hp41programs

Overview
 

 1°)  Program#1
 2°)  An M-Code Routine
 3°)  Program#2
 

Last Update:

>>>>  The coordinates of Puck have been added to the Uranian satellites ( perturbations are not taken into account for Puck )
           and several constants given in reference [7] have been used.
>>>>  In program#2, the position of Iapetus is also computed
 
 

-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 ) ------------Jup/Sat/Ura------------------ x   ( West )
                                      |
                                      |
                                ( South )
 
 

Data Registers:  R00 thru R20 are used for temporay data storage and when the program stops:

                            Mimas  -  Enceladus  -   Tethys  -    Dione    -    Rhea    -   Titan   -   Hyperion  -   Iapetus ( with program#2 )

                             R01 = x₁        R03 = x₂         R05 = x₃        R07 = x₄         R09 = x₅       R11 = x₆         R13 = x₇         R15 = x₈
                             R02 = y₁        R04 = y₂         R06 = y₃        R08 = y₄         R10 = y₅       R12 = y₆         R14 = y₇         R16 = y₈

      or                      Io      -    Europa  -  Ganymede - Callisto

      or                    Ariel   -    Umbriel  -   Titania    -   Oberon  -  Miranda  -  Puck
 

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

Flags:     F01  F02  F03  F04 F05  F06  F07  F08
              -Flag nn  is set when the distance Earth-Satellite n  is shorter than the distance Earth-Planet   ( 0 < nn < 8 )
 

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

1°)  Program#1
 

-Two M-code routines are used:  Z+Z  and  Z-Z
-They may be replaced by  XEQ "Z+Z"  and  XEQ "Z-Z"  respectively  ( cf "Complex Functions for the HP-41" )
  or, more directly, by   X<>Y  ST+ T  RDN  +   and   X<>Y  ST-T  RDN  -   respectively.

-If you have a Time module, lines 09-10 may be replaced by the 3 lines    1.012   DDAYS   -
-Lines 144-798-1012 are three-byte  GTOs
-If you don't have an HP-41CX, replace lines 408-409 by
  CF 01  CF 02  CF 03  CF 04  CF 05  CF 06  CF 07
 
 
 

 
      ( 1974 bytes / SIZE 021 )
 
 

        X = 1  for the Satellites of Jupiter             ---Execution time = 44s---
        X = 2  for the Satellites of Saturn             ---Execution time = 84s---
        X = 3  for the Satellites of Uranus            ---Execution time = 68s---

Example:      On  2018/01/24 at 16h41m  TT
 

  •   Jovian Satellites

     2018.0124  ENTER^
         16.41      ENTER^
             1         XEQ "STL"     >>>>    x₁ = -0.150     X<>Y     y₁ = -0.329        and in registers  R01 thru R08:

                   Io         -    Europa    -    Ganymede   -    Callisto

                  x₁ = -0.150       x₂ =  1.752         x₃ = -14.350         x₄ = 9.880           D_E = -3°21
                  y₁ = -0.329       y₂ = -0.593         y₃ = -0.278          y₄ = -1.317

-Flags F01 to F04 are clear:  all these 4 satellites are more distant to the Earth than Jupiter.
 

  •   Saturnian Satellites

     2018.0124  ENTER^
         16.41      ENTER^
             2           R/S             >>>>    x₁ = -2.812     X<>Y     y₁ = 0.543        and in registers  R01 thru R14:

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

                  x₁ = -2.812       x₂ = -0.239         x₃ = -4.877      x₄ = 4.342     x₅ = -8.125       x₆ = -9.839     x₇ =  5.021           D_E = 26°24
                  y₁ = 0.543        y₂ = -1.743         y₃ = -0.193      y₄ = 1.993     y₅ = -1.389       y₆ =  -7.704     y₇ = -10.076

-Flags   F02  F03  F05  F06  F07  are set, whence  Enceladus, Tethys, Rhea, Titan and Hyperion are closer to the Earth than Saturn.
 

  •   Uranian Satellites

     2018.0124  ENTER^
         16.41      ENTER^
             3   R/S            >>>>    x₁ = -2.061     X<>Y     y₁ = 4.281        and in registers  R01 thru R12:

                    Ariel     -    Umbriel    -    Titania    -   Oberon  -   Miranda  -  Puck

                  x₁ = -2.061      x₂ = 9.149       x₃ = 14.964     x₄ = -8.449     x₅ = 3.321      x₁₅ = 0.728               D_E = 36°60
                  y₁ = 4.281       y₂ = -2.982      y₃ = 4.850      y₄ = -12.660    y₅ = -2.075    y₁₅ = 1.957

-Flags  F02  F04  F05 are set, so  Umbriel, Oberon and Miranda are closer to the Earth than Uranus.
 

