Overview
*******************-LAST UPDATE-**********************
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-In this new version, the positions of the Plutinos are fitted to DE431
*
-Rhadamanthus & Typhon have also been added.
*
*
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-PLANETS is a module that computes the positions of the Sun, the Moon and the major planets.
-It is actually a small improvement of some of the programs in the ASTRO2010
module
-Nutation , aberration & parallax are taken into account
-The position of several transneptunian objects may also be computed:
>>> Pluto - Xena ( Eris ) - Sedna
-It may be used alone.
-The second mod file PLUTOIDS deals with 14 other transneptunian planets
>>> Altjira - Chaos - Deucalion - Hauméa
- Ixion - Makémaké - Orcus - Quaoar
- Rhadamanthus - Salacia
- Sila-Nunam - Typhon - Varda - Varuna
-These second programs calculate the heliocentric coordinates and then call "Z" ( XROM "Z" in PLANETS ) to get the geocentric & topocentric coordinates.
-For the Sun, the Moon and the major planets, the accuracy is about
0°01 over the time-span [1000-3000] ( at least )
-For Pluto, the same precision is obtained between 1880 & 2100
-For the other Plutinos, between 1900 & 2100.
-So, the accuracy is not so good as in the TRANSNEP module, but the time-span is longer.
-For the Sun, Mercury & Venus, truncated series from the VSOP87/VSOP09
theories are used.
-For Jupiter, Saturn, Uranus & Neptune, the perturbations come
from the theory TOP2010.
-They are expressed as functions of a unique variable µ with
µ = 20°599908944 T
-The perturbations of Mars are expressed with µ too.
-For Jupiter and Saturn, these series converge more rapidly than the usual perturbations expressed with the mean mean longitudes.
-The heliocentric spherical coordinates of most of the Plutinos are
obtained by polynomials fitted to the JPL DE431 ephemerides.
-However, there is an uncertainty on the orbital elements of the asteroids.
I've used "Solex" with the default option
which calculates the average of the Astorb database and the AstDys
database.
-So, significant differences may appear near 1900 or 2100 between the
results given by "PLUTOIDS" and those given by JPL, especially for Salacia.
Usage:
0-XEQ "SIZE" 025 at least and store the required data in registers R16 to R20 ( see below )
1-Set or clear flags F01 to F04 according the type of coordinates you want to compute ( see below )
2- YYYY.MNDD ENTER HH.MNSS ( UT ) XEQ "ST" to
get the local sidereal time
3- XEQ "SUN" - or simply R/S - to calculate the coordinates of
the Sun and to store the ecliptic rectangular coordinates of the Sun in
R01 & R02
4- XEQ "MO" or R/S for the Moon
5- XEQ "ME" or R/S ... to get the coordinates of the planets
Flags:
CF 01 CF 02 CF 03 to get the heliocentric
coordinates, the geocentric coordinates and the topocentric azimuthal coordinates
CF 01 CF 02 SF 03 to get the heliocentric
coordinates and the geocentric coordinates ( ecliptic long & lat and
right-ascension & declination )
CF 01 SF 02
to get the heliocentric coordinates, the geocentric ecliptic longitude
& latitude
SF 01
to get the heliocentric longitude & latitude only.
