Ephemerides 2024 December Module


 Overview
 

1°)  Ecliptic Geocentric Coordinates
2°)  Equatorial Geocentric Coordinates
3°)  Azimuthal Topocentric Coordinates
4°)  Numerical Results


-These programs compute accurate positions of the Sun, the Moon and the major planets ( this month, not enough room for Pluto )
    for a short time-span of 32 days, i-e  2024/11/30 0h TT to 2025/01/01  0h TT

-The longitudes & latitudes and the right-ascensions & declinations are geocentric apparent
  referred to the true equator & equinox of the date, corrected for aberration and light-time.

-The precision is about 0"01 for the longitudes & latitudes and of the order of 3 E-8 AU for the distances ( 5 E-11 AU for the Moon ).
-The distances are true distances.

-The azimuthal ( topocentric ) coordinates are also given, corrected for parallax & diurnal aberration.

-These coordinates are calculated by polynomials fitted to the JPL Ephemerides DE441
 

Notes:

-Always execute "ECL" first for the ecliptic coordinates, with at least SIZE 031
-Then "EQ" for the equatorial coordinates ( SIZE 039 )
-And then "AZ" for the azimuthal coordinates with at least SIZE 041.

-The azimuths are reckoned clockwise from North.
-Longitudes are positive East.
 

Data Registers

  R00 = ( DOM - 16 ) / 16 ( from -1  to +1 )  Terrestrial Time ( TT )

  R01 thru R30 = coordinates of the Sun, the Moon, Mercury, Venus, Mars, Jupiter, Saturn, Uranus, Neptune & Pluto.

  R31 = True obliquity of the ecliptic  ( deg )
  R32 = Local Sidereal Time  ( hh.mnss )

 • R33 = Longitude of the observer ( ° ' " )   positive East
 • R34 = Latitude of the observer ( ° ' " )                                                         Registers R33-R34-R35 are to be initialized before executing "AZ"
 • R35 = Observer altitude in meters

 ( R36 to R40:  temporary data storage )
 
 

XROM  Function  Desciption
 24,00
 24,01
 24,02
 24,03
 24,04
 24,05
  $
-EPH2024DEC
 V
 ECL
 EQ
 AZ
 Subroutine that is called by "V"
 Section Header
 Ecliptic Coordinates of the Sun, the Moon & the Planets

 Takes day of month & time and calls "V"
 Ecliptic -> Equatorial Coordinates
 Equatorial -> Azimuthal Coordinates
  


-"ECL"  "EQ"  &  "AZ"  calculate & store the coordinates in registers R01 thru R27 as follows:

>>>   h0 is the height, corrected for refraction
 
 

      Celestial Body    Registers                  "ECL"                  "EQ"            "AZ"
            SUN       R01
      R02
      R03
    Eclipt Longitude ( deg )
    Eclipt  Latitude ( deg )
    Dist from Earth ( AU )
    Right-Ascens(hh;mnss)
      Declination ( ° ' " )
    Dist from Earth ( AU )
   Azimuth ( ° ' " )
     height  ( ° ' " )
        h0  ( ° ' " )
          MOON       R04
      R05
      R06
    Eclipt Longitude ( deg )
    Eclipt  Latitude ( deg )
    Dist from Earth ( AU )
    Right-Ascens(hh;mnss)
      Declination ( ° ' " )
    Dist from Earth ( AU )
    Azimuth ( ° ' " )
     height  ( ° ' " )
        h0  ( ° ' " )
       MERCURY       R07
      R08
      R09
    Eclipt Longitude ( deg )
    Eclipt  Latitude ( deg )
    Dist from Earth ( AU )
    Right-Ascens(hh;mnss)
      Declination ( ° ' " )
    Dist from Earth ( AU )
    Azimuth ( ° ' " )
     height  ( ° ' " )
        h0  ( ° ' " )
         VENUS       R10
      R11
      R12
    Eclipt Longitude ( deg )
    Eclipt  Latitude ( deg )
    Dist from Earth ( AU )
   Right-Ascens(hh;mnss)
     Declination ( ° ' " )
   Dist from Earth ( AU )
    Azimuth ( ° ' " )
     height  ( ° ' " )
        h0  ( ° ' " )
          MARS       R13
      R14
      R15
    Eclipt Longitude ( deg )
    Eclipt  Latitude ( deg )
    Dist from Earth ( AU )
    Right-Ascens(hh;mnss)
      Declination ( ° ' " )
   Dist from Earth ( AU )
    Azimuth ( ° ' " )
     height  ( ° ' " )
        h0  ( ° ' " )
        JUPITER       R16
      R17
      R18
    Eclipt Longitude ( deg )
    Eclipt  Latitude ( deg )
    Dist from Earth ( AU )
    Right-Ascens(hh;mnss)
      Declination ( ° ' " )
    Dist from Earth ( AU )
    Azimuth ( ° ' " )
     height  ( ° ' " )
        h0  ( ° ' " )
        SATURN       R19
      R20
      R21
    Eclipt Longitude ( deg )
    Eclipt  Latitude ( deg )
    Dist from Earth ( AU )
    Right-Ascens(hh;mnss)
      Declination ( ° ' " )
    Dist from Earth ( AU )
    Azimuth ( ° ' " )
     height  ( ° ' " )
        h0  ( ° ' " )
        URANUS       R22
      R23
      R24
    Eclipt Longitude ( deg )
    Eclipt  Latitude ( deg )
    Dist from Earth ( AU )
    Right-Ascens(hh;mnss)
      Declination ( ° ' " )
    Dist from Earth ( AU )
    Azimuth ( ° ' " )
     height  ( ° ' " )
        h0  ( ° ' " )
       NEPTUNE       R25
      R26
      R27
    Eclipt Longitude ( deg )
    Eclipt  Latitude ( deg )
    Dist from Earth ( AU )
    Right-Ascens(hh;mnss)
      Declination ( ° ' " )
    Dist from Earth ( AU )
    Azimuth ( ° ' " )
     height  ( ° ' " )
        h0  ( ° ' " )

