hp41programs

Years & Months

Years & Months for the HP-41


Overview
 

-This routine computes the mean sidereal year, tropical year, anomalistic year and lunar ( synodic ) month for a given instant.
-The following formulas are used:

    1 sidereal year = 365.2563630 + 0.0000114 T - 0.0000007 T2 - 0.0000017 T3 - 0.0000002 T4 + 0.0000002 T5 + 0.0000002 T6
    1 tropical year = ( 3652421905 - 6117 T - 42 T2 + 2606 T3 + 118 T4 - 307 T5 - 94 T6 + 13 T7 + 18 T8 )  E-7
    1 anomalistic year = ( 3652596359 + 3117 T - 125 T2 + 1274 T3 + 673 T4 - 150 T5 - 84 T6 + 86 T7 + 26 T8 - 5 T9 )  E-7
    1 lunar month  =  29.53058886 + 0.00002496 T - 0.00000364 T2 + 0.00000235 T3

  where T is measured in unit of 10000 julian years from J2000.0
 

Program Listing
 

Data Registers:  R00 = sidereal year   R01 = tropical year   R02 = anomalistic year  R03 = Lunar month
Flags: /
Subroutines: /
 
 

 01  LBL "STAYM"
 02  2 E3
 03  -
 04   E4
 05  /
 06  2
 07  RCL Y
 08  2
 09  *
 10  +
 11  *
 12  2
 13  -
 14  *
 15  17                    
 16  -
 17  *
 18  7
 19  -
 20  *
 21  114
 22  +		  23  *
 24  63630
 25  +
 26  STO 00
 27  CLX
 28  18
 29  *
 30  13
 31  +
 32  *
 33  94                    
 34  -
 35  *
 36  307
 37  -
 38  *
 39  118
 40  +
 41  *
 42  2606
 43  +
 44  *		  45  42                    
 46  -
 47  *
 48  6117
 49  -
 50  *
 51  78095
 52  -
 53  STO 01
 54  CLX
 55  5
 56  *
 57  CHS
 58  26
 59  +
 60  *
 61  86
 62  +
 63  *
 64  84
 65  -
 66  *		  67  150                
 68  -
 69  *
 70  673
 71  +
 72  *
 73  1274
 74  +
 75  *
 76  125                   
 77  -
 78  *
 79  3117
 80  +
 81  *
 82  96359
 83  +
 84   E7
 85  ST/ 00
 86  ST/ 01
 87  /
 88  365.25		  89  ST+ 00
 90  ST+ 01
 91  +
 92  STO 02
 93  CLX
 94  235                   
 95  *
 96  364
 97  -
 98  *
 99  2496
100  +
101  *
102  2953058886
103  +
104   E8
105  /
106  STO 03
107  RCL 02
108  RCL 01
109  RCL 00
110  END

 
   ( 195 bytes / SIZE 004 )
 
 

      STACK        INPUTS      OUTPUTS
           T             /     lunar month
           Z             /  anomalistic year
           Y             /     tropical year
           X          year     sidereal year

   All the results are expressed in days

Examples:

  2000   XEQ "STYLM"   >>>>   365.2563630  days                                     ---Execution time = 7s---
                                        RDN    365.2421905  days
                                        RDN    365.2596359  days
                                        RDN     29.53058886  days

  5000      R/S      >>>>   365.2563663
                            RDN   365.2420137
                            RDN   365.2597322
                            RDN    29.53059608

 12000     R/S      >>>>   365.2563722
                            RDN   365.2418100
                            RDN   365.2601171
                            RDN    29.53061253

 -3000     R/S      >>>>   365.2563573
                            RDN   365.2424643
                            RDN   365.2594655
                            RDN    29.53057518

 -8000     R/S      >>>>   365.2563524
                            RDN   365.2425710
                            RDN   365.2592527
                            RDN    29.53055791

Notes:

-The input may be fractional.
-The results are less accurate for the lunar months because the tidal acceleration of the Moon is not known with a great precision.
-Outside [-8000,+12000] , the precision becomes doubtful.
 

Reference:

[1]  Jean Meeus - "Astronomical Algorithms" - Willmann-Bell  -  ISBN 0-943396-61-1
[2]  Jacques Laskar - "Secular terms of classical planetary theories using the results of general theory" - A&A 157, 59-70