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.
for a short time-span of 32 days, i-e
2025/07/31 0h TT to 2025/09/01
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 |
S -EPH2025AUG 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 R30 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 2025/08/24 at 16h41m TT
-Enter the day of the
month and the time expressed in
Terrestrial Time ( TT )
24
ENTER^
16.41 XEQ "ECL"
>>>> L0
= 151°771960
= R01
RDN
B0 = -0°000026
= R02
RDN
R0 = 1.01093429 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 [ 2025/07/31 0h TT , 2025/09/01
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
)
-"EQ" 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 2025/08/24 at 16h41m
TT
After executing "ECLI"
XEQ "EQ" or simply
R/S if you've just executed "ECL"
>>>>
RA0
= 10h15m06s80 =
R01
RDN Decl 0
= 10°50'38"35 =
R02
RDN eps
= 23°438545
= 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 |
Z | / | h0 ( ° ' " ) |
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
h0
= height ( corrected for refraction
) |
Example: Calculate the apparent topocentric
azimuthal coordinates of the Sun, the
Moon and the planets on 2025/08/24
at 16h41m TT
at the Palomar
Observatory, Longitude
= 116°51'50"4 W Latitude
= 33°21'22"4 N Altitude =
1706 m
>>> After executing "ECLI" & "EQUA"
-116.51504 STO 33
which are
the topocentric coordinates
of the Sun.
>>> We also have the local sidereal time in R32 = LST
= 7h05m14s47
Notes:
-Cf paragraph 4°) for the other results.
-The difference
TT - UTC = 69.184 seconds.
-> h0 is often meaningless
when h <
0
Celestial Body | Registers | "ECL" | "EQ" | "AZ" |
SUN |
R01 R02 R03 |
151.771960 -0.000026 1.01093429 |
10.150680 10.503835 unchanged |
106.014094 41.084555 41.095075 |
MOON |
R04 R05 R06 |
168.818682 -0.046881 0.00262470823 |
11.184857 4.225021 unchanged |
101.311162 23.400535 23.421462 |
MERCURY |
R07 R08 R09 |
134.580156 0.409525 1.04826738 |
9.084081 16.505985 unchanged |
113.071968 57.441090 57.444689 |
VENUS |
R10 R11 R12 |
118.817896 -0.252711 1.31473277 |
8.033444 20.085457 unchanged |
131.520457 71.293258 71.295165 |
MARS |
R13 R14 R15 |
191.197460 0.333938 2.23298820 |
12.414204 -4.072194 unchanged |
96.410473 2.374519 2.521047 |
JUPITER |
R16 R17 R18 |
106.522143 -0.044335 5.82639430 |
7.113858 22.222207 unchanged |
172.161843 78.553446 78.554559 |
SATURN |
R19 R20 R21 |
0.506532 -2.459610 8.66029743 |
0.054642 -2.031842 unchanged |
-83.263336 -13.313488 -13.313488 |
URANUS |
R22 R23 R24 |
61.397624 -0.209682 19.47993398 |
3.571728 20.140419 unchanged |
-95.145861 46.270276 46.275694 |
NEPTUNE |
R25 R26 R27 |
1.537616 -1.364307 29.00652419 |
0.074879 -0.382496 unchanged |
-82.315191 -12.184598 -12.184598 |
PLUTO |
R28 R29 R30 |
301.912638 -3.783064 34.45410548 |
20.202095 -23.250659 unchanged |
-63.442388 -70.461191 -70.461191 |
True obliquity of the ecliptic | R31 |
/ |
23.438545 |
unchanged |
Local Sidereal
Time |
R32 |
/ |
/ |
7.051447 |
-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 !!!
6°) Refraction
-The apparent heights are calculated by a refraction
formula which approximates
the Pulkovo refraction tables
for
standard conditions of temperature &
pressure ( T = 15°C , P = 1013.25
mbar, humidity = 0 , wave length = 0.59µ
)
-The precision is about 0"12 if -0°32'58"0 <= h <=
90°
h0 ~ h + 1° / 62.93951 /
Tan ( h +
4°80017 / ( h + 6°90263 / ( h +10°06891
/ ( h + 31°76812 / ( h + 8°87360
) ) ) ) )
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