# Description of this file is at bottom.

Remap: 3001 10  4001 28  4002 29  5005 47  5014 48  5015 49  5016 50
Remap: 5001 11  5002 12  5003 13  5004 14  6001 15  6002 16  6003 17  6004 18
Remap: 6005 19  6006 20  6007 21  6008 22  6009 40
Remap: 6015 51  6016 52  6017 53  6018 54
Remap: 7001 23  7002 24  7003 25  7004 26  7005 27  7006 55  7007 56  7008 57
Remap: 7009 58  7010 59  7011 60  7012 61  7013 62  7014 63  7015 64
Remap: 8001 30  8003 71  8004 70  8005 68  8006 69  8007 67  8008 66
Remap: 9001 31  9002 109 9003 108 9004 173 9005 174

# Not actually in use yet:

Remap: 6010 175 6011 176 6012 177 6013 178 6014 179

Planet: p

Obj: 0 # Sun
   r=695700
   a0=286.13
   d0=63.87
   W=84.176+14.1844000d

# See Mercury under 'H' (Mars uses 'M')

Obj: 2 # Venus
   r=6051.8
   a0= 272.76
   d0= 67.16
   W2=160.20-85.7142857d # (k)
   W=160.20-1.4813688d   # (b)

# Earth:  for reference only (see comment (m))
Obj: 3
   r=6378.136,6356.7519
   a0= 0.00-0.641T
   d0= 90.00-0.557T
   W= 190.147+360.9856235d

# See Mars under 'M'

Obj: 5 # Jupiter
   r=71492,66854
   a0= 268.056595-.006499T
   d0= 64.495303+.002413T
   W2=  43.3+870.270d        #     (System II)
   W3= 284.95+870.536d       # (d) (System III)
   W=  67.1+877.900d         #     (System I)

Obj: 6 # Saturn
   r=60268,54364
   a0= 40.589-0.036T
   d0= 83.537-0.004T
   W2= 104.90+812d           #     (System II)
   W3= 38.90+810.7939024d    # (d) (System III)
   W= 227.90+844.3d          #     (System I)

Obj: 7 # Uranus
   r=25559,24973
   a0= 257.311
   d0=-15.175
   W= 203.81-501.1600928d    # (d)

# (See Neptune under 'N'; it has trig terms)

Obj: 9 # Pluto
   r=1188.3
   a0= 132.993
   d0= -6.163
   W= 302.695+56.3625225d   # (e)

# Recommended values for the direction of the north pole of rotation and the
# prime meridian of the satellites (2000)

# a0, d0, T and d have the same meanings as in Table I (epoch 2000 January 1.5,
# i.e., JD 2451545.0 TCB).

Planet: H
  H1=174.7910857 + 4.092335d
  H2=349.5821714 + 8.184670d
  H3=164.3732571 + 12.277005d
  H4=339.1643429 + 16.369340d
  H5=153.9554286 + 20.461675d

Obj: 1 # Mercury
   r=2440.53,2438.26
   a0=281.0103-0.0328T
   d0= 61.4155-0.0049T
   W=329.5988+6.1385108d+0.01067257 sin H1 -0.00112309 sin H2 -0.00011040 sin H3 -0.00002539 sin H4 -0.00000571 sin H5
   # (a) (l)

Planet: E
  E1=125.045-0.0529921d
  E2=250.089-0.1059842d
  E3=260.008+13.0120009d
  E4=176.625+13.3407154d
  E5=357.529+0.9856003d
  E6=311.589+26.4057084d
  E7=134.963+13.0649930d
  E8=276.617+0.3287146d
  E9=34.226+1.7484877d
  E10=15.134-0.1589763d
  E11=119.743+0.0036096d
  E12=239.961+0.1643573d
  E13=25.053+12.9590088d

Obj: 3001 # Earth's moon
   r=1737.4
   a0=269.9949 +0.0031T -3.8787 sin E1 -0.1204 sin E2 +0.0700 sin E3 -0.0172 sin E4 +0.0072 sin E6 -0.0052 sin E10 +0.0043 sin E13
   d0=66.5392 +0.0130T +1.5419 cos E1 +0.0239 cos E2 -0.0278 cos E3 +0.0068 cos E4 -0.0029 cos E6 +0.0009 cos E7 +0.0008 cos E10 -0.0009 cos E13
   W=38.3213 +13.17635815d -1.4e-12d2 +3.5610 sin E1 +0.1208 sin E2 -0.0642 sin E3 +0.0158 sin E4 +0.0252 sin E5 -0.0066 sin E6 -0.0047 sin E7 -0.0046 sin E8 +0.0028 sin E9 +0.0052 sin E10 +0.0040 sin E11 +0.0019 sin E12 -0.0044 sin E13

