Overview
-These programs calculate the positions of 10 transneptunian planets between 2016/01/01 and 2026/01/08 namely:
• Eris / Xena / Lilah - temporarily
called the 10th planet.
• Haumea
• Ixion
• Makemake
• Orcus
• Pluto
• Quaoar
• Salacia
• Sedna
• Varuna
-The precision of the heliocentric longitudes & latitudes is around
0°00001
-They are computed by polynomials fitted to the
French Ephemerides INPOP13c
-The geocentric positions are also given - with a lesser accuracy -
including the azimuthal ( horizontal ) coordinates.
Usage:
0-XEQ "SIZE" 027 at least
1-XEQ "EPHTN" to store the required data in the proper registers and
calculate the rectangular coordinates of the Sun
2-XEQ "ERIS" ... and / or the other programs to get the position of
these 10 plutoids.
Data Registers:
R00 = T = Millenia since 2000/01/01 0h TT OR x = ( Nb of days since 2000/01/01 minus 7674 ) / 1830 ( -1 < x < +1 )
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-Plutoid ( 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-Plutoid ( AU )
R11 = Azimuth ( ° ' " ) clockwise from North
R12 = height ( ° ' " )
( aberrations & 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 aberration & parallax into account
R15 = True Local Sidereal Time ( hh.mnss )
R16 = Longitude of the observer ( ° ' " ) positive
East
R17 = Latitude of the observer ( ° ' " )
R18 = Altitude of the observer ( in meters )
R19 = Temperature ( in °C )
R20 = Atmospheric Pressure ( in mbar )
R21 = True obliquity of the ecliptic ( deg )
R22 = Nutation in longitude ( deg )
R23 = TT - UT1 ( in seconds )
R24 = Longitude of the Sun ( deg )
R25 = x or T ( contains x when R00 = T and contains T when R00
= x )
R26 = 180° + longitude of the perihelion of the Earth orbit
| XROM | Function | Desciption |
| 23,00
23,01 23,02 23,03 23,04 23,05 23,06 23,07 23,08 23,09 23,10 23,11 23,12 23,13 23,14 23,15 23,16 23,17 23,18 23,19 23,20 23,21 23,22 23,23 23,24 23,25 23,26 23,27 23,28 |
-TRANSNEP
EPHTN SUN+ ERIS HAUMEA IXION MAKEMAK ORCUS PLUTO QUAOAR SALACIA SEDNA VARUNA J2 EE REFR R-S S-R SEP ER HA IX MA OR PL QU SA SE VA |
Section Header
Initialization Ecliptic Coordinates of the Sun Position of Eris / Xena / Lilah Position of Haumea Position of Ixion Position of Makemake Position of Orcus Position of Pluto Position of Quaoar Position of Salacia Position of Sedna Position of Varuna Number of days since 2000/01/01 Equatorial <> Ecliptic Transformation Refraction Rectangular-Spherical Conversion Spherical-Rectangular Conversion Angular Separation Eris Heliocentric Ecliptic Coordinates Haumea Heliocentric Ecliptic Coordinates Ixion Heliocentric Ecliptic Coordinates Makemake Heliocentric Ecliptic Coordinates Orcus Heliocentric Ecliptic Coordinates Pluto Heliocentric Ecliptic Coordinates Quaoar Heliocentric Ecliptic Coordinates Salacia Heliocentric Ecliptic Coordinates Sedna Heliocentric Ecliptic Coordinates Varuna Heliocentric Ecliptic Coordinates |
-Suppose you want to calculate the position of these transneptunian
planets on 2016/01/07 at 16h48m TT = Terrestrial
Time
XEQ "EPHTN"
>>>> "YMD^HHMNSS?" Enter
the date in YMD format ( Gregorian calendar ) and the time.
"NONEXISTENT" will be displayed if the date is outside the interval
However, these programs may also be used one month before 2016/01/01
or after 2026/01/08: set F25 and R/S
2016.0107 ENTER^
16.48
R/S >>>>
"LON^LAT^ALT?" Enter the longitude - positive East
- the latitude and the altitude in meters of your location
Assuming your location = US naval obervatory
Longitude = 77°03'56"0 W Latitude = 38°55'17"2 N
Altitude = 67 m
-77.0356 ENTER^
Simply press R/S if these data are already stored from a previous
calculation
38.55172 ENTER^
67
R/S
"TEMP^PRESS" Enter the
temperature t ( in °C ) and the pressure P ( in mbar )
Assuming t = 15°C & P = 1013.25 mbar:
15
ENTER^
1013.25
R/S
"TT-UT1?"
