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 2024/06/30 0h TT
to 2024/08/01 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 -EPH2024JUL 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 2024/07/24 at 16h41m TT
-Enter the day of the month and the
time expressed in Terrestrial
Time ( TT )
24
ENTER^
16.41
XEQ "ECL"
>>>>
L0 = 122°264128
= R01
RDN
B0 = -0°000053
= R02
RDN
R0 = 1.01574849
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 [ 2024/06/30 0h TT , 2024/08/01
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 2024/07/24
at 16h41m TT
After executing "ECLI"
XEQ "EQ" or simply R/S if you've just executed
"ECL"
>>>>
RA0
= 8h18m07s39 = R01
RDN Decl
0 = 19°39'16"28
= R02
RDN
eps = 23°438542
= 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 2024/07/24 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
= 5h03m58s10
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 |
122.264128 -0.000053 1.01574849 |
8.180739 19.391628 unchanged |
95.004715 44.532117 44.541838 |
MOON |
R04 R05 R06 |
-13.420322 -1.923930 0.0024401559 |
23.133715 -7.040930 unchanged |
-97.133309 -2.523823 -2.523823 |
MERCURY |
R07 R08 R09 |
149.017312 -1.421478 0.82230520 |
10.023500 10.285761 unchanged |
89.274868 18.301123 18.325966 |
VENUS |
R10 R11 R12 |
135.990242 1.438333 1.66316057 |
9.153548 17.245655 unchanged |
89.151726 31.502149 31.515307 |
MARS |
R13 R14 R15 |
62.643626 -0.684749 1.63325368 |
4.025354 20.005953 unchanged |
-130.391348 70.574979 70.580945 |
JUPITER |
R16 R17 R18 |
73.054790 -0.691108 5.63811020 |
4.465342 21.404336 unchanged |
-161.002168 77.433935 77.435173 |
SATURN |
R19 R20 R21 |
348.923874 -2.078353 8.95330792 |
23.223271 -6.174029 unchanged |
-97.482444 0.235007 0.484464 |
URANUS |
R22 R23 R24 |
56.634605 -0.261664 19.97725674 |
3.373502 19.085338 unchanged |
-121.002757 66.040100 66.042630 |
NEPTUNE |
R25 R26 R27 |
359.800143 -1.298059 29.34099780 |
0.011993 -1.161355 unchanged |
-99.042291 11.132656 11.180445 |
PLUTO |
R28 R29 R30 |
300.835855 -3.227122 34.04825943 |
20.151466 -23.070890 unchanged |
-89.013206 -47.014874 -47.014874 |
True obliquity of the ecliptic |
R31 |
/ |
23.438542 |
unchanged |
Local Sidereal Time |
R32 |
/ |
/ |
5.035810 |
-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