Planet: M

  M1 = 190.72646643 + 15917.10818695T
  M2 = 21.46892470  + 31834.27934054T
  M3 = 332.86082793 + 19139.89694742T
  M4 = 394.93256437 + 38280.79631835T
  M5 = 189.63271560 + 41215158.18420050T # + 12.71192322 T2
  M6 = 121.46893664 + 660.22803474T
  M7 = 231.05028581 + 660.99123540T
  M8 = 251.37314025 + 1320.50145245T
  M9 = 217.98635955 + 38279.96125550T
  M10 = 196.19729402 + 19139.83628608T

  M11 =  79.398797 +     0.5042615T
  M12 = 166.325722 +     0.5042615T
  M13 =  95.391654 +     0.5042615T

Obj: 4001 # Phobos (s)
   r=13.0,11.4,9.1
   a0 = 317.67071657 -0.10844326T -1.78428399 sin M1 +0.02212824 sin M2
   d0 =  52.88627266 -0.06134706T -1.07516537 cos M1 +0.00668626 cos M2
   W  =  35.18774440 +1128.84475928d + 12.72192797 T2 + 1.42421769 sin M1 - 0.02273783 sin M2 - 1.145 sin M5

Obj: 4002 # Deimos (s)
   r=7.8,6.0,5.1
   a0 = 316.65705808 -0.10518014T +3.09217726 sin M6 + 0.22980637 sin M7
   d0 = 53.50992033 -0.0597909T + 1.83936044 cos M6 + 0.14325320 cos M7
   W = 79.39932954 +285.16188899d - 2.73954829 sin M6 - 0.39968606 sin M7

Obj: 4 # Mars
   r=3396.19,3376.20
   a0= 317.269202 − 0.10927547T + 0.419057 sin M11
   d0= 54.432516 - 0.05827105T + 1.591274 cos M12
   W= 176.049863 + 350.891982443297d + 0.584542 sin M13   # (c) See 2018 Jul 17 comments

Planet: J
  J1=73.32+91472.9T
  J2=24.62+45137.2T
  J3=283.90+4850.7T
  J4=355.80+1191.3T
  J5=119.90+262.1T
  J6=229.80+64.3T
  J7=352.35+2382.6T
  J8=113.35+6070.0T

Obj: 5016 # XVI Metis
   r=30,20,17
   a0=268.05    -0.009T
   d0=64.49   +0.003T
   W=346.09   +1221.2547301d

Obj: 5015 # XV Adrastea
   r=10,8,7
   a0=268.05    -0.009T
   d0=64.49   +0.003T
   W=33.29   +1206.9986602d

Obj: 5005 # V Amalthea
   r=125,73,64
   a0=268.05    -0.009T    -0.84 sin J1   +0.01 sin 2J1
   d0=64.49   +0.003T    -0.36 cos J1
   W=231.67   +722.6314560d   +0.76 sin J1    -0.01 sin 2J1

Obj: 5014 # XIV Thebe
   r=58,49,42
   a0=268.05    -0.009T    -2.11 sin J2   +0.04 sin 2J2
   d0=64.49   +0.003T    -0.91 cos J2   +0.01 cos 2J2
   W=8.56   +533.7004100d   +1.91 sin J2    -0.04 sin 2J2

Obj: 5001 # Io
   r=1829.4,1819.4,1815.7
   a0=268.05 -0.009T +0.094 sin J3 +0.024 sin J4
   d0=64.50 +0.003T +0.040 cos J3 +0.011 cos J4
   W=200.39 +203.4889538d -0.085 sin J3 -0.022 sin J4

Obj: 5002 # Europa
   r=1562.6,1560.3,1559.5
   a0=268.08 -0.009T +1.086 sin J4 +0.060 sin J5 +0.015 sin J6 +0.009 sin J7
   d0=64.51 +0.003T +0.468 cos J4 +0.026 cos J5 +0.007 cos J6 +0.002 cos J7
   W=36.022 +101.3747235d -0.980 sin J4 -0.054 sin J5 -0.014 sin J6 -0.008 sin J7 # (a)