Enter the value of TT - UT1 ( in seconds ) or press R/S without any digit
entry
In this case, DT = 68.109 s for the given date
Delta T is approximated by 58.21 + 618 T , probably accurate
in January 2016,
but probaby not in 2026 !
R/S
" READY"
is displayed after 32 seconds. The HP-41 has computed the coordinates of
the Sun,
the obliquity of the ecliptic and the nutations
-At this step,
X = 18h45m22s68 = Local Sidereal Time = R15
Y = 286°8178 = Longitude
of the Sun = R24
>>>> You can now execute the other programs - simply press R/S
to get Eris coordinates.
-After executing "EPHTN" key in XEQ "ERIS" or simply R/S
| STACK | INPUT | OUTPUTS |
| T | / | Elg = elongation from the Sun ( ° ' " ) |
| Z | / | h0 = apparent altitude ( ° ' '' ) |
| Y | / | h = true altitude ( ° ' '' ) |
| X | / | Az = Azimuth ( ° ' '' ) |
Execution time = 32 seconds
Example: With the example given in paragraph above, it yields:
Az = 83°29'09"61 = R11
RDN h = -12°40'38"99 = R12
RDN h0 = -12°40'38"99 = R13
RDN Elg = 95°21'26"
R03 = l = 22°30619
R06 = R.A. = 1h41m03s98
R08 = L = 22°902822
R04 = b = -12°53412
R07 = Decl = -2°58'02"75
R09 = B = -12°519770
R05 = r = 96.19725 AU
R10 = R = 96.294030 AU
| STACK | INPUT | OUTPUTS |
| T | / | Elg = elongation from the Sun ( ° ' " ) |
| Z | / | h0 = apparent altitude ( ° ' '' ) |
| Y | / | h = true altitude ( ° ' '' ) |
| X | / | Az = Azimuth ( ° ' '' ) |
Execution time = 32 seconds
Example: Same example
XEQ "HAUMEA" or simply R/S if you've just executed "ERIS"
Az = 270°33'43"25 = R11
RDN h = 26°28'12"32 = R12
RDN h0 = 26°30'06"26 = R13
RDN Elg = 83°59'03"
R03 = l = -156°37826
R06 = R.A. = 14h08m51s32
R08 = L = 202°374607
R04 = b = 27°79423
R07 = Decl = 16°40'13"00
R09 = B = 27°852806
R05 = r = 50.75902 AU
R10 = R = 50.665381 AU
| STACK | INPUT | OUTPUTS |
| T | / | Elg = elongation from the Sun ( ° ' " ) |
| Z | / | h0 = apparent altitude ( ° ' '' ) |
| Y | / | h = true altitude ( ° ' '' ) |
| X | / | Az = Azimuth ( ° ' '' ) |
Execution time = 33 seconds
Example: Same example
XEQ "IXION" or simply R/S if you've just executed "HAUMEA"
Az = 197°37'11"20 = R11
RDN h = 21°29'31"63 = R12
RDN h0 = 21°31'55"23 = R13
RDN Elg = 23°31'00"
R03 = l = -96°35958
R06 = R.A. = 17h31m24s73
R08 = L = 263°091844
R04 = b = -4°09565
R07 = Decl = -27°22'21"00
R09 = B = -4°188264
R05 = r = 40.95435 AU
R10 = R = 40.054555 AU
| STACK | INPUT | OUTPUTS |
| T | / | Elg = elongation from the Sun ( ° ' " ) |
| Z | / | h0 = apparent altitude ( ° ' '' ) |
| Y | / | h = true altitude ( ° ' '' ) |
| X | / | Az = Azimuth ( ° ' '' ) |
Execution time = 32 seconds
Example: Same example
XEQ "MAKEMAK" or simply R/S if you've just executed "IXION"
Az = 288°01'16"58 = R11
RDN h = 17°51'04"96 = R12
RDN h0 = 17°53'59"75 = R13
RDN Elg = 102°13'45"
R03 = l = -177°14208
R06 = R.A. = 12h58m54s39
R08 = L = 181°671070
R04 = b = 28°59278
R07 = Decl = 24°56'29"91
R09 = B = 28°466144
R05 = r = 52.21479 AU
R10 = R = 52.431906 AU
| STACK | INPUT | OUTPUTS |
| T | / | Elg = elongation from the Sun ( ° ' " ) |