CF 04 for Gregorian dates
SF 04 for Julian dates
Data Registers:
R00 = T = Millenia since 2000/01/01 0h TT
R01-R02 = Ecliptic rectangular mean coordinates of the Sun
R03 = Geocentric ecliptic longitude ( deg )
R04 = Geocentric ecliptic latitude ( deg )
( true ecliptic of the date )
R05 = Distance Earth-Planet ( AU )
R06 = Right-Ascension ( hh.mnss )
( true equator of the date )
R07 = Declination ( ° ' " )
R08 = Heliocentric ecliptic longitude ( deg )
R09 = Heliocentric ecliptic latitude ( deg )
( mean ecliptic of the date )
R10 = Distance Sun-Planet ( AU )
R11 = Azimuth ( ° ' " ) clockwise from North
R12 = height ( ° ' " )
( planetary aberration & parallax are taken into account )
R13 = height corrected for refraction ( ° ' " )
R14 = Elongation from the Sun ( ° ' " ) ( not very accurate since it's calculated without taking the parallax into account )
R15 = temp
• R16 = Longitude of the observer ( ° ' " )
( positive East ) >>>
Initialize Registers R16 thru R20 before executing "ST"
• R17 = Latitude of the observer ( ° ' " )
• R18 = Temperature ( in °C )
• R19 = Atmospheric Pressure ( in mbar )
• R20 = TT - UT ( seconds )
R21 = Local Sidereal Time ( hh.mnss )
R22 = Obliquity of the Ecliptic ( deg )
R23 = Nutation in Longitude ( deg )
R24 = Longitude of the Sun ( deg )
| XROM | Function | Desciption |
| 09,00
09,01 09,02 09,03 09,04 09,05 09,06 09,07 09,08 09,09 09,10 09,11 09,12 09,13 09,14 09,15 09,16 10,00 10,01 10,02 10,03 10,04 10,05 10,06 10,07 10,08 10,09 10,10 10,11 10,12 10,13 10,14 |
-PLANETS
ST SUN MO ME VE MA JU SA UR NE PL XE SD K L Z -PLUTOIDS ALT CHA DEU HAU IXI MAK ORC QUA RHD SAL SIL TYP VRD VRN |
Section Header
Local Sidereal Time Coordinates of the Sun Position of the Moon Position of Mercury Position of Venus Position of Mars Position of Jupiter Position of Saturn Position of Uranus Position of Neptune Position of Pluto Position of Xena / Lilah / Eris ( 10th Planet ) Sedna Subroutine1 solves Kepler Equation etc... Subroutine2 calc. angles which are functions of µ Subroutine3 calculates geoc. coord from helio. coord Section Header Altjira Chaos Deucalion Hauméa Ixion Makémaké Orcus Quaoar Rhadamanthus Salacia Sila-Nunam Typhon Varda Varuna |
THE STACK:
| STACK | INPUTS | CF01-CF02-CF03 OUTPUTS | CF01-CF02-SF03 OUTPUTS | CF01-SF02 OUTPUTS | SF 01 OUTPUTS |
| T | / | Elg = elongation from the Sun ( ° ' '' ) | / | Elg = elongation from the Sun ( ° ' '' ) | / |
| Z | / | h0 = apparent altitude ( ° ' '' ) | / | Dist Earth-Planet ( AU ) | Radius Vector ( AU ) |
| Y | / | h = true altitude ( ° ' '' ) | Declination ( ° ' '' ) | Ecliptic Geocentric Latitude ( deg ) | Eclipt. Hel. Lat (deg ) |
| X | / | Az = Azimuth ( ° ' '' ) | Right-Ascension ( hh.mnss ) | Ecliptic Geocentric Longitude ( deg ) | Eclipt. Hel. Long (deg ) |
Example: Suppose we are at the US Naval Observatory
at Washington ( D.C. ) on 2100/01/01 7h41m UT
,
Temperature = 10°C & Pressure = 1010 mbar
Assuming TT-UT = 203 seconds (?)
