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 2024/05/31 0h TT
to 2024/07/02 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 -EPH2024JUN 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 2024/06/24 at 16h41m TT
-Enter the day of the month and the time
expressed in Terrestrial
Time ( TT )
24
ENTER^
16.41
XEQ "ECL"
>>>>
L0 = 93°648672
= R01
RDN
B0 = -0°000157
= R02
RDN
R0 = 1.01642031 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 [ 2024/05/31 0h TT , 2024/07/02
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 2024/06/24
at 16h41m TT
After executing "ECLI"
XEQ
"EQ" or simply R/S if you've just executed
"ECL"
>>>>
RA0
= 6h15m54s19 = R01
RDN Decl
0 = 23°23'16"49
= R02
RDN
eps = 23°438412
= 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 2024/06/24 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
= 3h05m41s33
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 |
93.648672 -0.000157 1.01642031 |
6.155419 23.231649 unchanged |
90.455181 47.214347 47.223595 |
MOON |
R04 R05 R06 |
307.876207 -4.509321 0.0024865305 |
20.461096 -22.390701 unchanged |
-106.510098 -17.021488 -17.021488 |
MERCURY |
R07 R08 R09 |
105.366209 1.880510 1.26423701 |
7.073840 24.251709 unchanged |
82.535580 37.003598 37.015151 |
VENUS |
R10 R11 R12 |
99.128001 0.708234 1.72389614 |
6.395672 23.495081 unchanged |
86.590731 42.313577 42.323789 |
MARS |
R13 R14 R15 |
41.399257 -1.007545 1.76512529 |
2.370944 14.173206 unchanged |
-159.322113 69.515602 69.521692 |
JUPITER |
R16 R17 R18 |
66.834257 -0.698796 5.91156120 |
4.202940 20.454054 unchanged |
122.292158 69.104876 69.111043 |
SATURN |
R19 R20 R21 |
349.406312 -1.956145 9.38694305 |
23.240814 -5.593365 unchanged |
-115.551363 24.290308 24.310756 |
URANUS |
R22 R23 R24 |
55.424201 -0.260775 20.37335829 |
3.323634 18.515182 unchanged |
155.473749 74.183524 74.185124 |
NEPTUNE |
R25 R26 R27 |
359.915756 -1.273498 29.81580530 |
0.014304 -1.120688 unchanged |
-119.030385 34.391945 34.404177 |
PLUTO |
R28 R29 R30 |
301.512739 -3.172636 34.14124367 |
20.180323 -22.545305 unchanged |
-103.453798 -21.532874 -21.532874 |
True obliquity of the ecliptic |
R31 |
/ |
23.438412 |
unchanged |
Local Sidereal Time |
R32 |
/ |
/ |
3.054133 |
-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