| Z | / | h0 = apparent altitude ( ° ' '' ) |
| Y | / | h = true altitude ( ° ' '' ) |
| X | / | Az = Azimuth ( ° ' '' ) |
Execution time = 33 seconds
Example: Same example
XEQ "ORCUS" or simply R/S if you've just executed "MAKEMAK"
Az = 288°49'35"71 = R11
RDN h = -35°52'24"98 = R12
RDN h0 = -35°52'24"98 = R13
RDN Elg = 126°16'44"
R03 = l = 157°95027
R06 = R.A. = 110h09m32s20
R08 = L = 156°980652
R04 = b = -19°44849
R07 = Decl = -9°28'50"09
R09 = B = -19°202481
R05 = r = 47.45951 AU
R10 = R = 48.047956 AU
| STACK | INPUT | OUTPUTS |
| T | / | Elg = elongation from the Sun ( ° ' " ) |
| Z | / | h0 = apparent altitude ( ° ' '' ) |
| Y | / | h = true altitude ( ° ' '' ) |
| X | / | Az = Azimuth ( ° ' '' ) |
Execution time = 35 seconds
Example: Same example
XEQ "PLUTO" or simply R/S if you've just executed "ORCUS"
Az = 174°33'54"68 = R11
RDN h = 29°53'56"68 = R12
RDN h0 = 29°55'35"48 = R13
RDN Elg = 2°12'06"
R03 = l = -74°71973
R06 = R.A. = 19h05m33s56
R08 = L = 285°241686
R04 = b = 1°57620
R07 = Decl = -20°59'35"64
R09 = B = 1°622817
R05 = r = 34.00038 AU
R10 = R = 33.017773 AU
| STACK | INPUT | OUTPUTS |
| T | / | Elg = elongation from the Sun ( ° ' " ) |
| Z | / | h0 = apparent altitude ( ° ' '' ) |
| Y | / | h = true altitude ( ° ' '' ) |
| X | / | Az = Azimuth ( ° ' '' ) |
Execution time = 34 seconds
Example: Same example
XEQ "QUAOAR" or simply R/S if you've just executed "PLUTO"
Az = 195°19'05"67 = R11
RDN h = 33°57'18"00 = R12
RDN h0 = 33°58'42"47 = R13
RDN Elg = 20°03'01"
R03 = l = -91°76383
R06 = R.A. = 17h52m44s09
R08 = L = 267°821194
R04 = b = 7°66946
R07 = Decl = -15°45'13"98
R09 = B = 7°835408
R05 = r = 43.89076 AU
R10 = R = 42.968300 AU
| STACK | INPUT | OUTPUTS |
| T | / | Elg = elongation from the Sun ( ° ' " ) |
| Z | / | h0 = apparent altitude ( ° ' '' ) |
| Y | / | h = true altitude ( ° ' '' ) |
| X | / | Az = Azimuth ( ° ' '' ) |
Execution time = 34 seconds
Example: Same example
XEQ "SALACIA" or simply R/S if you've just executed "QUAOAR"
Az = 87°20'11"30 = R11
RDN h = 30°23'41"58 = R12
RDN h0 = 30°25'18"45 = R13
RDN Elg = 72°29'10"
R03 = l = -2°31812
R06 = R.A. = 23h12m45s97
R08 = L = -1°013257
R04 = b = 23°36147
R07 = Decl = 20°25'46"43
R09 = B = 23°518154
R05 = r = 44.88791 AU
R10 = R = 44.601868 AU
| STACK | INPUT | OUTPUTS |
| T | / | Elg = elongation from the Sun ( ° ' " ) |
| Z | / | h0 = apparent altitude ( ° ' '' ) |
| Y | / | h = true altitude ( ° ' '' ) |
| X | / | Az = Azimuth ( ° ' '' ) |
Execution time = 33 seconds
Example: Same example
XEQ "SEDNA" or simply R/S if you've just executed "SALACIA"
Az = 53°31'47"19 = R11
RDN h = -27°03'43"29 = R12
RDN h0 = -27°03'43"29 = R13
RDN Elg = 126°46'55"
R03 = l = 54°56479
R06 = R.A. = 3h40m32s43
R08 = L = 55°093082
R04 = b = -12°01177
R07 = Decl = 7°14'17"23
R09 = B = -11°926646
R05 = r = 85.18556 AU
R10 = R = 85.777935 AU
| STACK | INPUT | OUTPUTS |
| T | / | Elg = elongation from the Sun ( ° ' " ) |
| Z | / | h0 = apparent altitude ( ° ' '' ) |
| Y | / | h = true altitude ( ° ' '' ) |
