hp41programs

Satellites The Satellites of Jupiter for the HP-41

Overview

-This program calculates the coordinates x and y of the 4 greatest satellites of Jupiter ( Io , Europe , Ganymede , Callisto ), as seen from the Earth.
-The x-axis coincides with the equator of the planet, the y-axis is the planet's rotation axis.
-Jupiter is the origin and x , y are measured in units of Jupiter's equatorial radius. ( the polar radius of Jupiter is 0.933 )

y ( North )
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( East ) ----------------JUP------------------ x   ( West )
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( South )

Data Registers:    R00 = the number of days since 01/01/2000  0h ET

R01 = x1 ;   R03 = x2 ; R05 = x3 ;  R07 = x4
R02 = y1 ;   R04 = y2 ; R06 = y3 ;  R08 = y4   and  R09 =  - sin DE  where DE is the planetocentric declination of the Earth.

Satellite 1 = Io  ;   Satellite 2 = Europe  ;  Satellite 3 =  Ganymede  ;  Satellite 4 = Callisto.

Flags:  F01  F02  F03  F04

-Flag nn  is set when the distance Earth-Satellite n  is shorter than the distance Earth-Jupiter:
-This is useful to distinguish inferior conjunctions from superior conjunctions.

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

-If you don't have a Time-module, replace lines  07 to 09  by  XEQ "J0"   +
-If you don't have an X-Functions module, replace lines 60-61 by  CF 01  CF 02  CF 03  CF 04

 01  LBL "IEGC"   02  DEG   03  HR   04  24   05  /   06  X<>Y   07  1.012      08  DDAYS   09  -   10  STO 00   11  .9856   12  *   13  3   14  -   15  STO 01   16  SIN   17  1.92   18  *   19  RCL 01   20  ST+ X   21  SIN   22  50   23  /   24  +   25  RCL 00   26  12.036   27  /   28  RCL 00   29  896   30  /   31  7   32  -   33  SIN   34  3   35  /   36  STO 02   37  ST+ Z   38  -   39  20   40  +   41  STO 03   42  SIN   43  5.56   44  *   45  RCL 03   46  ST+ X   47  SIN   48  6 49  /   50  +   51  STO 09   52  -   53  RCL 00          54  .902518   55  *   56  +   57  65.66   58  +   59  STO 04   60  CLX      61  X<> F    62  1   63  RCL 01   64  COS   65  60   66  /   67  -   68  5209   69  RCL 03   70  COS   71  252   72  *   73  -   74  RCL 03   75  ST+ X   76  COS   77  6   78  *   79  -   80   E3   81  /   82  STO 05   83  X^2   84  LASTX   85  R^   86  *   87  ST+ X   88  RCL 04   89  COS   90  *   91  -   92  X<>Y   93  X^2   94  +   95  SQRT   96  STO 07 97  /   98  RCL 04   99  SIN 100  * 101  ASIN 102  STO 08        103  LASTX 104  RCL 00 105  12.035 106  / 107  56.3 108  + 109  RCL 02 110  - 111  RCL 09 112  ST- 08 113  + 114  STO 06 115  COS 116  * 117  2.22 118  * 119  RCL 06 120  20.8 121  + 122  SIN 123  3.12 124  * 125  - 126  RCL 06 127  32.5 128  - 129  COS 130  RCL 05 131  RCL 07 132  ST- Y 133  / 134  * 135  1.3 136  * 137  - 138  SIN 139  STO 09 140  368 141  LN 142  RCL 00 143  RCL 07 144  173 145  / 146  - 147  STO 07        148  101.291633 149  * 150  52.24 151  - 152  RCL 08 153  + 154  STO 03 155  3 156  * 157  RCL 07 158  50.234518 159  * 160  19.4 161  - 162  RCL 08 163  + 164  STO 05 165  ST+ X 166  - 167  180 168  + 169  STO 01 170  RCL 03 171  - 172  ST+ X 173  STO 06 174  COS 175  41 176  / 177  - 178  STO 02 179  RCL 06 180  SIN 181  .47 182  * 183  ST+ 01 184  9.4 185  RCL 03 186  RCL 05 187  - 188  ST+ X 189  STO 06 190  COS 191  5 192  D-R 193  * 194  - 195  STO 04        196  RCL 06 197  SIN 198  2.9 199  LN 200  * 201  ST+ 03 202  859 203  D-R 204  RCL 07 205  50.31048 206  * 207  54 208  - 209  STO 06 210  COS 211  46 212  / 213  - 214  X<> 06 215  SIN 216  6 217  / 218  ST+ 05 219  26.37 220  RCL 07 221  21.48798 222  * 223  214.07 224  + 225  RCL 08 226  + 227  X<> 07 228  21.56923 229  * 230  76.6 231  + 232  STO 08 233  COS 234  11 235  D-R 236  * 237  - 238  RCL 08 239  SIN 240  .84 241  * 242  RCL 07        243  + 244  X<>Y 245  P-R 246  X>0? 247  SF 04 248  RCL 09 249  * 250  STO 08 251  X<>Y 252  STO 07 253  RCL 05 254  RCL 06 255  P-R 256  X>0? 257  SF 03 258  RCL 09 259  * 260  STO 06 261  X<>Y 262  STO 05 263  RCL 03 264  RCL 04 265  P-R 266  X>0? 267  SF 02 268  RCL 09 269  * 270  STO 04 271  X<>Y 272  STO 03 273  RCL 01 274  RCL 02 275  P-R 276  X>0? 277  SF 01 278  RCL 09 279  * 280  STO 02 281  X<>Y 282  STO 01 283  END

( 453 bytes / SIZE 010 )

 STACK INPUTS OUTPUTS Y Date y1 X hh.mnss ( ET ) x1

Example1:    Find the configuration of the 4 Galilean satellites of Jupiter on 1992 December 16 at 0h UT = 0h00m59s  ET

12.161992  ENTER^         ( if your HP-41 is in MDY format )
0.0059      XEQ "IEGC"

and 31 seconds later    x1 = -3.45
X<>Y    y1 =   0.21

RCL 03  >>>>   x2 = 7.45     RCL 05  >>>>  x3 = 1.24    RCL 07  >>>>  x4 = 7.09
RCL 04 >>>>   y2 =  0.25    RCL 06  >>>>  y3 = 0.65     RCL 08 >>>>  y4 = 1.10

-Flags F01 F02 F03 F04 are set but it's not particularly useful here!

Example2:    Find the configuration of the Galilean satellites of Jupiter on 1984 September 20 at 6h34m  ET

20.091984  ENTER^
6.34            R/S                 yields    x1 =  0.00
X<>Y                          y1 =  0.20

RCL 03  >>>>   x2 = -8.08     RCL 05  >>>>  x3 = 14.97    RCL 07  >>>>  x4 = -4.95
RCL 04  >>>>   y2 =  -0.16    RCL 06  >>>>  y3 =  -0.01    RCL 08  >>>>  y4 = -0.86

-Since F01 is set , Io is in transit over Jupiter's disk because its distance to the planet's center is significantly inferior to 1.

Notes:

-If you use "J0" , dates must be keyed in  1992.1216  and  1984.0920
-The accuracy is of the order of  0.1 ( but x-values are more accurate than y-values )
-The reference below also provides a high-accuracy method.

Reference:

[1]  Jean Meeus  "Astronomical Algorithms"  Willmann-Bell    ISBN 0-943396-61-1