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
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.
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 |
-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