Illuminated Fraction of the Moon's Disk for the HP-41

Overview
 

-Given a date and a time expressed in TT, this short program returns the illuminated fraction of the Moon at that instant.
-The results - though not extremely accurate - are valid over the time span [1000,3000]
 

Data Registers:  R00 = T in millennia since 2000/01/01 0h
                             R01 = D , R02 = M' then M' - 2D
Flags: /
Subroutine:   "J0"  ( cf "Julian & Gregorian Calendars for the HP-41" )  or "J1" or "J2"
 
 

01  LBL "IFMD" 02  DEG 03  HR 04  24 05  / 06  X<>Y 07  XEQ "J0" 08  + 09  365250 10  / 11  STO 00 12  4452671.11 13  RCL 00 14  .19 15  * 16  -

17  * 18  68.25 19  - 20  STO 01 21  SIN 22  55 23  * 24  X<>Y 25  .87 26  * 27  4771988.68 28  + 29  R^ 30  * 31  128.43 32  +

33  STO 02 34  ST+ X 35  SIN 36  107 37  * 38  + 39  RCL 02        40  SIN 41  3144 42  * 43  + 44  RCL 01 45  ST+ X 46  ST- 02 47  SIN 48  329

49  * 50  + 51  RCL 02 52  SIN 53  637 54  * 55  - 56  359990.5 57  RCL 00        58  65 59  / 60  - 61  RCL 00 62  * 63  2.96 64  -

65  SIN 66  1050 67  * 68  - 69   E3 70  / 71  RCL 01         72  2 73  / 74  + 75  SIN 76  X^2 77  END

 
   ( 154 bytes / SIZE 003 )
 
 

STACK	INPUTS	OUTPUTS
Y	YYYY.MNDD	/
X	HH.MNSS	f

  where  f  = illuminated fraction of the Moon's disk  ( 0 < f < 1 )        ---Execution time = 11s---

Examples:

   2008.0827   ENTER^
       20.0607   XEQ "IFMD"  >>>>   f = 0.1121                  So,  f = 11%

   3000.0404   ENTER^
          0              R/S              >>>>    f = 0.4942                         f = 49%

   1001.0708   ENTER^
         8.3916      R/S              >>>>    f = 1.0000                      f = 100%   ( almost )
 

->   1001/07/08  Julian Calendar correponds to 1001/07/14  Gregorian

Reference:

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