| X | / | Az = Azimuth ( ° ' '' ) |
Execution time = 34 seconds
Example: Same example
XEQ "VARNA" or simply R/S if you've just executed "SEDNA"
Az = 340°15'34"28 = R11
RDN h = -21°37'48"21 = R12
RDN h0 = -21°37'48"21 = R13
RDN Elg = 166°50'03"
R03 = l = 118°37852
R06 = R.A. = 8h07m40s44
R08 = L = 118°114642
R04 = b = 6°34346
R07 = Decl = 26°41'18"53
R09 = B = 6°204484
R05 = r = 42.83197 AU
R10 = R = 43.790068 AU
-All these programs are called to compute the heliocentric ecliptic
coordinates of Eris, Haumea, ..... , Varuna.
-They may also be used if you don't need the geocentric coordinates.
-Register R00 must contain x = ( d -7674 ) / 1830 where d = Nb of days since 2000/01/01 0h TT
-However, unlike "EPHTN" , they don't check that -1 < x <
+1
-So, meaningless results may be returned...
Example: With x = 0.314
( i-e 2022/08/01 at 14h52m48s TT )
0.314 STO 00 XEQ "PL" gives the heliocentric ecliptic coordinates of Pluto - in 10 seconds.
L = 297°415810
in registers X & R08
B = -2°089925
in registers Y & R09
R = 34.575596 AU
in registers Z & R10
-Likewise for the other Plutoids...
-Unlike the other programs which are valid for about 10 years,
"SUN+" gives the ecliptic coordinates of the Sun between the
years 1000 and 3000 at least.
-Register R00 must contain the number of millenia since 2000/01/01
0h TT
Example: With T = 1.2 i-e 3200/01/10 0h TT
1.2 STO 00 XEQ "SUN+" returns in 19 seconds
X = L = 288°7833
Y = R = 0.98436 AU
-The precision is around 4 arcseconds for the longitude L and
0.00001 AU for the distance Sun-Earth R
-"SUN+" also returns the longitude of the perihelion in Z-register,
-56°3641 in the example above
Note:
-"SUN+" uses just one data register: R00, but the alpha "register" is
cleared.
Number of days since 2000/01/01
-"J2" is only a variant of a routine listed in the PPC ROM user's manual.
-Y-register is saved in Y Z T
-Synthetic register M is used
>>> Set flag F04 for the Julian Calendar
Clear flag F04 for the Gregorian
Calendar
| STACK | INPUTS | OUTPUTS |
| T | / | Y |
| Z | / | Y |
| Y | Y | Y |
| X | YYYY.MNDD | N |
Examples:
CF 04 2134.0404 XEQ "J2" >>>
N = 49036
SF 04 1234.0428 XEQ "J2" >>>
N = -279651
Notes:
-Here, the days cannot have decimals
-You can choose the Julian Calendar after 1582/10/15
and you can choose the Gregorian Calendar before 1582/10/04
-This program only works since 0000/03/01 ( March 1st Year 0 )
Spherical-Rectangular Conversion
x = r cos b cos l
y = r cos b sin l
z = r sin b
where x , y , z = rectangular coordinates,
r = ( x2 + y2 + z2 )1/2
, l = longitude , b = latitude
| STACK | INPUTS | OUTPUTS |
| T | T | T |
| Z | b | z |
| Y | l | y |
| X | r | x |
| L | / | (x2+y2)1/2 |
Example: r = 10 ; l =
124° ; b = 37° find x ; y
; z ( in DEG mode )
37 ENTER^
124 ENTER^
10 XEQ "S-R" x = -4.465913097
RDN y = 6.620988446
RDN z = 6.018150232
Note:
- "S-R" works in all angular modes
Rectangular-Spherical Conversion
x = r cos b cos l
y = r cos b sin l
z = r sin b
where x , y , z = rectangular coordinates,
r = ( x2 + y2 + z2 )1/2
, l = longitude , b = latitude
