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 2024/03/31 0h TT
to 2024/05/01 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 -EPH2024APR 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 2024/04/24 at 16h41m TT
-Enter the day of the month and the time
expressed in Terrestrial
Time ( TT )
24
ENTER^
16.41
XEQ "ECL"
>>>>
L0 = 34°983199
= R01
RDN
B0 = -0°000135
= R02
RDN
R0 = 1.00587257 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 [ 2024/03/31 0h TT , 2024/05/01
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 2024/04/24 at 16h41m
TT
After executing "ECLI"
XEQ
"EQ" or simply R/S if you've just executed
"ECL"
>>>>
RA0 =
2h10m48s42 = R01
RDN Decl
0 = 13°10'56"63
= R02
RDN
eps = 23°438623
= 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 2024/04/24 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
= 23h05m11s27
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 |
34.983199 -0.000135 1.00587257 |
2.104842 13.105663 unchanged |
104.130711 43.193661 unchanged |
MOON |
R04 R05 R06 |
222.901249 -2.414077 0.0026595041 |
14.384401 -18.003526 unchanged |
-85.584203 -40.460379 unchanged |
MERCURY |
R07 R08 R09 |
16.010813 -1.125722 0.62569716 |
1.004429 5.153385 unchanged |
129.563258 51.080725 unchanged |
VENUS |
R10 R11 R12 |
24.101859 -1.353381 1.68788686 |
1.311645 8.052156 unchanged |
118.300709 47.534591 unchanged |
MARS |
R13 R14 R15 |
355.404003 -1.266062 2.00041587 |
23.450832 -2.591890 unchanged |
163.292149 52.265793 unchanged |
JUPITER |
R16 R17 R18 |
52.657199 -0.768644 5.95881364 |
3.215003 17.413033 unchanged |
88.174116 30.552912 unchanged |
SATURN |
R19 R20 R21 |
346.065687 -1.726667 10.33599948 |
23.112414 -7.051555 unchanged |
177.372695 49.314464 unchanged |
URANUS |
R22 R23 R24 |
52.030061 -0.266906 20.55438929 |
3.184485 18.010036 unchanged |
88.222597 31.433101 unchanged |
NEPTUNE |
R25 R26 R27 |
358.733549 -1.228945 30.70590955 |
23.571846 -1.375257 unchanged |
158.030388 52.550672 unchanged |
PLUTO |
R28 R29 R30 |
302.088390 -3.009769 ~ 34.935 |
20.201931 -22.373230 unchanged |
-139.082377 21.370643 unchanged |
True obliquity of the ecliptic |
R31 |
/ |
23.438623 |
unchanged |
Local Sidereal Time |
R32 |
/ |
/ |
23.051127 |
-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
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