.
-So, significant differences may appear near 1900 or 2100 between the results given by "PLUTOIDS" and those given by JPL, especially for Salacia.
 

Usage:

0-XEQ "SIZE" 025 at least and store the required data in registers R16 to R20 ( see below )

1-Set or clear flags F01 to F04 according the type of coordinates you want to compute ( see below )

2-  YYYY.MNDD  ENTER  HH.MNSS ( UT )  XEQ "ST" to get the local sidereal time
3-  XEQ "SUN" - or simply R/S - to calculate the coordinates of the Sun and to store the ecliptic rectangular coordinates of the Sun in R01 & R02

4-  XEQ "MO" or R/S  for the Moon
5-  XEQ "ME" or R/S ... to get the coordinates of the planets

Flags:

 CF 01   CF 02  CF 03   to get the heliocentric coordinates, the geocentric coordinates and the topocentric azimuthal coordinates
 CF 01   CF 02  SF 03   to get the heliocentric coordinates and the geocentric coordinates ( ecliptic long & lat and right-ascension & declination )
 CF 01   SF 02               to get the heliocentric coordinates, the geocentric ecliptic longitude & latitude
 SF 01                            to get the heliocentric longitude & latitude only.

 CF 04  for Gregorian dates
 SF 04  for Julian dates

Data Registers:

 R00 = T = Millenia since 2000/01/01 0h TT

 R01-R02 = Ecliptic rectangular mean coordinates of the Sun

 R03 = Geocentric ecliptic longitude ( deg )
 R04 = Geocentric ecliptic latitude ( deg )              ( true ecliptic of the date )
 R05 = Distance Earth-Planet ( AU )

 R06 = Right-Ascension ( hh.mnss )                       ( true equator of the date )
 R07 = Declination ( ° ' " )

 R08 = Heliocentric ecliptic longitude ( deg )
 R09 = Heliocentric ecliptic latitude ( deg )             ( mean ecliptic of the date )
 R10 = Distance Sun-Planet ( AU )

 R11 = Azimuth ( ° ' " )  clockwise from North
 R12 = height ( ° ' " )                                              ( planetary aberration & parallax are taken into account )
 R13 = height corrected for refraction ( ° ' " )

 R14 = Elongation from the Sun ( ° ' " )  (  not very accurate since it's calculated without taking the parallax into account )

 R15 = temp

    R16 = Longitude of the observer ( ° ' " )    ( positive East )         >>> Initialize Registers R16 thru R20 before executing "ST"
    R17 = Latitude of the observer ( ° ' " )
    R18 = Temperature ( in °C )
    R19 = Atmospheric Pressure ( in mbar )
    R20 = TT - UT ( seconds )

 R21 = Local Sidereal Time ( hh.mnss )
 R22 = Obliquity of the Ecliptic ( deg )
 R23 = Nutation in Longitude ( deg )
 R24 = Longitude of the Sun ( deg )
 
 
 
XROM  Function  Desciption
 09,00
 09,01
 09,02
 09,03
 09,04
 09,05
 09,06
 09,07
 09,08
 09,09
 09,10
 09,11
 09,12
 09,13
 09,14
 09,15
 09,16
 10,00
 10,01
 10,02
 10,03
 10,04
 10,05
 10,06
 10,07
 10,08
 10,09
 10,10
 10,11
 10,12
 10,13
 10,14
-PLANETS
 ST
 SUN
 MO
 ME
 VE
 MA
 JU
 SA
 UR
 NE
 PL
 XE
 SD
 K
 L
 Z
-PLUTOIDS
 ALT
 CHA
 DEU
 HAU
 IXI
 MAK
 ORC
 QUA
 RHD
 SAL
 SIL
 TYP
 VRD
 VRN
 Section Header
 Local Sidereal Time
 Coordinates of the Sun
 Position of the Moon
 Position of Mercury
 Position of Venus
 Position of Mars
 Position of Jupiter
 Position of Saturn
 Position of Uranus
 Position of Neptune
 Position of Pluto
 Position of Xena / Lilah / Eris ( 10th Planet )
 Sedna
 Subroutine1 solves Kepler Equation etc...
 Subroutine2 calc. angles which are functions of µ
 Subroutine3 calculates geoc. coord from helio. coord
 Section Header
 Altjira
 Chaos
 Deucalion
 Hauméa
 Ixion
 Makémaké
 Orcus
 Quaoar
 Rhadamanthus
 Salacia
 Sila-Nunam
 Typhon
 Varda
 Varuna