| STACK | INPUTS | OUTPUTS |
| T | T | T |
| Z | z | b |
| Y | y | l |
| X | x | r |
| L | / | (x2+y2)1/2 |
Example: x = 3 ; y = 4 ; z =
-7 find the spherical coordinates ( in DEG mode )
-7 ENTER^
4 ENTER^
3 XEQ "R-S" r
= 8.602325267
RDN l = 53.13010235°
RDN b = -54.46232221°
Note:
- "R-S" works in all angular modes
Equatorial <> Ecliptic Transformation
-Many transformations use the same type of formulae which appear in the equatorial-ecliptic conversion, namely:
sin b = cos e sin d - sin e cos d sin a
cos b cos l = cos d cos a
cos b sin l = sin e sin d +
cos e cos d sin a
| STACK | INPUTS | OUTPUTS |
| Z | e | e |
| Y | decl | b |
| X | RA | l |
where e = obliquity of the ecliptic
Example: if right-ascension = RA = 116.328942 , declination = decl = 28.026183 and e = 23.4392911
23.4392911 ENTER^
28.026183 ENTER^
116.328942 XEQ "EE" >>>> l
= 113.215630° RDN b
= 6.684170°
Notes:
-With Z = -e , "EE" performs the reverse trasformation.
-Like "R-S" and "S-R" , "EE" works in all angular modes.
"REFR" takes the height h , the temperature & pressure and
returns the height h0 corrected for refraction
| STACK | INPUT | OUTPUT |
| Z | t ( °C ) | h ( deg ) |
| Y | P( mbar ) | h ( deg ) |
| X | h ( ° ' " ) | h0 ( ° ' " ) |
Example1: t = 15°C
P = 1013.25 mbar h = 16°
15
ENTER^
1013.25 ENTER^
16
XEQ "REFR" >>>> h0 = 16°03'15"63
Example2: t = 0°C P = 1020 mbar h = 16°
0
ENTER^
1020 ENTER^
16 XEQ "REFR"
>>>> h0 = 16°03'27"80
Notes:
-The alpha register is cleared.
-"REFR" approximates the Pulkovo refraction table with a precision better
than 0"06 over the whole range [ -0°32'58"0 , 90° ]
for the standard conditions of temperature & pressure.
Formula:
h0 ~ h + 57"1798 / Tan ( h + 4°8043
/ ( h + 7°0822 / ( h +11°1187 / ( h + 38°2290 / ( h + 9°9098
) ) ) ) )
-Otherwise, the correction is multiplied by ( P/1013.25 ) [ 287 / ( t + 272 ) ]
and if t # 15°C and / or P # 1013.25 hPa, we get a lesser
accuracy, especially near the horizon.
-"SEP" takes, for example, 2 longitudes & latitudes or 2 azimuths
& heights and returns the angular separation
-All angles are expressed in ° ' "
| STACK | INPUTS | OUTPUTS |
| T | L1 ( ° ' " ) | / |
| Z | b1 ( ° ' " ) | / |
| Y | L2 ( ° ' " ) | / |
| X | b2 ( ° ' " ) | A ( ° ' " ) |
Example: L1
= 2°41'24" b1 = 49°51'12"
& L2 = -116°15'33" b2
= 33°21'22"
2.4124 ENTER^
49.5112 ENTER^
-116.1533 ENTER^
33.2122 XEQ "SEP" >>>>
A = 80°48'53"17
Note:
-"SEP" may also be used with right-ascensions & declinations,
but in this case, convert the right-ascension in ° ' "
( HR 15 * HMS )
-Here are the polynomials that are used to approximate the heliocentric ecliptic coordinates, with d = Nb of days since 2000/01/01 0h TT
-They are displayed as vectors [ a0 a1 ................ an ] meaning that p(x) = a0 + a1 x + ................ + an xn with x = ( d -7674 ) / 1830
Between 2016/01/01 and 2026/01/08 i-e -1 < x <
+1
-Units:
0°000001
for the longitudes & latitudes
0.000001 AU for the distances
ERIS
L [ 24051359. 1160957. 12081. -1192. -7473. -1210. 2912. 1366. -1022.
