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 2022/11/30 0h TT to
2023/01/01 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 "ECLI" first for the ecliptic coordinates, with at least
SIZE 031
-Then "EQUA" for
the equatorial coordinates ( SIZE 039 )
-And then "AZIM"
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 R27 = coordinates of the Sun, the Moon, Mercury, Venus, Mars, Jupiter, Saturn, Uranus & Neptune.
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 "AZIM"
• 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 24,06 24,07 24,08 24,09 24,10 24,11 24,12 |
-EPH2022DEC SUN MOON MER VEN MAR JUP SAT URA NEP ECLI EQUA AZIM |
Section Header Ecliptic Coordinates of the Sun Ecliptic Coordinates of the Moon Ecliptic Coordinates of Mercury Ecliptic Coordinates of Venus Ecliptic Coordinates of Mars Ecliptic Coordinates of Jupiter Ecliptic Coordinates of Saturn Ecliptic Coordinates of Uranus Ecliptic Coordinates of Neptune Ecliptic Coordinates of the Sun, Planets & Moon Ecliptic -> Equatorial Coordinates Equatorial -> Azimuthal Coordinates |
-"ECLI" "EQUA"
& "AZIM" calculate & store
the coordinates in registers R01 thru R27 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 ( ° ' " ) |
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 2022/12/24 at 16h41m TT
-Enter the day of the month and
the time expressed in Terrestrial
Time ( TT )
24
ENTER^
16.41
XEQ "ECLI"
>>>> L0 =
272°838616 = R01
---Execution time = 81s---
RDN
B0 = -0°000174
= R02
RDN
R0 = 0.98362858 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 [ 2022/11/30 0h TT , 2023/01/01
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 "ECLI", use "EQUA" 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 2022/12/24
at 16h41m TT
After executing "ECLI"
XEQ "EQUA"
or simply R/S if you've just executed "ECLI"
>>>> RA0 =
18h12m22s42 = R01
---Execution time = 45s---
RDN
Decl 0 = -23°24'27"87
= R02
RDN
eps = 23.4380415
= R31
-The distances in R03-R06-.....-R27 are unchanged.
-Cf paragraph 4°)
for the other results
3°)
Azimuthal Topocentric Coordinates
-AFTER executing "ECLI" & "EQUA" use "AZIM" 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 |
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 2022/12/24 at 16h41m
TT
at the Palomar Observatory, Longitude
= 116°51'50"4 W Latitude = 33°21'22"4
N Altitude = 1706 m
>>> After executing "ECLI" & "EQUA"
-116.51504 STO 33
which are
the topocentric coordinates of the Sun.
>>> We also have the local sidereal time in R32 = LST
= 15h05m08s50
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 | "ECLI" | "EQUA" | "AZIM" |
SUN |
R01 R02 R03 |
272.838616 -0.000174 0.98362858 |
18.122242 -23.242787 unchanged |
135.204549 17.494260 17.523762 |
MOON |
R04 R05 R06 |
290.784183 -4.753719 0.0023956255 |
19.330741 -26.313928 unchanged |
124.274990 1.384483 1.564443 |
MERCURY |
R07 R08 R09 |
292.519495 -1.096554 0.92433272 |
19.380305 -22.381934 unchanged |
120.442788 4.153129 4.260730 |
VENUS |
R10 R11 R12 |
288.226632 -1.203249 1.62763390 |
19.194075 -23.232307 unchanged |
124.025597 7.005921 7.080626 |
MARS |
R13 R14 R15 |
70.591349 2.731785 0.60004299 |
4.341536 24.441359 unchanged |
-22.591772 -28.094233 -28.094233 |
JUPITER |
R16 R17 R18 |
0.385164 -1.317666 4.89486041 |
0.033061 -1.032066 unchanged |
62.301842 -36.365547 -36.365547 |
SATURN |
R19 R20 R21 |
321.715223 -1.245987 10.45621679 |
21.380109 -15.264581 unchanged |
98.443038 -15.094131 -15.094131 |
URANUS |
R22 R23 R24 |
45.303065 -0.359757 18.99363073 |
2.514737 16.044690 unchanged |
4.130181 -40.274160 -40.274160 |
NEPTUNE |
R25 R26 R27 |
352.768815 -1.190657 30.06903517 |
23.351954 -3.574862 unchanged |
70.434606 -33.044555 -33.044555 |
True obliquity of the ecliptic | R31 |
/ |
23.4380415 |
unchanged |
Local Sidereal Time |
R32 |
/ |
/ |
15.050850 |
5°) SUN-MOON-MER-VEN-MAR-JUP-SAT-URA-NEP
-All these subroutines may be used for themselves to calculate the geocentric
ecliptic coordinates
-First initialize
R00 before executing them.
STACK | INPUTS | OUTPUTS |
Z | / | R ( AU ) |
Y | / | B ( deg ) |
X | / | L ( deg ) |
Where L = Longitude B = Latitude R = radius vector
WARNING !!!
-Unlike "ECLI" , these routines do not check that R00 is between
-1 and +1
Remark:
-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 better than 0"06 over the whole range [ -0°32'58"0
, 90° ]
h0 ~ h + 1° / 62.95929 /
Tan ( h + 4°8043 / ( h + 7°0822 / ( h
+11°1187 / ( h + 38°2290 / ( h + 9°9098
) ) ) ) )
References:
[1] Aldo Vitagliano SOLEX http://www.solexorb.it/