 
THE STACK:
 
 
 STACK  INPUTS       CF01-CF02-CF03  OUTPUTS    CF01-CF02-SF03 OUTPUTS          CF01-SF02 OUTPUTS     SF 01 OUTPUTS
      T       /    Elg = elongation from the Sun ( ° ' '' )                          /  Elg = elongation from the Sun ( ° ' '' )               /
      Z       /      h0 = apparent altitude  ( ° ' '' )                          /          Dist Earth-Planet ( AU )  Radius Vector ( AU )
      Y       /         h = true altitude  ( ° ' '' )            Declination  ( ° ' '' )    Ecliptic Geocentric Latitude ( deg )  Eclipt. Hel. Lat (deg ) 
      X       /          Az = Azimuth  ( ° ' '' )      Right-Ascension  ( hh.mnss )   Ecliptic Geocentric Longitude ( deg ) Eclipt. Hel. Long (deg )

 
Example:   Suppose we are at the US Naval Observatory at Washington ( D.C. )  on 2100/01/01  7h41m UT ,

  Temperature = 10°C & Pressure = 1010 mbar

  Assuming TT-UT = 203 seconds (?)

         Longitude = 77°03'56" W = -77°03'56"   STO 16
         Latitude  =  38°55'17" N = +38°55'17"   STO 17

           10    STO 18
         1010  STO 19

          203   STO 20

      CF 01   CF 02   CF 03

    TRUE LOCAL SIDEREAL TIME

    2100.0101  ENTER^
          7.41      XEQ "ST"  >>>>   TLST = 9h16m57s3 = R21

-We also have

  true  obliquity of the ecliptic = 23°4288 = R22
      nutation in longitude         =  0°0008  = R23

    THE SUN

      R/S or  XEQ "SUN"  >>>>   Az =   74°23'27"  = R11
                                        RDN     h  =  -54°33'13" = R12
                                        RDN     h0 = -54°33'13" = R13        ( here , h0 is meaningless )
                                        RDN   Elg = 0

  R03 = l = 280°931               R06 = R.A. = 18h47m33s
  R04 = b = 0                         R07 = Decl =  -22°58'45"
  R05 = r = 0.983347 AU

 the rectangular coordinates of the Sun:  R01 = X = 0.186555  &  R02 = Y = -0.965489
 apparent longitude of Sun = R24 = 280°931

    THE MOON

      R/S or  XEQ "MO"    >>>>   Az = 138°31'47"  = R11
                                        RDN     h  =   51°16'54" = R12
                                        RDN     h0 =  51°17'40" = R13
                                        RDN   Elg = 119°00'28" = R14

  R03 = l = 161°921               R06 = R.A. = 10h54m23s
  R04 = b = 0°699                  R07 = Decl =  7°44'04"
  R05 = r = 0.002483 AU

    MERCURY

      R/S  or   XEQ "ME"  >>>>   Az =   67°30'42"  = R11
                                       RDN     h  =  -61°33'30" = R12
                                       RDN     h0 = -61°33'30" = R13
                                       RDN   Elg =    7°53'05" = R14

  R03 = l = -71°473                                 R08 = L = 306°251                                R06 = R.A. = 19h21m31s
  R04 = b = -2°120                                  R09 = B =  -6°822                                  R07 = Decl = -24°14'53"
  R05 = r = 1.38309 AU                          R10 = R = 0.43077 AU

    VENUS

      R/S  or   XEQ "VE"  >>>>   Az =  -10°30'23"  = R11
                                       RDN     h  =  -67°11'25" = R12
                                       RDN     h0 = -67°11'25" = R13
                                       RDN   Elg =    39°33'45" = R14

  R03 = l = -39°542                                 R08 = L = 20°246                                  R06 = R.A. = 21h33m52s
  R04 = b = -1°845                                  R09 = B = -2°860                                  R07 = Decl = -16°24'46"
  R05 = r = 1.1236 AU                            R10 = R = 0.7252 AU

    MARS

      R/S  or   XEQ "MA"  >>>>   Az =  -66°27'03"  = R11
                                        RDN     h  =  -8°43'03" = R12
                                        RDN     h0 = -8°43'03" = R13
                                        RDN   Elg =   108°43'42" = R14