 

1°) Ecliptic Geocentric Coordinates of the Sun, the Moon & the major Planets


            STACK            INPUTS      OUTPUTS
                 Z                 /       R0  ( AU )
                 Y       Day of the Month       B0  ( deg )
                 X        HH.MNSS(TT)       L0  ( deg )

    Where  L = Longitude   B = Latitude   R = radius vector

Example:    Calculate the apparent geocentric ecliptic coordinates of the Sun, the Moon and the planets on 2024/12/24 at 16h41m  TT


-Enter the day of the month and the time expressed in  Terrestrial Time ( TT )

       24       ENTER^
    16.41     XEQ "ECL"            >>>>     L0 =  273°366394          = R01
                                                RDN      B0 =  -0°000085            = R02
                                                RDN      R0 =  0.98356002  AU   = R03

Notes:

-All the angles are expressed in decimal degrees.
-Cf  paragraph 4°) for the other results.

-If you key in a date outside the interval [ 2024/11/30 0h TT , 2025/01/01   0h TT ]  you'll get a DATA ERROR message.
-However, this program may probably be used a few hours outside the prescribed interval: set F25 and R/S
-But the precision is less guaranteed and the results may even become completely meaningless several days before 00 or after 32, especially for the Moon.
 

2°) Equatorial Geocentric Coordinates
 

-AFTER executing "ECL", use "EQ" to get the equatorial coordinates
-The right-ascensions are expressed in hh.mnss and the declinations in ° ' "
-They replace the ecliptic longitudes & latitudes ( cf the tableau in the paragraph above )

-"EQUA" also calculates the true obliquity of the ecliptic which is returned in Z-register
-A polynomial is also used for that.
 
 

           STACK          INPUTS        OUTPUTS
               Z               /        eps   ( deg )
               Y               /       Decl0 ( ° ' " )
               X               /     RA0  ( hh.mnss )

  Where  RA = Right-Ascension   Decl = declination  eps = true obliquity of the ecliptic

Example:    Calculate the apparent geocentric equatorial coordinates of the Sun, the Moon and the planets on 2024/12/24 at 16h41m  TT

After executing "ECL"


       XEQ "EQ"  or simply R/S if you've just executed "ECL"

                           >>>>     RA0 =     18h14m40s40     = R01              
                            RDN    Decl 0 =    -23°23'44"36     = R02
                            RDN      eps  =       23°438425       = R31
 

-The distances in R03-R06-.....-R27  are unchanged.  
-Cf paragraph 4°) for the other results 


3°) Azimuthal Topocentric Coordinates
 

-AFTER executing "ECL" & "EQ" use "AZ" to get the horizontal coordinates
-The azimuths & heights are expressed in ° ' "

