Barycenter of the Solar System for the HP-41

Overview
 

-This program calculates the rectangular heliocentric ecliptic coordinates X , Y of the center of mass of the Solar system ( we make the approximation Z = 0 )
-It takes a date YYYY.MNDD and returns the distance G between the Solar system barycenter B and the center of the Sun S.

-Only the 4 giant planets are taken into account: the other planets have a negligible effect.
-The positions of these planets are not computed very accurately: the terms in e² are neglected ( e = eccentricity ),
  and only one term in the perturbations is taken into account.
 

Data Registers:   R00 = T in millennia since 2000/01/01 0h TT

                              R01 = X
                              R02 = Y        R03 to R11: temp
Flags: /
Subroutine:    "J0"  ( cf "Julian & Gregorian Calendars" )  or  "J1"  or  "J2"

-Line 12 may be replaced by  20
 
 

01  LBL "BOSS"   02  DEG   03  XEQ "J0"   04  365250   05  /   06  STO 00   07  CLX   08  STO 01   09  STO 02   10  12.4   11  STO 03   12  19.98   13  STO 04   14  20.6   15  STO 05   16  10   17  STO 06   18  16.13   19  STO 07   20  14.33   21  STO 08   22  1.066   23  STO 09   24  178   25  RCL 00   26  407   27  *   28  -   29  STO 10

30  .32   31  CHS   32  STO 11           33  30346.9   34  XEQ 01   35  31   36  STO 03   37  43   38  CHS   39  STO 04   40  18   41  STO 05   42  12   43  STO 06   44  19.64   45  STO 07   46  93.06   47  STO 08   48  .586   49  STO 09   50  .8   51  STO 11   52  12215.47   53  XEQ 01   54  111   55  CHS   56  STO 03   57  141.04   58  STO 04

59  21.6   60  STO 05   61  47   62  STO 06           63  14.86   64  STO 07   65  173   66  STO 08   67  .18   68  STO 09   69  65   70  RCL 00   71  85   72  *   73  -   74  STO 10   75  .86   76  CHS   77  STO 11   78  4283.78   79  XEQ 01   80  143   81  STO 03   82  256.22   83  STO 04   84  111   85  STO 05   86  27   87  STO 06

88  14.26   89  STO 07   90  48.12   91  STO 08           92  .335   93  STO 09   94  .58   95  STO 11   96  2184.57   97  LBL 01   98  RCL 00   99  RCL 03 100  / 101  - 102  RCL 00 103  * 104  RCL 04 105  + 106  ENTER^ 107  SIN 108  RCL 05 109  / 110  ST+ X 111  R-D 112  RCL 00 113  RCL 06 114  / 115  RCL 07 116  +

117  RCL 00 118  * 119  RCL 08         120  + 121  + 122  + 123  RCL 10 124  SIN 125  RCL 11 126  * 127  + 128  1 129  R^ 130  COS 131  RCL 05 132  / 133  - 134  RCL 09 135  * 136  P-R 137  ST+ 01 138  X<>Y 139  ST+ 02 140  RCL 02 141  RCL 01 142  R-P 143  END

 
   ( 285 bytes / SIZE 012 )
 
 

STACK	INPUTS	OUTPUTS
Y	/	µ
X	YYYY.MNDD	G

   where   G = distance Barycenter-Center of the Sun  ( unit = solar radius )
     and     µ  = ( Sx , SB )

Example:

   2008.0824   XEQ "BOSS"    >>>>    G =     1.0761                    ---Execution time = 27s---
                                                X<>Y    µ =  -74°0782

  Since G > 1 , the Solar system barycenter is currently outside the Sun's globe.
  G will be smaller than one in April 2010

  We have also

     X = R01 =  0.2952
     Y = R02 = -1.0348

Other Checkings:

  on  1983/03/15    G = 2.098   ( exact result - almost the maximum possible value )
  on  1990/04/23    G = 0.069   ( exact value = 0.066 )
  on  2130/03/10    G = 0.016   ( exact value = 0.021 )

Note:

  Errors seem smaller than 0.01 over the time span [ 1000 , 3000 ]
  µ may be inaccurate if G is very small
 

Reference:

 [1]  Jean Meeus - "Mathematical Astronomy Morsels" - Willmann-Bell  -  ISBN 0-943396-51-4