• Longitude = 77°03'56"
W = -77°03'56" STO 16
• Latitude =
38°55'17" N = +38°55'17" STO 17
• 10
STO 18
• 1010 STO 19
• 203 STO 20
CF 01 CF 02 CF 03
2100.0101 ENTER^
7.41
XEQ "ST" >>>> TLST = 9h16m57s3 = R21
-We also have
true obliquity of the ecliptic = 23°4288 = R22
nutation in longitude
= 0°0008 = R23
R/S or XEQ "SUN" >>>>
Az = 74°23'27" = R11
RDN h = -54°33'13" = R12
RDN h0 = -54°33'13" = R13
( here , h0 is meaningless )
RDN Elg = 0
R03 = l = 280°931
R06 = R.A. = 18h47m33s
R04 = b = 0
R07 = Decl = -22°58'45"
R05 = r = 0.983347 AU
the rectangular coordinates of the Sun: R01 = X = 0.186555
& R02 = Y = -0.965489
apparent longitude of Sun = R24 = 280°931
R/S or XEQ "MO"
>>>> Az = 138°31'47" = R11
RDN h = 51°16'54" = R12
RDN h0 = 51°17'40" = R13
RDN Elg = 119°00'28" = R14
R03 = l = 161°921
R06 = R.A. = 10h54m23s
R04 = b = 0°699
R07 = Decl = 7°44'04"
R05 = r = 0.002483 AU
R/S or XEQ "ME"
>>>> Az = 67°30'42" = R11
RDN h = -61°33'30" = R12
RDN h0 = -61°33'30" = R13
RDN Elg = 7°53'05" = R14
R03 = l = -71°473
R08 = L = 306°251
R06 = R.A. = 19h21m31s
R04 = b = -2°120
R09 = B = -6°822
R07 = Decl = -24°14'53"
R05 = r = 1.38309 AU
R10 = R = 0.43077 AU
R/S or XEQ "VE"
>>>> Az = -10°30'23" = R11
RDN h = -67°11'25" = R12
RDN h0 = -67°11'25" = R13
RDN Elg = 39°33'45" = R14
R03 = l = -39°542
R08 = L = 20°246
R06 = R.A. = 21h33m52s
R04 = b = -1°845
R09 = B = -2°860
R07 = Decl = -16°24'46"
R05 = r = 1.1236 AU
R10 = R = 0.7252 AU
R/S or XEQ "MA"
>>>> Az = -66°27'03" = R11
RDN h = -8°43'03" = R12
RDN h0 = -8°43'03" = R13
RDN Elg = 108°43'42" = R14
R03 = l = 29°662
R08 = L = 67°745
R06 = R.A. = 1h48m59s
R04 = b = 0°957
R09 = B = 0°553
R07 = Decl = 12°14'36"
R05 = r = 0.8729 AU
R10 = R = 1.5100 AU
R/S or XEQ "JU"
>>>> Az = 114°44'54" = R11
RDN h = 17°20'45" = R12
RDN h0 = 17°23'48" = R13
RDN Elg = 79°41'27" = R14
R03 = l = -158°757
R08 = L = 191°020
R06 = R.A. = 13h20m27s
R04 = b = 1°277
R09 = B = 1°298
R07 = Decl = -7°05'55"
R05 = r = 5.540 AU
R10 = R = 5.451 AU
R/S or XEQ "SA"
>>>> Az = 111°54'36" = R11
RDN h = 13°42'40" = R12
RDN h0 = 13°46'32" = R13
RDN Elg = 75°17'53" = R14
R03 = l = -154°353
R08 = L = 199°997
R06 = R.A. = 13h38m40s
R04 = b = 2°424
R09 = B = 2°475
R07 = Decl = -7°39'01"
R05 = r = 9.868 AU
R10 = R = 9.665 AU
R/S or XEQ "UR"
>>>> Az = -63°10'52" = R11
RDN h = -20°18'51" = R12
RDN h0 = -20°18'51" = R13
RDN Elg = 96°48'49" = R14
R03 = l = 17°745
R08 = L = 20°547
R06 = R.A. = 1h06m25s
R04 = b = -0°631
R09 = B = -0°626
R07 = Decl = 6°22'38"
R05 = r = 19.834 AU
R10 = R = 19.974 AU
R/S or XEQ "NE"
>>>> Az = 133°30'18" = R11
RDN h = 47°36'39" =
R12
RDN h0 = 47°37'32"
= R13
RDN Elg = 113°38'22" = R14
R03 = l = 167°288
R08 = L = 165°577
R06 = R.A. = 11h14m44s
R04 = b = 0°966
R09 = B = 0°953