  R03 = l = 29°662                                  R08 = L = 67°745                                  R06 = R.A. =  1h48m59s
  R04 = b = 0°957                                   R09 = B = 0°553                                    R07 = Decl = 12°14'36"
  R05 = r = 0.8729 AU                            R10 = R = 1.5100 AU

    JUPITER

      R/S  or   XEQ "JU"  >>>>   Az =  114°44'54"  = R11
                                      RDN     h  =  17°20'45" = R12
                                      RDN     h0 = 17°23'48" = R13
                                      RDN   Elg =   79°41'27" = R14

  R03 = l = -158°757                               R08 = L = 191°020                                R06 = R.A. = 13h20m27s
  R04 = b = 1°277                                   R09 = B = 1°298                                    R07 = Decl = -7°05'55"
  R05 = r = 5.540 AU                              R10 = R = 5.451 AU

    SATURN

      R/S  or   XEQ "SA"  >>>>   Az =  111°54'36"  = R11
                                      RDN     h  =  13°42'40" = R12
                                      RDN     h0 = 13°46'32" = R13
                                      RDN   Elg =   75°17'53" = R14

  R03 = l = -154°353                               R08 = L = 199°997                                R06 = R.A. = 13h38m40s
  R04 = b = 2°424                                   R09 = B = 2°475                                    R07 = Decl = -7°39'01"
  R05 = r = 9.868 AU                              R10 = R = 9.665 AU

    URANUS

      R/S  or   XEQ "UR"  >>>>   Az =  -63°10'52"  = R11
                                      RDN     h  =  -20°18'51" = R12
                                      RDN     h0 = -20°18'51" = R13
                                      RDN   Elg =   96°48'49" = R14

  R03 = l = 17°745                               R08 = L = 20°547                                   R06 = R.A. =  1h06m25s
  R04 = b = -0°631                               R09 = B = -0°626                                   R07 = Decl =   6°22'38"
  R05 = r = 19.834 AU                         R10 = R = 19.974 AU

    NEPTUNE

      R/S  or   XEQ "NE"  >>>>   Az =  133°30'18"  = R11
                                      RDN     h  =    47°36'39" = R12
                                      RDN     h0 =    47°37'32" = R13
                                      RDN   Elg =   113°38'22" = R14

  R03 = l = 167°288                             R08 = L = 165°577                                   R06 = R.A. =  11h14m44s
  R04 = b =  0°966                               R09 = B = 0°953                                       R07 = Decl =   5°54'31"
  R05 = r = 29.801 AU                         R10 = R = 30.209 AU

    PLUTO

      R/S  or   XEQ "PL"  >>>>   Az =   -84°25'29"  = R11
                                      RDN     h  =   -12°35'27" = R12
                                      RDN     h0 =  -12°35'27" = R13
                                      RDN   Elg =   110°29'54" = R14

  R03 = l =  32°402                              R08 = L =  33°519                                        R06 = R.A. =   2h23m51s
  R04 = b = -16°919                             R09 = B = -16°793                                       R07 = Decl =   -3°37'21"
  R05 = r = 48.588 AU                         R10 = R = 48.941 AU

    XENA

      R/S  or   XEQ "XE"  >>>>   Az =   -66°41'24"  = R11
                                      RDN     h  =    5°45'31" = R12
                                      RDN     h0 =    5°54'02" = R13
                                      RDN   Elg =   122°03'08" = R14

  R03 = l =  43°193                              R08 = L =  43°761                                        R06 = R.A. =   2h34m58s
  R04 = b = 6°180                                R09 = B =   6°141                                         R07 = Decl =   21°40'31"
  R05 = r = 83.424 AU                         R10 = R = 83.950 AU

    SEDNA

      R/S  or   XEQ "SD"  >>>>   Az =   -133°03'03"  = R11
                                      RDN     h  =    58°28'59" = R12
                                      RDN     h0 =    58°29'34" = R13
                                      RDN   Elg =   164°28'46" = R14

  R03 = l =  115°169                              R08 = L = 114°985                                        R06 = R.A. =   7h43m48s
  R04 = b = -6°243                                R09 = B =   -6°167                                         R07 = Decl =   14°56'52"
  R05 = r = 76.873 AU                          R10 = R = 77.821 AU
 

Note:

-If you press R/S just after executing "SD" , you will execute "ST" again
 

    ALTJIRA

             XEQ "ALT"  >>>>   Az =   134°54'30"  = R11
                                  RDN     h  =    50°34'39" = R12
                                  RDN     h0 =    50°35'26" = R13
                                  RDN   Elg =   116°37'05" = R14