Obj: 5003 # Ganymede
   r=2631.2
   a0=268.20 -0.009T -0.037 sin J4 +0.431 sin J5 +0.091 sin J6
   d0=64.57 +0.003T -0.016 cos J4 +0.186 cos J5 +0.039 cos J6
   W=44.064 +50.3176081d +0.033 sin J4 -0.389 sin J5 -0.082 sin J6

Obj: 5004 # Callisto
   r=2410.3
   a0=268.72 -0.009T -0.068 sin J5 +0.590 sin J6 +0.010 sin J8
   d0=64.83 +0.003T -0.029 cos J5 +0.254 cos J6 -0.004 cos J8
   W=259.51 +21.5710715d +0.061 sin J5 -0.533 sin J6 -0.009 sin J8

Planet: S
  S1=353.32+75706.7T
  S2=28.72+75706.7T
  S3=177.40-36505.5T
  S4=300.00-7225.9T
  S5=316.45+506.2T
  S6=345.20-1016.3T
# S7=29.80-52.1T

Obj: 6018 # XVIII Pan
   r=17.2,15.4,10.4
   a0=40.6   -0.036T
   d0=83.5   -0.004T
   W=48.8   +626.0440000d

Obj: 6015 # XV Atlas
   r=20.5,17.8,9.4
   a0=40.58   -0.036T
   d0=83.53   -0.004T
   W=137.88   +598.3060000d

Obj: 6016 # XVI Prometheus
   r=68.2,41.6,28.2
   a0=40.58   -0.036T
   d0=83.53   -0.004T
   W=296.14   +587.289000d

Obj: 6017 # XVII Pandora
   r=52.2,40.8,31.5
   a0=40.58 -0.036T
   d0=83.53 -0.004T
   W=162.92 +572.7891000d

Obj: 6010 # X Janus
   r=101.7,93.0,76.3
   a0=40.58 -0.036T   -1.623 sin S2   +0.023 sin 2S2
   d0=83.52 -0.004T   -0.183 cos S2   +0.001 cos 2S2
   W=58.83  +518.2359876d   +1.613 sin S2   -0.023 sin 2S2      # (j)

Obj: 6011 # XI Epimetheus
   r=64.9,57.3,53.0
   a0=40.58 -0.036T   -3.153 sin S1   +0.086 sin 2S1
   d0=83.52 -0.004T   -0.356 cos S1   +0.005 cos 2S1
   W=293.87 +518.4907239d   +3.133 sin S1   -0.086 sin 2S1      # (j)

Obj: 6001 # I Mimas
   r=207.8,196.7,190.6
   a0=40.66   -0.036T   +13.56 sin S3
   d0=83.52   -0.004T   -1.53 cos S3
   W=337.46 +381.9945550d -13.48 sin S3   -44.85 sin S5     # (d)

Obj: 6002 # II Enceladus
   r=256.6,251.4,248.3
   a0=40.66   -0.036T
   d0=83.52   -0.004T
   W=2.82   +262.7318996d     # (e)

Obj: 6003 # III Tethys
   r=538.4,428.3,526.3
   a0=40.66   -0.036T   +9.66 sin S4
   d0=83.52   -0.004T   -1.09 cos S4
   W=10.45   +190.6979085d   -9.60 sin S4  +2.23 sin S5    # (f)

Obj: 6013 # XIII Telesto
   r=16.3,11.8,9.8
   a0=50.51   -0.036T
   d0=84.06   -0.004T
   W=56.88   +190.6979332d       # (j)

Obj: 6014 # XIV Calypso
   r=15.3,9.3,6.3
   a0=36.41   -0.036T
   d0=85.04   -0.004T
   W=153.51   +190.69792373d     # (j)

Obj: 6004 # IV Dione
   r=563.4,561.3,559.6
   a0=40.66  -0.036T
   d0=83.52  -0.004T
   W=357.00  +131.5349316d      # (g)

Obj: 6012 # XII Helene
   r=22.5,19.6,13.3
   a0=40.85  -0.036T
   d0=83.34  -0.004T
   W=245.12  +131.6174056d

Obj: 6005 # V Rhea
   r=765,763.1,762.4
   a0=40.38 -0.036T   +3.10 sin S6
   d0=83.55 -0.004T   -0.35 cos S6
   W=235.16 +79.6900478d  -3.08 sin S6     # (h)

