Ephemerides 2025 October 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  2025/09/30 0h TT to 2025/11/01  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
  $
-EPH2025OCT
 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                "ECLI"                 "EQUA"          "AZIM"
            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  ( ° ' " )
         PLUTO       R28
      R29
      R30
    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 2025/10/24 at 16h41m  TT


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

       24       ENTER^
    16.41     XEQ "ECL"            >>>>     L0 =  211.528155          = R01
                                                RDN      B0 =  -0°000140            = R02
                                                RDN      R0 =  0.99459216  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 [ 2025/09/30 0h TT , 2025/11/01   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 2025/10/24 at 16h41m  TT

After executing "ECL"


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

                           >>>>     RA0 =     13h57m29s59     = R01              
                            RDN    Decl 0 =    -12°00'18"55     = R02
                            RDN      eps  =       23°438429       = R31
 

-The distances in R03-R06-.....-R30  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 ..... R30
 
 

      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   = 130°25'07"74   = R01          
                                                        RDN         h   =  28°55'40"62     = R02
  

         which are the topocentric coordinates of the Sun.
 

>>>  We also have the local sidereal time in R32 = LST = 11h05m44s25
 

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
    211.528155
     -0.000140
    0.99459216
     13.572959
    -12.001855
     unchanged
   130.250774
    28.554062
    unchanged
               MOON       R04
      R05
      R06
    246.094993
     -5.028592
 0.00271549423
    16.125890
   -26.162620
     unchanged
   118.544432
    -5.031283
    unchanged
            MERCURY       R07
      R08
      R09
    234.698374
     -2.602558
    1.10815619
    15.263864
   -21.275763
     unchanged
   121.364277
     7.090089
    unchanged
              VENUS       R10
      R11
      R12
    193.443445
      1.530619
    1.59444098
    12.515179
    -3.534320
     unchanged
   140.512567
    45.052276
    unchanged
              MARS       R13
      R14
      R15
    232.287690
     -0.321608
    2.40033708
     15.190956
    -18.390570
     unchanged
   120.354618
    10.185045
    unchanged
             JUPITER       R16
      R17
      R18
    114.625869
      0.069091
    4.97257418
      7.461443
     21.155623
     unchanged
   -92.113348
    44.304642
    unchanged
             SATURN       R19
      R20
      R21
    356.165231
     -2.481808
    8.71192501
     23.495233
     -3.480673
     unchanged
   -21.340473
   -58.420984
    unchanged
            URANUS       R22
      R23
      R24
     60.544926
     -0.209722
    18.62637441
      3.534396
     20.033258
     unchanged 
   -63.275248
    -3.051959
    unchanged
            NEPTUNE       R25
      R26
      R27
    359.947589
     -1.370782
    29.03503729
      0.015934
     -1.164261
     unchanged
   -25.161432
   -55.185729
    unchanged
              PLUTO       R28
      R29
      R30
    301.393561
     -3.774712
    35.36282134
     20.180848
    -23.314130
     unchanged
    86.054145
   -52.082637
    unchanged
  True obliquity of the ecliptic       R31
           /
    23.438429
    unchanged
      Local Sidereal Time
      R32
           /
             /
    11.054425

 


    
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