  R03 = l =  164°299                              R08 = L = 163°207                                        R06 = R.A. =   11h04m58s
  R04 = b =  1°809                                R09 = B =   1°792                                          R07 = Decl =     7°50'47"
  R05 = r = 45.801 AU                          R10 = R = 46.250 AU

    CHAOS

     R/S or XEQ "CHA"  >>>>   Az =   110°26'14"  = R11
                                      RDN     h  =    22°09'35"   = R12
                                      RDN     h0 =    22°11'56"   = R13
                                       RDN   Elg =   82°42'12"   = R14

  R03 = l =  -161°720                             R08 = L = 197°032                                        R06 = R.A. =   13h17m50s
  R04 = b =   6°835                                R09 = B =   6°853                                          R07 = Decl =    -0°50'17"
  R05 = r = 45.173 AU                           R10 = R = 45.059 AU

    DEUCALION

     R/S or XEQ "DEU"  >>>>   Az =   -39°41'12"  = R11
                                      RDN     h  =  -52°45'16"   = R12
                                      RDN     h0 =  -52°45'16"   = R13
                                       RDN   Elg =   59°38'57"   = R14

  R03 = l =  -19°420                               R08 = L = 341°737                                         R06 = R.A. =   22h48m50s
  R04 = b =  -0°347                                R09 = B =  -0°351                                          R07 = Decl =    -7°55'05"
  R05 = r = 42.602 AU                           R10 = R = 42.114 AU

    HAUMEA

     R/S or XEQ "HAU"  >>>>   Az =   36°55'02"   = R11
                                      RDN     h  =  -66°51'16"   = R12
                                      RDN     h0 =  -66°51'16"   = R13
                                       RDN   Elg =   21°33'58"   = R14

  R03 = l =  -57°503                               R08 = L = 303°050                                         R06 = R.A. =   20h18m57s
  R04 = b =  0°135                                 R09 = B =   0°138                                           R07 = Decl =    -19°27'44"
  R05 = r = 38.711 AU                           R10 = R = 37.798 AU

    IXION

     R/S or XEQ "IXI"  >>>>   Az =   -85°03'25"   = R11
                                   RDN     h  =    35°43'06"   = R12
                                   RDN     h0 =   35°44'26"    = R13
                                   RDN   Elg =  156°25'05"   = R14

  R03 = l =   77°436                               R08 = L =  78°097                                          R06 = R.A. =   5h04m32s
  R04 = b =  2°084                                 R09 = B =   2°029                                           R07 = Decl =   24°54'38"
  R05 = r = 32.896 AU                           R10 = R = 33.799 AU

    MAKEMAKE

     R/S or XEQ "MAK"  >>>>   Az =    90°26'33"   = R11
                                      RDN     h  =   -34°49'04"   = R12
                                      RDN     h0 =  -34°49'04"    = R13
                                       RDN   Elg =   22°40'31"   = R14

  R03 = l =  -101°691                             R08 = L =  257°864                                        R06 = R.A. =  17h09m46s
  R04 = b =    1°596                               R09 = B =   1°627                                           R07 = Decl =   -21°19'27"
  R05 = r =  49.026 AU                          R10 = R = 48.120 AU

    ORCUS

     R/S or XEQ "ORC"  >>>>   Az =    98°40'35"   = R11
                                      RDN     h  =   -36°15'12"   = R12
                                      RDN     h0 =  -36°15'12"    = R13
                                       RDN   Elg =   24°45'48"   = R14

  R03 = l =  -103°343                             R08 = L =  256°033                                          R06 = R.A. =  16h59m45s
  R04 = b =   -5°052                               R09 = B =   -5°174                                           R07 = Decl =   -27°47'09"
  R05 = r =  37.893 AU                          R10 = R = 37.003 AU

    QUAOAR

     R/S or XEQ "QUA"  >>>>   Az =   -65°05'09"   = R11
                                      RDN     h  =   -18°27'31"   = R12
                                      RDN     h0 =  -18°27'31"    = R13
                                       RDN   Elg =   99°13'15"   = R14

  R03 = l =  20°156                               R08 = L =  381°480 = 21°480                         R06 = R.A. =  1h16m49s
  R04 = b = -1°560                               R09 = B =   -1°554                                           R07 = Decl =   6°25'43"
  R05 = r =  41.809 AU                        R10 = R = 41.978 AU

