hp41programs

Overview
 

-This program calculates the coordinates x and y of the first 7 satellites of Saturn, namely:
    1 = Mimas        3 = Tethys   5 = Rhea   7 = Hyperion
    2 = Enceladus   4 = Dione    6 = Titan
-The x-axis coincides with the equator of the planet.
-The center of Saturn is the origin and x , y are measured in units of Saturn's equatorial radius ( the polar radius of Saturn is 0.895 ).

                                     y ( North )
                                      |
                                      |
                                      |
( East ) --------------Saturn------------------ x   ( West )
                                      |
                                      |
                                ( South )
 
 
 

Data Registers:  R00 thru R14 are used for temporay data storage and when the program stops:

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

                             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

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

Subroutine:   none if you have a Time Module
                       "J0" otherwise  .( cf  for instance "Phases of the Moon for the HP-41" )
 

Program listing
 

-If you have a Time module, replace lines 07-08  by   the 3 lines    1.012   DDAYS   -
-If you don't have an HP-41 CX , replace lines 187-188 by  CF 01  CF 02  CF 03  CF 04  CF 05  CF 06  CF 07
 
 

 
( 909 bytes / SIZE 015 )
 
 

  where  L_E  is the saturnicentric latitude of the Earth.        ---Execution time = 67s---

Example1:    On  2005 July 1st at 0h12m34s  TT

     2005.0701  ENTER^
           0.1234  XEQ "METDRTH"   >>>>    x₁ = 1.58     X<>Y     y₁ = 1.01        and in registers  R01 thru R14:

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

                  x₁ = 1.58       x₂ = 2.10         x₃ =  2.25        x₄ = 0.59      x₅ = 2.12       x₆ =  6.91        x₇ = -20.00
                  y₁ = 1.01       y₂ = 1.24         y₃ = -1.62       y₄ = -2.32     y₅ = 3.16       y₆ = -7.23        y₇ = -5.32

-Flags  F01  F02  F05  are set, whence  Mimas; Enceladus and Rhea are closer to the Earth than Saturn.

Example2:   Every 15 years, the Earth is approximately in the plane of the rings. For instance on 1995/09/18 at 0h20m TT  we find:

                  x₄ =  0.00      with  flag  F04  set:       Dione is in transit over the planet's disk
                  y₄ = -0.14

Notes:

-This program uses a simplified method where the inclinations of the orbits of the satellites on the equatorial plane of Saturn have been neglected.
 ( 1.5° - 0° - 1.9° - 0° - 0.4° - 0.3° - 0.4°  from Mimas to Hyperion respectively )
-Therefore, the satellite phenomena ( occultations, transits ... etc ... ) can't always be determined with certainty.
-However, the most important perturbations have been taken into account and the satellites may usually be identified.
-y-values are less accurate than x-values.
-The coordinates of Hyperion are less accurate than the other ones.
-If you don't want to compute the position of Hyperion, replace lines 391-392-393  ( STO Y   RCL 06  -  )  by
  16.1   RCL 00   1412   *    -   +   and delete lines 189 thru 376
 

References:    More complete series may be found in

[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