R07 = Decl = 5°54'31"
R05 = r = 29.801 AU
R10 = R = 30.209 AU
R/S or XEQ "PL"
>>>> Az = -84°25'29" = R11
RDN h = -12°35'27" = R12
RDN h0 = -12°35'27" = R13
RDN Elg = 110°29'54" = R14
R03 = l = 32°402
R08 = L = 33°519
R06 = R.A. = 2h23m51s
R04 = b = -16°919
R09 = B = -16°793
R07 = Decl = -3°37'21"
R05 = r = 48.588 AU
R10 = R = 48.941 AU
R/S or XEQ "XE"
>>>> Az = -66°41'24" = R11
RDN h = 5°45'31" =
R12
RDN h0 = 5°54'02"
= R13
RDN Elg = 122°03'08" = R14
R03 = l = 43°193
R08 = L = 43°761
R06 = R.A. = 2h34m58s
R04 = b = 6°180
R09 = B = 6°141
R07 = Decl = 21°40'31"
R05 = r = 83.424 AU
R10 = R = 83.950 AU
R/S or XEQ "SD"
>>>> Az = -133°03'03" = R11
RDN h = 58°28'59" =
R12
RDN h0 = 58°29'34"
= R13
RDN Elg = 164°28'46" = R14
R03 = l = 115°169
R08 = L = 114°985
R06 = R.A. = 7h43m48s
R04 = b = -6°243
R09 = B = -6°167
R07 = Decl = 14°56'52"
R05 = r = 76.873 AU
R10 = R = 77.821 AU
Note:
-If you press R/S just after executing "SD" , you will execute "ST"
again
XEQ "ALT" >>>> Az = 134°54'30"
= R11
RDN h = 50°34'39" =
R12
RDN h0 = 50°35'26"
= R13
RDN Elg = 116°37'05" = R14
R03 = l = 164°299
R08 = L = 163°207
R06 = R.A. = 11h04m58s
R04 = b = 1°809
R09 = B = 1°792
R07 = Decl = 7°50'47"
R05 = r = 45.801 AU
R10 = R = 46.250 AU
R/S or XEQ "CHA" >>>> Az
= 110°26'14" = R11
RDN h = 22°09'35"
= R12
RDN h0 = 22°11'56"
= R13
RDN Elg = 82°42'12" = R14
R03 = l = -161°720
R08 = L = 197°032
R06 = R.A. = 13h17m50s
R04 = b = 6°835
R09 = B = 6°853
R07 = Decl = -0°50'17"
R05 = r = 45.173 AU
R10 = R = 45.059 AU
R/S or XEQ "DEU" >>>> Az
= -39°41'12" = R11
RDN h = -52°45'16"
= R12
RDN h0 = -52°45'16"
= R13
RDN Elg = 59°38'57" = R14
R03 = l = -19°420
R08 = L = 341°737
R06 = R.A. = 22h48m50s
R04 = b = -0°347
R09 = B = -0°351
R07 = Decl = -7°55'05"
R05 = r = 42.602 AU
R10 = R = 42.114 AU
R/S or XEQ "HAU" >>>> Az
= 36°55'02" = R11
RDN h = -66°51'16"
= R12
RDN h0 = -66°51'16"
= R13
RDN Elg = 21°33'58" = R14
R03 = l = -57°503
R08 = L = 303°050
R06 = R.A. = 20h18m57s
R04 = b = 0°135
R09 = B = 0°138
R07 = Decl = -19°27'44"
R05 = r = 38.711 AU
R10 = R = 37.798 AU
R/S or XEQ "IXI" >>>> Az
= -85°03'25" = R11
RDN h = 35°43'06"
= R12
RDN h0 = 35°44'26"
= R13
RDN Elg = 156°25'05" = R14
R03 = l = 77°436
R08 = L = 78°097
R06 = R.A. = 5h04m32s
R04 = b = 2°084
R09 = B = 2°029
R07 = Decl = 24°54'38"
R05 = r = 32.896 AU
R10 = R = 33.799 AU
R/S or XEQ "MAK" >>>> Az
= 90°26'33" = R11
RDN h = -34°49'04"
= R12
RDN h0 = -34°49'04"
= R13
RDN Elg = 22°40'31" = R14
R03 = l = -101°691
R08 = L = 257°864
R06 = R.A. = 17h09m46s
R04 = b = 1°596
R09 = B = 1°627
R07 = Decl = -21°19'27"
R05 = r = 49.026 AU
R10 = R = 48.120 AU
R/S or XEQ "ORC" >>>> Az
= 98°40'35" = R11
RDN h = -36°15'12"
= R12
RDN h0 = -36°15'12"
= R13
RDN Elg = 24°45'48" = R14
R03 = l = -103°343