Notes:
 

-The accuracy is of order of a few hundredths of the planet's radius.
-Hyperion's coordinates are less accurate than those of the other Saturnian Satellites.
-For Hyperion, the series converge slowly and several terms should be added to get more accurate results.

-To obtain a better accuracy, one should use more terms not only in the series that give the satellites' position with respect to the planet,
  but also in the series that give the position of the planet itself with respect to the Earth ! I've used only the main terms ( lines 14 to 342 )
 

-If you don't want to compute the coordinates of the satellites of Jupiter, delete lines 1038 to 1080 and lines 270 to 342
-If you don't want to compute the coordinates of the satellites of Saturn, -----------  411  to  798  ---------  57  to 144
-If you don't want to compute the coordinates of the satellites of Uranus, ----------- 799  to 1012 --------- 145 to 270

 ( If you don't want to get the position of Puck, delete lines 800 to 818 and replace line 269 by 5 instead of 6 )
 

2°)  An M-Code Routine
 

-The M-Code routine "VR" takes the eccentricity e < 1 in Y-register and the mean anomaly M in X-register
-It returns the true anomaly v in X-register and r/a in Y-register
-The eccentric anomaly E is also given in T-register

-The angles must be expressed in decimal degrees.
-There is no check for alpha data

-VR is used in the version below
 

092  "R"
016  "V"
071  ?NCXQ
05C  DEG
2A0  SETDEC
0F8  C=X
128  L=C
10E  A=C ALL
0B8  C=Y
05E  C= | C |
0E8  X=C
0AE  A<>C ALL
0A8  Y=C
04E  C
2BE
35C
050  =
21C
250
250
110  -10^(-6)
028  T=C
046  C=0 S&X
01D  C=
060  A+C
2EE  ?C#0 ALL
01B  JNC+03
2FE  ?C<0 ALL
01F  JC+03
0B5  ?NCGO
0A2  DATAERROR
0B8  C=Y                    loop
10E  A=C ALL
0F8  C=X
070  polar
3C4 rectangular
1D5
078  conversion
2BE  C=-C
00E  A
35C =
162  1
01D  C=
060  A+C
068  Z=C
0B0  C=N ALL
231  ?NCXQ
064  R-D
10E  A=C ALL
0B8  C=Y
2BE  C=-C
01D  C=
061  A+C
138  C=L
025  C=
060  AB+C
078  C=Z
269  C=
060  AB/C
070  N=C ALL
0B8  C=Y
025  C=
060  AB+C
0A8  Y=C
0B0  C=N ALL
05E  C=| C |
10E  A=C ALL
046  C
270  =
038  T
01D  C=
060  A+C
2FE  ?C<0
2B3  JNC-42d           goto loop
0F8  C=X
068  Z=C
0B8  C=Y
028  T=C
10E  A=C ALL
04E  C
35C  =
090  2
261  C=
060  A/C
070  C
209  =
048  tan(C°)
070  N=C ALL
078  C=Z
2BE  C=-C
00E  A
35C  =
162  1
01D  C=
060  A+C
05E  C=| C |
128  L=C
078  C=Z
00E  A
35C  =
162  1
01D  C=
060  A+C
0A8  Y=C
138  C=L
269  C=
060  AB/C
305  C=
060  sqrt(AB)
0B0  C=N ALL
13D  C=
060  AB*C
070  C
2A9  =
040  atan(C°)
10E  A=C ALL
01D  C=
060  A+C
0E8  X=C
070  C
1F1  =
048  cos(C°)
10E  A=C ALL
078  C=Z
135  C=
060  A*C
001  C=
060  AB+1
070  N=C ALL
0B8  C=Y
10E  A=C ALL
138  C=L
135  C=
060  A*C
0B0  C=N
269  C=
060  AB/C
0A8  Y=C
3E0  RTN

( 139 words )
 
 

 
Example:

   0.2   ENTER^
   24    XEQ "VR"  >>>>   35°94864074
                             X<>Y   0.826226700

-And the eccentric anomaly in T-register is  E = 29°67281468

Notes:

-It may take several seconds...
-If e < 0 , it's replaced by -e
-If e = 1 or e > 1 , there will be a DATA ERROR message.
 