Obj: 6006 # VI Titan
   r=2575.15,2574.78,2574.47
   a0=39.4827
   d0=83.4279
   W=186.5855+22.5769768d
# Previous (pre-2009 resolution) version:
#  a0=36.41   -0.036T   +2.66 sin S7
#  d0=83.94   -0.004T   -0.30 cos S7
#  W=189.64   +22.5769768d   -2.64 sin S7

Obj: 6008 # VIII Iapetus
   r=745.7,712.1
   a0=318.16  -3.949T
   d0=75.03   -1.143T
   W=350.20   +4.5379572d        # (i)

Obj: 6009 # IX Phoebe
   r=109.4,108.5,101.8
   a0=356.90
   d0=77.80
   W=178.58   +931.639d

Planet: U
  U1=115.75+54991.87T
  U2=141.69+41887.66T
  U3=135.03+29927.35T
  U4=61.77+25733.59T
  U5=249.32+24471.46T
  U6=43.86+22278.41T
  U7=77.66+20289.42T
  U8=157.36+16652.76T
  U9=101.81+12872.63T
  U10=138.64+8061.81T
  U11=102.23-2024.22T
  U12=316.41+2863.96T
  U13=304.01-51.94T
  U14=308.71-93.17T
  U15=340.82-75.32T
  U16=259.14-504.81T

Obj: 7006   # VI Cordelia
   r=13
   a0=257.31  -0.15 sin U1
   d0=-15.18  +0.14 cos U1
   W=127.69   -1074.5205730d   -0.04 sin U1

Obj: 7007 # VII Ophelia
   r=15
   a0=257.31  -0.09 sin U2
   d0=-15.18  +0.09 cos U2
   W=130.35   -956.4068150d   -0.03 sin U2

Obj: 7008  # VIII Bianca
   r=21
   a0=257.31  -0.16 sin U3
   d0=-15.18  +0.16 cos U3
   W=105.46   -828.3914760d   -0.04 sin U3

Obj: 7009 # IX Cressida
   r=31
   a0=257.31  -0.04 sin U4
   d0=-15.18  +0.04 cos U4
   W=59.16   -776.5816320d   -0.01 sin U4

Obj: 7010 # X Desdemona
   r=27
   a0=257.31  -0.17 sin U5
   d0=-15.18  +0.16 cos U5
   W=95.08   -760.0531690d   -0.04 sin U5

Obj: 7011 # XI Juliet
   r=42
   a0=257.31  -0.06 sin U6
   d0=-15.18  +0.06 cos U6
   W=302.56   -730.1253660d   -0.02 sin U6

Obj: 7012 # XII Portia
   r=54
   a0=257.31  -0.09 sin U7
   d0=-15.18  +0.09 cos U7
   W=25.03   -701.4865870d   -0.02 sin U7

Obj: 7013 # XIII Rosalind
   r=27
   a0=257.31  -0.29 sin U8
   d0=-15.18  +0.28 cos U8
   W=314.90   -644.6311260d   -0.08 sin U8

Obj: 7014 # XIV Belinda
   r=33
   a0=257.31  -0.03 sin U9
   d0=-15.18  +0.03 cos U9
   W=297.46   -577.3628170d   -0.01 sin U9

Obj: 7015 # XV Puck
   r=77
   a0=257.31  -0.33 sin U10
   d0=-15.18  +0.31 cos U10
   W=91.24   -472.5450690d   -0.09 sin U10

Obj: 7001 # I Ariel
   r=581.1,577.9,577.7
   a0=257.43  +0.29 sin U13
   d0=-15.10  +0.28 cos U13
   W=156.22   -142.8356681d   +0.05 sin U12   +0.08 sin U13

Obj: 7002 # II Umbriel
   r=584.7
   a0=257.43  +0.21 sin U14
   d0=-15.10  +0.20 cos U14
   W=108.05   -86.8688923d   -0.09 sin U12   +0.06 sin U14

Obj: 7003 # III Titania
   r=788.9
   a0=257.43  +0.29 sin U15
   d0=-15.10  +0.28 cos U15
   W=77.74   -41.3514316d   +0.08 sin U15

Obj: 7004 # IV Oberon
   r=761.4
   a0=257.43 +0.16 sin U16
   d0=-15.10 +0.16 cos U16
   W=6.77 -26.7394932d +0.04 sin U16

