hp41programs

Overview
 

-This program calculates the coordinates x and y of the first 7 satellites of Saturn if flag F10 is set,  or of the first 4 satellites of Jupiter if flag F10 is clear.
-Actually, it combines "IEGC" & "METDRTH"  ( cf "Satellites of Jupiter" & "Saturnian Satellites" )

-However, "IEGC" has been re-written so that the same types of formulas are used.
-Moreover, the inclinations of the orbits on the equatorial plane are now taken into account
  for Mimas, Tethys, Rhea, Titan, Hyperion and Europe, Ganymede, Callisto
-Thus, the y-values are obtained more accurately.
 

-The x-axis coincides with the equator of the planet.
-The center of the Planet is the origin and x , y are measured in equatorial radii.
 

                                     y ( North )
                                      |
                                      |
                                      |
( East ) --------------Sat/Jup------------------ x   ( West )
                                      |
                                      |
                                ( South )
 
 

Data Registers:  R00 thru R19 are used for temporay data storage and when the program stops:

                               Io      -    Europa   - Ganymede - Callisto                                                                if  CF 10

                             R01 = x₁        R03 = x₂         R05 = x₃        R07 = x₄
                             R02 = y₁        R04 = y₂         R06 = y₃        R08 = y₄

      or                  Mimas  -  Enceladus  -   Tethys  -   Dione    -    Rhea    -    Titan    -   Hyperion         if  SF 10

                             R01 = x₁        R03 = x₂         R05 = x₃        R07 = x₄         R09 = x₅       R11 = x₆         R13 = x₇
                             R02 = y₁        R04 = y₂         R06 = y₃        R08 = y₄         R10 = y₅       R12 = y₆         R14 = y₇

                             R19 =  - sin D_E  where D_E is the planetocentric declination of the Earth.

Flags:     F01  F02  F03  F04 F05  F06  F07
              -Flag nn  is set when the distance Earth-Satellite n  is shorter than the distance Earth-Planet   ( 0 < nn < 8 )

                CF 10  for the Satellites of Jupiter
                SF 10  for the Satellites of Saturn

Subroutine:   none if you have a Time Module
                       "J0" otherwise  .( cf  for instance "Julian & Gregorian Calendars for the HP-41" )
 

Program listing
 

-If you have a Time module, replace lines 07-08  by   the 3 lines    1.012   DDAYS   -
-Lines 46-267-680 are three-byte  GTOs
-If you don't have an HP-41CX, replace lines 264-265 by  CF 01  CF 02  CF 03  CF 04  CF 05  CF 06  CF 07
 
 

 
   ( 1351 bytes / SIZE 020  )
 
 

    Execution time = 42s  if  CF 10  ( Moons of Jupiter )
    Execution time = 82s  if  SF 10  ( Moons of Saturn )

Example:    On  2004/12/31 at 0h  TT
 

     •  CF 10     JUPITER

     2004.1231  ENTER^
             0         XEQ "STL"        >>>>    x₁ = -4.929     X<>Y     y₁ = 0.155        and in registers  R01 thru R08:

                     Io        -    Europa    -    Ganymede   -    Callisto

                  x₁ = -4.929       x₂ = -4.834         x₃ = -14.516        x₄ = -8.557                  D_E = -2°69
                  y₁ =  0.155       y₂ = -0.306         y₃ =  -0.203         y₄ =  -1.076

-Flag F01 is set:  Io is closer to the Earth than Jupiter.
 

     •  SF 10     SATURN

     2004.1231  ENTER^
             0            R/S       >>>>    x₁ = -0.289     X<>Y     y₁ = 1.169        and in registers  R01 thru R14:

                   Mimas     -   Enceladus  -     Tethys    -     Dione     -    Rhea      -     Titan     -    Hyperion

                  x₁ = -0.288       x₂ =  3.911         x₃ = 0.781        x₄ = -0.103     x₅ = -8.730       x₆ = 3.585        x₇ = 21.825           D_E = -22°52
                  y₁ =  1.170       y₂ = -0.213         y₃ = 1.778        y₄ =  2.398      y₅ =  0.255       y₆ = 7.338        y₇ = 3.645

-Flags  F01  F03  F04  F05  F06  F07  are set, whence  Mimas, Tethys, Dione, Rhea, Titan and Hyperion are closer to the Earth than Saturn.
 
 

Notes:

-The accuracy is of order of a few hundredths of the planet's radius.
-Hyperion's coordinates are less accurate than the other ones.
-For Hyperion, the series converge slowly and several terms might be added to get more accurate results.
-The complete series are available from   ftp://ftp.imcce.fr
-But if you don't want to compute the position of Hyperion, delete lines 268 to 469  and replace line 130 by 6
 

References:

[1]   A. Vienne and L. Duriez 1995  "TASS1.6:  Ephemerides of the major Saturnian Satellites"  Astronomy & Astrophysics  297 ,  588-605
[2]   L. Duriez and A. Vienne 1997  "Theory of motion and Ephemerides of Hyperion"  Astronomy & Astrophysics  324 , 366-380
[3]   Jean Meeus - "Astronomical Algorithms"  - Willmann-Bell  -  ISBN 0-943396-61-1