3°)  Program#2
 

-Same specifications as the first version in §1, except that the coordinates of Iapetus x₈ & y₈ are stored in R15 & R16

-Lines 144-948-1162 are three-byte  GTOs
 
 
 

 
        ( 2206 bytes / SIZE 023 )
 
 

        X = 1  for the Satellites of Jupiter             ---Execution time = 44s---
        X = 2  for the Satellites of Saturn             ---Execution time = 105s---
        X = 3  for the Satellites of Uranus            ---Execution time = 68s---

Example:      On  2018/01/24 at 16h41m  TT
 

  •   Jovian Satellites

     2018.0124  ENTER^
         16.41      ENTER^
             1         XEQ "STL"     >>>>    x₁ = -0.150     X<>Y     y₁ = -0.329        and in registers  R01 thru R08:

                   Io         -    Europa    -    Ganymede   -    Callisto

                  x₁ = -0.150       x₂ =  1.752         x₃ = -14.350         x₄ = 9.880           D_E = -3°21
                  y₁ = -0.329       y₂ = -0.593         y₃ = -0.278          y₄ = -1.317

-Flags F01 to F04 are clear:  all these 4 satellites are more distant to the Earth than Jupiter.
 

  •   Saturnian Satellites

     2018.0124  ENTER^
         16.41      ENTER^
             2           R/S             >>>>    x₁ = -2.812     X<>Y     y₁ = 0.543        and in registers  R01 thru R16:

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

                  x₁ = -2.812       x₂ = -0.239         x₃ = -4.877      x₄ = 4.342     x₅ = -8.125       x₆ = -9.837     x₇ =  5.013       x₈ = -2.177        D_E = 26°24
                  y₁ = 0.543        y₂ = -1.743         y₃ = -0.193      y₄ = 1.993     y₅ = -1.389       y₆ =  -7.705     y₇ = -10.078    y₈ = 11.220

-Flags   F02  F03  F05  F06  F07  are set, whence  Enceladus, Tethys, Rhea, Titan and Hyperion are closer to the Earth than Saturn.
 

  •   Uranian Satellites

     2018.0124  ENTER^
         16.41      ENTER^
             3   R/S            >>>>    x₁ = -2.061     X<>Y     y₁ = 4.281        and in registers  R01 thru R12:

                     Ariel     -     Umbriel    -   Titania    -   Oberon  -   Miranda   -   Puck

                  x₁ = -2.061      x₂ = 9.149       x₃ = 14.964     x₄ = -8.449     x₅ = 3.321      x₁₅ = 0.728               D_E = 36°60
                  y₁ = 4.281       y₂ = -2.982      y₃ = 4.850      y₄ = -12.660    y₅ = -2.075    y₁₅ = 1.957

-Flags  F02  F04  F05 are set, so  Umbriel, Oberon and Miranda are closer to the Earth than Uranus.
 

Note:

-The precision of Iapetus coordinates is of the same order as Hyperion's coordinates.
 

References:

[1]   Jean Meeus - "Astronomical Algorithms"  - Willmann-Bell  -  ISBN 0-943396-61-1
[2]   D. Harper & D.B. Taylor 1993 - "The orbits of the Major Satellites of Saturn" - Astronomy & Astrophysics  268 , 326-349
[3]   A. Vienne & L. Duriez 1995 - "TASS1.6:  Ephemerides of the major Saturnian Satellites" - Astronomy & Astrophysics  297 ,  588-605
[4]   L. Duriez & A. Vienne 1997 - "Theory of motion and Ephemerides of Hyperion" - Astronomy & Astrophysics  324 , 366-380
[5]   J. Laskar & R.A. Jacobson 1987 - "GUST86.  An Analytical Ephemeris of the Uranian Satellites" - Astronomy & Astrophysics  188 , 212-224
[6]   D. Lazzaro 1991 - "Semi-analytical Theory for the motion of Uranus' Satellites" - Astronomy & Astrophysics 250 , 253-265
[7]   R. A. Jacobson 2014 - THE ORBITS OF THE URANIAN SATELLITES AND RINGS, THE GRAVITY FIELD OF THE
       URANIAN SYSTEM, AND THE ORIENTATION OF THE POLE OF URANUS- The Astronomical Journal, 148:76 (13pp)