R08 = L = 256°033
R06 = R.A. = 16h59m45s
R04 = b = -5°052
R09 = B = -5°174
R07 = Decl = -27°47'09"
R05 = r = 37.893 AU
R10 = R = 37.003 AU
R/S or XEQ "QUA" >>>> Az
= -65°05'09" = R11
RDN h = -18°27'31"
= R12
RDN h0 = -18°27'31"
= R13
RDN Elg = 99°13'15" = R14
R03 = l = 20°156
R08 = L = 381°480 = 21°480
R06 = R.A. = 1h16m49s
R04 = b = -1°560
R09 = B = -1°554
R07 = Decl = 6°25'43"
R05 = r = 41.809 AU
R10 = R = 41.978 AU
R/S or XEQ "RHD" >>>>
Az = 44°03'13" = R11
RDN h = -78°28'35"
= R12
RDN h0 = -78°28'35"
= R13
RDN Elg = 26°04'31" = R14
R03 = l = -55°501
R08 = L = 305°031
R06 = R.A. = 20h39m56s
R04 = b = -11°490
R09 = B = -11°725
R07 = Decl = -30°15'27"
R05 = r = 44.556 AU
R10 = R = 43.675 AU
R/S or XEQ "SAL" >>>>
Az = -94°33'19" = R11
RDN h = 50°55'16"
= R12
RDN h0 = 50°56'03"
= R13
RDN Elg = 172°23'51" = R14
R03 = l = 94°078
R08 = L = 94°222
R06 = R.A. = 6h18m14s
R04 = b = 3°299
R09 = B = 3°228
R07 = Decl = 26°39'48"
R05 = r = 44.136 AU
R10 = R = 45.111 AU
R/S or XEQ "SIL" >>>>
Az = 100°15'32" = R11
RDN h = -25°20'53"
= R12
RDN h0 = -25°20'53"
= R13
RDN Elg = 34°52'41" = R14
R03 = l = -113°900
R08 = L = 245°367
R06 = R.A. = 16h15m26s
R04 = b = -1.929
R09 = B = -1°964
R07 = Decl = -23°12'55"
R05 = r = 44.482 AU
R10 = R = 43.679 AU
R/S or XEQ "TYP" >>>>
Az = -6°35'45" = R11
RDN h = -67°20'35"
= R12
RDN h0 = -67°20'35"
= R13
RDN Elg = 38°06'53" = R14
R03 = l = -40°974
R08 = L = 319°647
R06 = R.A. = 21h27'32s
R04 = b = -1°337
R09 = B = -1°355
R07 = Decl = -16°22'58"
R05 = r = 57.208 AU
R10 = R = 56.437 AU
R/S or XEQ "VRD" >>>>
Az = -63°52'56" = R11
RDN h = -25°56'60"
= R12
RDN h0 = -25°56'60"
= R13
RDN Elg = 91°52'31"
= R14
R03 = l = 12°810
R08 = L = 374°247 = 14°247
R06 = R.A. = 0h52m29s
R04 = b = -3°433
R09 = B = -3°430
R07 = Decl = 1°53'38"
R05 = r = 39.203 AU
R10 = R = 39.247 AU
R/S or XEQ "VRN" >>>>
Az = 94°50'31" = R11
RDN h = 4°17'32"
= R12
RDN h0 = 4°28'13"
= R13
RDN Elg = 61°15'18" = R14
R03 = l = -139°258
R08 = L = 219°618
R06 = R.A. = 14h51m26s
R04 = b = 14°682
R09 = B = 14°838
R07 = Decl = -1°03'29"
R05 = r = 45.335 AU
R10 = R = 44.870 AU
Notes:
-The refraction is computed by a formula that duplicates the Pulkovo
refraction tables with a precision better than 1 arcsecond if t = 10°C
& P = 1010 mbar
-If t # 10°C & P # 1010 mbar, the errors may be larger, especially
near the horizon.
-The dates YYYY.MNDD must not be before 0000/03/00 ( otherwise, you
get NONEXISTENT )
References:
[1] Jean Meeus - "Astronomical Algorithms" - Willmann-Bell
- ISBN 0-943396-61-1
[2] VSOP87D Series ftp://ftp.imcce.fr/pub/ephem/planets/vsop87/
[3] VSOP09 & TOP2010 Series http://www.imcce.fr/~jlsimon
[4] A fantastic software by Aldo Vitagliano: "SOLEX" which may
be downloaded freely from
http://www.solexorb.it/