Obj: 7005 # V Miranda
   r=240.4,234.2,232.9
   a0=257.43 +4.41 sin U11 -0.04 sin 2U11
   d0=-15.08 +4.25 cos U11 -0.02 cos 2U11
   W=30.70 -254.6906892d -1.27 sin U12 +0.15 sin 2U12 +1.15 sin U11 -0.09 sin 2U11

Planet: N
  N0=357.85+52.316T
  N1=323.92+62606.6T
  N2=220.51+55064.2T
  N3=354.27+46564.5T
  N4=75.31+26109.4T
  N5=35.36+14325.4T
  N6=142.61+2824.6T
  N7=177.85+52.316T

Obj: 8 # Neptune
   r=24764,24341
   a0= 299.36+0.70 sin N0
   d0= 43.46-0.51 cos N0
   W= 249.978 + 541.1397757d -0.48 sin N0   # (d) (2018 Jul 17)

Obj: 8003 # III Naiad
   r=29
   a0=299.36 +0.70 sin N0 -6.49 sin N1 +0.25 sin 2N1
   d0=43.36 -0.51 cos N0 -4.75 cos 2N1 +0.09 cos 2N1
   W=254.06 +1222.8441209d -0.48 sin N0 +4.40 sin N1 -0.27 sin 2N1

Obj: 8004 # IV Thalassa
   r=40
   a0=299.36 +0.70 sin N0 -0.28 sin N2
   d0=43.45 -0.51 cos N0 -0.21 cos N2
   W=102.06 +1155.7555612d -0.48 sin N0 +0.19 sin N2

Obj: 8005 # V Despina
   r=74
   a0=299.36 +0.70 sin N0 -0.09 sin N3
   d0=43.45 -0.51 cos N0 -0.07 cos N3
   W=306.51 +1075.7341562d -0.49 sin N0 +0.06 sin N3

Obj: 8006 # VI Galatea
   r=79
   a0=299.36 +0.70 sin N0 -0.07 sin N4
   d0=43.43 -0.51 cos N0 -0.05 cos N4
   W=258.09 +839.6597686d -0.48 sin N0 +0.05 sin N4

Obj: 8007 # VII Larissa
   r=96
   a0=299.36 +0.70 sin N0 -0.27 sin N5
   d0=43.41 -0.51 cos N0 -0.20 cos N5
   W=179.41 +649.0534470d -0.48 sin N0 +0.19 sin N5

Obj: 8008 # VIII Proteus
   r=208
   a0=299.27 +0.70 sin N0 -0.05 sin N6
   d0=42.91 -0.51 cos N0 -0.04 cos N6
   W=93.38 +320.7654228d -0.48 sin N0 +0.04 sin N6

Obj: 8001 # I Triton
   r=1352.6
   a0=299.36 -32.35 sin N7 -6.28 sin 2N7 -2.08 sin 3N7 -0.74 sin 4N7 -0.28 sin 5N7 -0.11 sin 6N7 -0.07 sin 7N7 -0.02 sin 8N7 -0.01 sin 9N7
   d0=41.17 +22.55 cos N7 +2.10 cos 2N7 +0.55 cos 3N7 +0.16 cos 4N7 +0.05 cos 5N7 +0.02 cos 6N7 +0.01 cos 7N7
   W=296.53 -61.2572637d +22.25 sin N7 +6.73 sin 2N7 +2.05 sin 3N7 +0.74 sin 4N7 +0.28 sin 5N7 +0.11 sin 6N7 +0.05 sin 7N7 +0.02 sin 8N7 +0.01 sin 9N7

Planet: P

Obj: 9001 # Charon/Pluto I
   r=606.0
   a0= 132.993
   d0= -6.163
   W=122.695 +56.3625225d

Obj: 9002 # Nix/Pluto II = S/2005 P 2      (n)
   r=48.7,33.2,31.1
   a0= 132.993
   d0= -6.163
   W=272.24 +14.483934d

Obj: 9003 # Hydra/Pluto III = S/2005 P 1   (n)
   r=50.9,36.1,30.9
   a0= 132.993
   d0= -6.163
   W=57.19 +9.422837d

Obj: 9004 # Kerberos/Pluto IV = S/2011 (134340) 1 (n)
   r=19,10,9
   a0= 132.993
   d0= -6.163
   W=90.19 +11.1913026d

