Nutation - Obliquity of the Ecliptic - Sidereal Time for the HP-41

Overview
 

 1°) Nutation in Longitude & in Obliquity
 2°) Obliquity of the Ecliptic
 3°) Sidereal Time at Greenwich
 

1°) Nutation in Longitude & in Obliquity
 

-The complete series involve more than 1000 terms, and the following program uses the first few terms only:
-The nutation in longitude Dpsi is obtained with an accuracy of  0"5
  and the nutation in obliquity De with an accuracy of   0"1
-Add more terms if you want to get a better accuracy.
 

Data Register:       •  R00 = T = number of millenia of 365250 Julian days since 2000/01/01 0h     ( this register is to be initialized before executing "NUT" )
Flags: /
Subroutines: /
 
 

 
   ( 91 bytes / SIZE 001 )
 
 

 where  Dpsi  is the nutation in longitude
   and     De   is the nutation in obliquity.

Example:    With  T = 1  ( 3000/01/08  0h )

  1  STO 00   XEQ "NUT"  >>>>   Dpsi = 0.00353°   X<>Y   De = -0.00198°
 

2°) Obliquity of the Ecliptic
 

-The following program uses the series given in reference [3] to compute the obliquity of the ecliptic.
 

Data Register:       •  R00 = T = number of millenia of 365250 Julian days since 2000/01/01 0h     ( this register is to be initialized before executing "OBL" )

Flag:  F01     if flag F01 is set, "OBL" calculates the mean obliquity and the true obliquity,
                      if flag F01 is clear, "OBL" calculates the mean obliquity only.

Subroutine:  "NUT" if F01 is set, none otherwise.
 
 

 
   ( 62 bytes / SIZE 001 )
 
 

  where  e_m  is the mean obliquity
    and    e    is the true obliquity

  Z-output is used by  "ST" below

Example:   Once again with T = 1

 SF 01    1  STO 00   XEQ "OBL"  >>>>  e = 23°18'27"89   RDN  e_m = 23°18'35"02
 CF 01    1  STO 00        R/S          >>>>  e_m = 23°18'35"02 = X- and Y-registers.

-"OBL" is of course much faster if flag F01 is clear!
- e_m  is calculated more accurately than e.
 

3°) Sidereal Time at Greenwich
 

-A short routine which computes the mean sidereal time is listed in "Rising-Transit-Setting for the HP-41"
-The following one is more accurate and take the nutation into account if flag F01 is set.
 

Data Register:  R00 = T

Flag:    F01   if flag F01 is set, "ST" calculates the mean sidereal time MST & the apparent sidereal time AST
                      if flag F01 is clear, calculates the mean sidereal time MST only.

Subroutines:  "J0"  ( cf "Julian & Gregorian Calendars for the HP-41" ) , "OBL" and  "NUT" if SF 01

-If you have a Time module, lines 05 to 08 may be replaced by   1.012  DDAYS  24  *  -
-Line 11 stores the number of millenia since 2000/01/01  0h   into R00
-Synthetic register M may of course be replaced by any unused data register.
 
 

 
   ( 81 bytes / SIZE 001 )
 
 

Example:      Find the mean & apparent sidereal times at Greenwich on 2006/12/28 at 16h41m37s ( UT )

        SF 01
   2006.1228  ENTER^
       16.4137  XEQ "ST"  >>>>   AST =  23h09m39s86   RDN  MST =  23h09m39s67   RDN   e = 23°26'26"66

-With CF 01  both X- and Y-registers = MST = 23h09m39s67  and Z = e_m = 23°26'18"13

-MST is calculated more accurately than AST.
-In order to know the sidereal time in another place, simply add the longitude ( measured positively eastwards from the meridian of Greenwich )
 For instance, the US Naval Observatory at Washington ( D.C. ):   Longitude = -77°03'56" = -77.06555° = -5.137704h = -5h08m15s73
-So, subtract  5h08m15s73 to the sidereal times above.
 

References:

[1]  Jean Meeus - "Astronomical Algorithms" - Willmann-Bell -  ISBN 0-943396-61-1
[2]  "Introduction aux Ephemerides Astronomiques" - EDP Sciences - ISBN 2-86883-298-9  ( in French )
[3]  United States Naval Observatory, Circular n° 179  http://aa.usno.navy.mil/publications/docs/circular_179.html