    RHADAMANTHUS

     R/S or XEQ "RHD"   >>>>   Az =   44°03'13"   = R11
                                      RDN     h  =  -78°28'35"   = R12
                                      RDN     h0 =  -78°28'35"   = R13
                                      RDN    Elg =  26°04'31"    = R14

  R03 = l =   -55°501                                 R08 = L =  305°031                                             R06 = R.A. =  20h39m56s
  R04 = b =  -11°490                                 R09 = B =  -11°725                                             R07 = Decl =  -30°15'27"
  R05 = r =  44.556 AU                             R10 = R = 43.675 AU

    SALACIA

     R/S or XEQ "SAL"   >>>>   Az =   -94°33'19"   = R11
                                      RDN     h  =    50°55'16"   = R12
                                      RDN     h0 =   50°56'03"    = R13
                                      RDN    Elg =  172°23'51"   = R14

  R03 = l =  94°078                              R08 = L =  94°222                                            R06 = R.A. =  6h18m14s
  R04 = b = 3°299                                R09 = B =   3°228                                             R07 = Decl =  26°39'48"
  R05 = r =  44.136 AU                        R10 = R = 45.111 AU

    SILA-NUNAM

     R/S or XEQ "SIL"   >>>>    Az =   100°15'32"   = R11
                                      RDN     h  =   -25°20'53"   = R12
                                      RDN     h0 =  -25°20'53"    = R13
                                      RDN    Elg =  34°52'41"    = R14

  R03 = l =  -113°900                               R08 = L =  245°367                                            R06 = R.A. =  16h15m26s
  R04 = b =   -1.929                                 R09 = B =  -1°964                                               R07 = Decl =  -23°12'55"
  R05 = r =  44.482 AU                            R10 = R = 43.679 AU

    TYPHON

     R/S or XEQ "TYP"   >>>>   Az =    -6°35'45"   = R11
                                      RDN     h  =  -67°20'35"   = R12
                                      RDN     h0 = -67°20'35"    = R13
                                      RDN    Elg =  38°06'53"    = R14

  R03 = l =  -40°974                                  R08 = L =  319°647                                            R06 = R.A. =  21h27'32s
  R04 = b =  -1°337                                   R09 = B =  -1°355                                              R07 = Decl =  -16°22'58"
  R05 = r =  57.208 AU                             R10 = R = 56.437 AU

    VARDA

     R/S or XEQ "VRD"   >>>>   Az =   -63°52'56"   = R11
                                      RDN     h  =    -25°56'60"   = R12
                                      RDN     h0 =   -25°56'60"    = R13
                                      RDN    Elg =   91°52'31"    = R14

  R03 = l =  12°810                                    R08 = L =  374°247 = 14°247                             R06 = R.A. =  0h52m29s
  R04 = b =  -3°433                                   R09 = B =  -3°430                                               R07 = Decl =    1°53'38"
  R05 = r =  39.203 AU                             R10 = R = 39.247 AU

    VARUNA

     R/S or XEQ "VRN"   >>>>   Az =   94°50'31"   = R11
                                      RDN     h  =     4°17'32"   = R12
                                      RDN     h0 =    4°28'13"    = R13
                                      RDN    Elg =  61°15'18"    = R14

  R03 = l =  -139°258                                R08 = L =  219°618                                            R06 = R.A. =  14h51m26s
  R04 = b =   14°682                                 R09 = B =  14°838                                               R07 = Decl =  -1°03'29"
  R05 = r =  45.335 AU                             R10 = R = 44.870 AU
 
 

Notes:

-The refraction is computed by a formula that duplicates the Pulkovo refraction tables with a precision better than 1 arcsecond if t = 10°C & P = 1010 mbar
-If t # 10°C & P # 1010 mbar, the errors may be larger, especially near the horizon.

-The dates YYYY.MNDD must not be before 0000/03/00 ( otherwise, you get NONEXISTENT )
 
 

References:

[1]  Jean Meeus - "Astronomical Algorithms" - Willmann-Bell  -  ISBN 0-943396-61-1
[2]  VSOP87D Series  ftp://ftp.imcce.fr/pub/ephem/planets/vsop87/
[3]  VSOP09 & TOP2010 Series  http://www.imcce.fr/~jlsimon
[4]  A fantastic software by Aldo Vitagliano: "SOLEX" which may be downloaded freely from http://www.solexorb.it/