Obj: 9005 # Styx/Pluto V = S/2012 (134340) 1      (n)
   r=16,9,8
   a0= 132.993
   d0= -6.163
   W=11.7 +17.8551357d

Obj: -1      # Ceres  (r), (t)
   r=487.3,487.3,446
   a0=291.42763
   d0=66.76033
   W=170.309 +952.1532635d

Obj: -2     # Pallas
   r=568,532,448
   a0= 33
   d0= -3
   W= 38 + 1105.8036d

Obj: -4     # Vesta
   r=289,280,229
   a=309.031   # +/- 0.01   (p)
   d=42.235    # +/- 0.01
   W=285.39+1617.3329428d

Obj: -21     # Lutetia
   r=62.0,50.5,46.5
   a0=52   # +/- 5
   d0=12   # +/- 5
   W=94 + 1057.7515d

Obj: -52      # Europa
   r=379,330,249
   a0=257
   d0=12   # no uncertainties given
   W=55 + 1534.6472187d

Obj: -243     # Ida
   r=26.8,12.0,7.6
   a0=168.76
   d0=-87.12
   W=274.05 + 1864.6280070d  (2018 Jul 17)

Obj: -433    # Eros
   r=17.0,5.5,5.5
   a0=11.35    # +/- 0.02
   d0=17.22    # +/- 0.02
   W=326.07+1639.38864745d

Obj: -511    # Davida
   r=180,147,127
   a0=297
   d0=5
   W=268.1 +1684.4193549d

Obj: -951    # (951) Gaspra
   r=9.1,5.2,4.4
   a0 = 9.47
   d0 = 26.70
   W = 83.67 + 1226.9114850d

Obj: -2867   # (2867) Šteins
   r=3.24,2.73,2.04
   a0 = 90
   d0 =-62
   W = 93.94 + 1428.852332d

Obj: -25143  # (25143) Itokawa
   r=0.268,0.147,0.104
   a0 = 90.53
   d0 =-66.30
   W = 0+ 712.143d      # No central meridian defined yet

END      (This is the for-real end!  Everything after this is a comment.)

(a) The 182 meridian is defined by the crater Cilix.
(b) The 128 meridian is defined by the crater Anat.
(c) The 326 meridian is defined by the crater Saga.
(d) The 162 meridian is defined by the crater Palomides.
(e) The 5 meridian is defined by the crater Salih.
(f) The 299 meridian is defined by the crater Arete.
(g) The 63 meridian is defined by the crater Palinurus.
(h) The 340 meridian is defined by the crater Tore.
(i) The 276 meridian is defined by the crater Almeric.
(j) These equations are correct for the period of the Voyager encounters.
   Because of precession they may not be accurate at other time periods.
(k) "System II" for Venus is a proposed system for tracking clouds.
   See 8 Jan 2008 comments below.
(l) Mercury updated from this comment at
http://ssd.jpl.nasa.gov/?horizons_news :

Feb 07, 2008:
    -- The Mercury rotation model was updated based on radar observations
        reported by Margot et al., Science 316, 2007, and a 2007-Dec-2 memo:

         alpha-0 (RA J2000) = 281.0097 -0.0328T
         delta-0 (DEC J200) = 61.4143 - 0.0049T
                          W = 329.548 + 6.1385025d

       ... where T is time in Julian centuries (36525 days) from J2000 epoch,
       and d is interval in days (86400 SI seconds) from J2000 epoch, with the
       J2000 epoch being JD 2451545.0 Coordinate Time (2000-Jan-1.5)