-420. 252. ]
B [ -11542513. 987528. 5475. -1615. 96. 788. 268. -231. -212. 37. 59.
]
R [ 95936827. -373787. -27392. -16559. -310. 7422. 3006. -2108. -2067.
331. 543. ]
HAUMEA
L [ 207593517. 5274587. 28501. 977. 14257. 3253. -5279. -2938. 1825.
864. -469. ]
B [ 28126074. 183710. -98293. -9923. -800. 3372. 1711. -872. -1078.
121. 279. ]
R [ 50277400. -431057. -31705. 14152. 944. -5885. -2791. 1578. 1815.
-234. -473. ]
IXION
L [ 269871109. 7046477. 239292. -5243. 5281. 10822. 2713. -5589. -3756.
2742. 2261. -746. -618. ]
B [ -6471420. -2325874. -29634. 6875. 2723. 335. -801. -498. 115. 278.
120. -68. -68. ]
R [ 38838893. -1251175. -28348. 11028. 9759. -847. -3953. -1241. 355.
591. 1068. -56. -555. ]
MAKEMAKE
L [ 186636947. 4926059. -60628. 8114. 13389. -244. -6188. -1780. 2588.
649. -668. ]
B [ 27945609. -605918. -88583. -5500. 1605. 3418. 647. -1209. -665.
239. 178. ]
R [ 52597654. 135360. -20045. 12698. -2538. -6350. -1375. 2202. 1272.
-430. -332. ]
ORCUS
[ 162060393. 5096218. 4443. 17191. 10742. -3938. -5785. -109.
1611. 48. 581. 116. -475. ]
[ -19759914. -488967. 76486. 5212. -2746. -3080. -162. 1766.
943. -826. -713. 203. 223. ]
[ 48061701. -31294. -34066. 9446. -6547. -6437. -43. 3942. 1861.
-1954. -1464. 500. 465. ]
PLUTO
L [ 294596217. 9080138. -316597. -12502. -421. 10729. 4693. -4662. -3341.
2349. 1053. -707. -86. ]
B [ -1233409. -2763928. 112745. 8044. -996. 701. -44. -374. -128. 220.
103. -70. -30. ]
R [ 34193780. 1210271. 18583. -4659. 10185. 2357. -2800. -2674. -769.
1268. 1650. -247. -696. ]
QUAOAR
L [ 274398278. 6632324. 14114. -19173. 3960. 9911. 2540. -5017. -3187.
2467. 1755. -678. -443. ]
B [ 7958922. 76209. -47891. -1330. -1921. -222. 672. 376. 33. -139.
-251. 9. 115. ]
R [ 42802570. -177466. -11852. 7327. 9983. -237. -3905. -1585. 232.
765. 1131. -104. -569. ]
SALACIA
L [ 5346881. 6364140. -19827. -11637. -14090. 215. 5483. 2312. -309.
-1117. -1594. 156. 800. ]
B [ 23846317. 197779. -123913. 9149. -1507. -4033. -1012. 1979. 1258.
-937. -681. 251. 169. ]
R [ 44992142. 376130. -27171. -12962. 2643. 6675. 1712. -3392. -2108.
1686. 1138. -468. -281. ]
SEDNA
[ 58170737. 3143432. 62152. 4790. -6430. -4413. 770. 2991. 1142.
-1469. -1130. 359. 394. ]
[ -11904940. 40307. 18417. -1274. -1017. 579. 627. -108. -228.
71. -15. -36. 35. ]
[ 84355771. -1368821. 53350. -13296. -6611. 4968. 4568. -1019.
-1870. 479. 48. -218. 207. ]
VARUNA
L [ 124097963. 5984217. -6012. 22120. 3027. -8658. -4698. 3266. 2863.
-1619. -754. 516. 4. ]
B [ 7857956. 1610500. -52877. -2631. 1833. 775. -407. -670. -222. 351.
322. -88. -125. ]
R [ 44010792. 225770. 10860. 286. -10330. -3456. 2581. 3266. 880. -1594.
-1567. 344. 638. ]
References:
[1] http://www.imcce.fr
[2] Jean Meeus - "Astronomical Algorithms" - Willmann-Bell
- ISBN 0-943396-61-1