-The heights corrected for refraction are also computed and replace the distances in R03  R06 ..... R27
 
 

      STACK        INPUTS      OUTPUTS
           Y             /       h  ( ° ' " )
           X             /      Az  ( ° ' " )

                  Long = longitude ( positive East )       Az = Azimuth ( clockwise from North )    |
  Where       Lat  =  latitude                                   h  =  height                                             >       of the Sun
                   Alt  =  altitude in meters                                                                                 |

Example:    Calculate the apparent topocentric azimuthal coordinates of the Sun, the Moon and the planets on 2024/12/24  at 16h41m  TT
                    at the Palomar Observatory,   Longitude = 116°51'50"4 W   Latitude = 33°21'22"4 N   Altitude = 1706 m
 

>>>  After executing "ECL" & "EQ"


    -116.51504   STO 33
       33.21224   STO 34
          1706       STO 35    R/S         >>>>      Az   = 135°17'26"03   = R01          
                                                        RDN         h   =  17°48'01"06     = R02
  

         which are the topocentric coordinates of the Sun.
 

>>>  We also have the local sidereal time in R32 = LST = 15h07m11s16
 

Notes:

-This month, not enough room to compute the refraction. 

-Cf paragraph 4°) for the other results.
-The difference TT - UTC = 69.184 seconds.
 

4°) Numerical Results

-Longitudes & latitudes are expressed in decimal degrees   and the distances in Astronomical Units ( "ECL" )
-Right-ascensions in hh.mnss & declinations in ° ' "  ( "EQ"   )
-Azimuths & heights in ° ' "  too   ( "AZ" )
  
-Obliquity of the ecliptic  in decimal degrees ( R31 )
-Local sidereal time in hh.mnss  ( R32 )



           Celestial Body    Registers          "ECL"          "EQ"          "AZ"
                 SUN       R01
      R02
      R03
    273.366394
     -0.000085
    0.98356002
     18.144040
    -23.234436
    unchanged
   135.172603
    17.480106
    unchanged
               MOON       R04
      R05
      R06
    202.391690
     -1.754894
  0.0027031814
    13.201038
   -10.203645
    unchanged
  -145.011604
    38.430368
    unchanged
            MERCURY       R07
      R08
      R09
    251.419066
      2.115606
    1.00704084
    16.404448
   -20.031377
    unchanged
   153.524430
    32.064476
    unchanged
              VENUS       R10
      R11
      R12
    319.749645
     -1.845459
    0.80441876
    21.310426
   -16.383739
     unchanged
   100.571464 
   -13.555882
    unchanged
              MARS       R13
      R14
      R15
    124.016576
      3.626355
    0.67966085
      8.290375
     22.461963
     unchanged
   -65.522721
     4.532365
    unchanged
             JUPITER       R16
      R17
      R18
     74.050223
     -0.624728
    4.14164484
      4.510668
     21.515471
     unchanged
   -27.502629
   -29.283676
    unchanged
             SATURN       R19
      R20
      R21
    344.008832
     -1.994610
    9.91368605
     23.041044
     -8.075365
     unchanged
    80.172544
   -28.480253
    unchanged
            URANUS       R22
      R23
      R24
     53.832345
     -0.254987
    18.78601156
      3.260480
     18.285927
     unchanged 
    -5.410630
   -37.575386
    unchanged
            NEPTUNE       R25
      R26
      R27
     357.212018
     -1.289873
    29.98397178
    23.514912
    -2.173190
    unchanged
    66.255348
   -34.502108
    unchanged
  True obliquity of the ecliptic       R31
           /
    23.438425
    unchanged
      Local Sidereal Time
      R32
           /
             /
   15.071116

 
    
5°) V

 

-This subroutine may be used for itself to calculate the geocentric ecliptic coordinates
-First initialize R00 before executing "V".
 
 -With the example above,  R00 = 0.5434461806


WARNING !!!


-Unlike "ECL" , this routine does not check if R00 is between -1 and +1

 

6°)  Refraction


-This month, not enough room to compute the refraction. 



References:

[1]  Aldo Vitagliano SOLEX  http://www.solexorb.it/
[2]  ftp://ssd.jpl.nasa.gov/pub/eph/planets/ascii/
[3]  Jean Meeus - "Astronomical Algorithms" - Willmann-Bell  -  ISBN 0-943396-61-1