(m) COSPAR data for the earth is provided for reference only.  At least in
  my code,  the earth's orientation is actually computed using the IAU
  precession and nutation models (see 'precess.cpp').  WGCCRE dropped this
  model in their 2015 report.
(n) As far as I know,  there is no "official" rotation model for Nix and
   Hydra.  I took the polar axis for Pluto and Charon,  then came up with
   values for the constant and linear term in W that produced near-zero
   longitudes facing Pluto over the 2000-2020 period (the time span for
   which I have Nix and Hydra ephemerides).
      Once the COSPAR folks come up with official values,  I expect they
   will be close to (but not exactly equal to) the results I've given.
   Note: on 2015 May 12,  I added similarly "unofficial" rotation models
   for Pluto IV = Kerberos and Pluto V = Styx.
(o) (2013 May 17) Mercury updated to IAU 2009 version,  with trig terms.
(p) (2013 Nov 26) Updated Vesta to use Dawn-based spin axis.  The COSPAR
   axes,  which as you can see have much higher sigmas,  are :
   a=305.8    # +/- 3.1
   d=41.4     # +/- 1.5
   Note that W is unchanged here,  though I'm sure Dawn got a better
   rotation period and fiddled with the zero point a little.
(q) (2015 May 6) Follow-up to the above:  Dawn _did_ get a better rotation
   period and offset.  I modified Vesta's W to use the value from
   http://astropedia.astrogeology.usgs.gov/download/Docs/WGCCRE/IAU-WGCCRE-Coordinate-System-for-Vesta.pdf
   (pole RA/dec didn't change).
(r) (2016 Oct 2) Updated Ceres to use Dawn measurements from
   https://naif.jpl.nasa.gov/pub/naif/DAWN/kernels/pck/dawn_ceres_v05.tpc
(s) (2018 Mar 26) Updated Phobos & Deimos to use
   ftp://ssd.jpl.nasa.gov/pub/eph/satellites/orientation/iom.392R-17-004.pdf
   This has a small effect on Deimos and a larger one on Phobos,  partly
   because the sign for the sin(M1) term was reversed.
(t) Ceres now uses v06 from Dawn.  See 2020 Oct 19 "news item" at
   https://ssd.jpl.nasa.gov/?horizons_news .

Satellites for which no suitable data are yet available have been omitted
from this table. Nereid is not included in this table because it is not in
synchronous rotation.

Errata to the published version:

In Table 2, Page 87, of the 2000 report (Seidelmann, et al., 2002): For the
Moon, for "0.1204 E2", read "0.1204 sin E2".

DESCRIPTION OF THIS FILE

   Comments can be added freely within the file.  However,  if you put
them after the actual data,  the code doesn't have to dig through all
this text.  That speeds things up very slightly.

   The file is processed by 'cospar.cpp',  which should give insight as
to what's going on here.

   Some of my software used a numbering system in which sun=0,  Mer-Plu
=1...9,  Moon=10,  Io...Callisto=11..14,  and so on,  with the numbering
reflecting the order in which objects were added.  Now,  I (mostly) use
the JPL/IAU scheme,  in which numbered satellites have four digits,  the
first specifying the planet,  the remaining three the object number.  So
5014 = Jupiter XIV,  803 = Neptune III.  For backward compatibility,  a
"remap" table is given at the top;  some of my software uses this to
convert the old numbers to the JPL/IAU style.

   All lines are considered comments until a line starting with 'Planet'
or 'Obj' is encountered.  After a 'Planet' line,  the code starts looking
for angular coefficients;  after an 'Obj' line,  it starts to look for
lines describing a0, d0, and W.  Data are from

http://astrogeology.usgs.gov/Projects/WGCCRE/

   with corrections/updates as described below.  Asteroid rotation data is
given at the above sites,  too,  but that will have to wait for another day.

   (8 Jan 2008) Added the proposed coordinate system for cloud observations of
Venus made in UV.  This system has a rotational period of exactly 4.2 days,
and coincides with the "usual" system at J2000. Nothing official yet, and it
means several changes will eventually be needed in Guide:  to display both
systems in 'more info',  to ensure that features and radar-based bitmaps are
shown in System I while clouds are shown in System II,  and probably more.

   (8 Feb 2008) Altered Mercury rotation _very_ slightly,  as described
at comment (l) above.

   (29 Jan 2010) Added data for Nix and Hydra.  See comment (n) above.

   (2 Feb 2010) Revised the Sun,  Jupiter, Pluto,  Charon,  and Phoebe in
accordance with the 'report of the IAU/IAG Working Group on cartographic
coordinates and rotational elements: 2006' (Celestial Mech Dyn Astr (2007)
98:155-180.)  Also revised a0 and d0 for Nix and Hydra to match the new
Pluto/Charon values.

