# 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  6010 173 6011 174 6012 175
Remap: 6013 176 6014 177 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

Planet: p

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

Obj: 1 # Mercury
   a0=281.0097-0.0328T
   d0= 61.4143-0.0049T
   W=329.548+6.1385025d   # (a) (l)

Obj: 2 # Venus
   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
   a0= 0.00-0.641T
   d0= 90.00-0.557T
   W= 190.147+360.9856235d

Obj: 4 # Mars
   a0= 317.68143-0.1061T
   d0= 52.88650-0.0609T
   W= 176.630+350.89198226d   # (c)

Obj: 5 # Jupiter
   a0= 268.056595-.006499T
   d0= 64.495303+.002413T
   W2=  43.3+870.270d        #     (System II)
   W3= 284.95+870.5366420d   # (d) (System III)
   W=  67.1+877.900d         #     (System I)

Obj: 6 # Saturn
   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
   a0= 257.311
   d0=-15.175
   W= 203.81-501.1600928d    # (d)

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

Obj: 9 # Pluto
   a0= 312.993
   d0= 6.163
   W= 237.305-56.3625225d   # (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: 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
   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=169.51-0.4357640d
  M2=192.93+1128.4096700d+8.864T2
  M3=53.47-0.0181510d

Obj: 4001 # Phobos
   a0=317.68 -0.108T +1.79 sin M1
   d0=52.90  -0.061T -1.08 cos M1
   W=35.06 +1128.8445850d   +8.864T2 -1.42 sin M1    -0.78 sin M2

Obj: 4002 # Deimos
   a0=316.65 -0.108T   +2.98 sin M3
   d0=53.52 -0.061T    -1.78 cos M3
   W=79.41 +285.1618970d -0.520T2 -2.58 sin M3   +0.19 cos M3

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
   a0=268.05    -0.009T
   d0=64.49   +0.003T
   W=346.09   +1221.2547301d

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

Obj: 5005 # V Amalthea
   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
   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
   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
   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
   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
   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
   a0=40.6   -0.036T
   d0=83.5   -0.004T
   W=48.8   +626.0440000d

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

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

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

Obj: 6010 # X Janus
   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
   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
   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
   a0=40.66   -0.036T
   d0=83.52   -0.004T
   W=2.82   +262.7318996d     # (e)

Obj: 6003 # III Tethys
   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
   a0=50.51   -0.036T
   d0=84.06   -0.004T
   W=56.88   +190.6979332d       # (j)

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

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

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

Obj: 6005 # V Rhea
   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
   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
   a0=318.16  -3.949T
   d0=75.03   -1.143T
   W=350.20   +4.5379572d        # (i)

Obj: 6009 # IX Phoebe
   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
   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
   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
   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
   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
   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
   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
   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
   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
   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
   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
   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
   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
   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
   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
   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
   a0= 299.36+0.70 sin N0
   d0= 43.46-0.51 cos N0
   W= 253.18+536.3128492d -0.48 sin N0   # (d)

Obj: 8003 # III Naiad
   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
   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
   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
   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
   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
   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
   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
   a0=312.993
   d0=6.163
   W=57.305 -56.3625225d

Obj: 9003 # Hydra/Pluto III   (n)
   a0=312.993
   d0=6.163
   W=126.81 -9.422837d

Obj: 9002 # Nix/Pluto II      (n)
   a0=312.993
   d0=6.163
   W=267.76 -14.483934d

Obj: -1
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').
(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.

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.)
