TRANSNEPTUNIAN PLANETS 2016-2025

By Jean-Marc Baillard


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

 

Initialization
 

-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.
 

Eris / Xena / Lilah
 

-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
 

Haumea
 
 
 
 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
 

Ixion
 
 
 
 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
 

Makemake
 
 
 
 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
 

Orcus
 
 
 
 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
 

Pluto
 
 
 
 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
 

Quaoar
 
 
 
 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
 

Salacia
 
 
 
 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
 

Sedna
 
 
 
 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
 

Varuna
 
 
 
 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
 

ER-HA-IX-MA-OR-PL-QU-SA-SE-VA
 

-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...
 

Position of the Sun
 

-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     = 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 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.
 

Refraction
 

 "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.
 

Angular Separation
 

-"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 )
 

Polynomial Approximations
 

-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