   The 2006 report modified Jupiter's pole position,  both constant and
linear terms,  and also has some periodic terms.  They don't add up
to more than .003 degree,  so for the nonce,  I've not added them:

a0 += .000117 sin Ja + .000938 sin Jb + .001432 sin Jc + .000030 sin Jd
         + .002150 sin Je
d0 += .000050 cos Ja + .000404 cos Jb + .000617 cos Jc - .000013 sin Jd
         + .000926 cos Je

   where Ja = 99.360714 + .4850.4046T, Jb = 175.895369 + 1191.9605T,
         Jc = 300.323162 + 252.5475T, Jd = 114.012305 + 6070.2476T,
         Je = 49.511251 + 64.3000T

   Note,  though,  that these _could_ be added in the same manner in which
periodic terms have been added for Neptune.

   (23 May 2011) After comments from Jean-Claude Pelle,  cleaned up some
spurious text that didn't interfere with my code,  but _would_ confuse
other code and really shouldn't have been there.  Un-commented data for
five Saturnian satellites Helene,  Calypso,  Telesto,  Epimetheus, Janus.

   Also,  I had some hard-wired code that allowed for multiple systems
("system II and III") longitudes only for Jupiter and Saturn.  This is now
fixed in 'cospar.cpp',  and requires that the 'W=' line _must_ follow the
'W2=' and 'W3=' lines.  (The idea is that if you ask for a system II result
for an object that has no W2 line,  the code will eventually trickle down
to the W= line and use that instead.)

   Also switched from Guide's semi-random numbering of objects to the JPL
one,  wherein numbered satellites have four digits:  one giving the planet,
the remaining three the IAU numbering.  (With remapping given at the top so
that the "old" Guide-style numbering can be used.)

   (2013 May 17) Modified Mercury to use the IAU 2009 model,  complete with
rotation terms;  Titan to use IAU 2009,  i.e.,  no more trig terms.

   (2013 Jul 13) Added COSPAR 2009 data for minor/"dwarf" planets from

http://astropedia.astrogeology.usgs.gov/download/Docs/WGCCRE/WGCCRE2009reprint.pdf

   (2013 Aug 26) Because Pluto is now a "dwarf planet",  the poles of it
and its satellites are flipped and W increases with time rather than
decreasing.  I should have made those changes when switching to the 2009
rotation models,  but failed to do so.  This is now corrected (including
for Hydra and Nix,  which have unofficial models as described above...
and so do Kerberos and Styx,  as of 2015 May.)  See the 2011 erratum to
the COSPAR 2009 data at

http://astropedia.astrogeology.usgs.gov/download/Docs/WGCCRE/WGCCRE-Erratum-2011reprint.pdf

for details.

   (2015 Nov 17) The 2009 WGCCRE report mentions that the change in the
System III rotation rate,  to 870.5366420 degrees/day,  had some problems.
Further determinations didn't quite match up with it,  and they decided to
go back to the old value of 870.536 degrees/day.  That change has now been
made in this file.  Also found that some of the trig terms for Mercury were
botched (used 'M' instead of 'H'),  resulting in not getting any value at all.

   (2018 Jul 17) Corrections based on the WGCCRE 2015 report,  at

https://astrogeology.usgs.gov/search/map/Docs/WGCCRE/WGCCRE2015reprint

   Mercury's rotation has the same general form as before,  but various
coefficients have changed.  I caught and corrected a spurious extra term in
W that caused a sub-arcsecond error.

   Mars now includes five trig terms for the pole position and
six for W.  One term for each has considerable amplitude;  the others are
below an arcsecond and are omitted here.  Small changes made for Phobos and
Deimos have been incorporated,  again with some lesser terms dropped. The
quadratic bit for M5 is dropped,  mostly because I've no straightforward
way of including it anyway (and it's small).

   W for Neptune has changed,  with the rotation rate increasing from 536.3128
degrees/day to 541.1397757 degrees/day,  based on observations of two unusually
stable features : https://doi.org/10.1016/j.icarus.2011.05.013

   (243) Ida was far off in previous WGCCRE reports (dec for pole off by 90
degrees!).  It should now be correct.

   WGCCRE has dropped orientation models for the earth and moon.  I've not
used the former for some time (the IAU precession/nutation model is much more
accurate).  I do still use the latter in situations where the accurate
alternative (orientations from DE-4xx) would be overkill.

   (2022 Feb 02) Added some planetary radii,  for future use.
   (2022 Oct 06) Added still more planetary radii.

   (2023 Jan 24) Two corrections for the equation for W for Phobos,  from
_Celestial Mechanics & Dynamical Astronomy_, 131, 12.

   https://rdcu.be/b32WL     doi: 10.1007/s10569-019-9925-1
