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IAU/IAG Working Group (WG) on Cartographic Coordinates and Rotational Elements

Rotation and pole position for planetary satellites

Corrected for known errata as of 2006 February 17. See list following the Table.

Tables: I - II - III - IV - V - VI
TABLE II
Recommended values for the direction of the north pole of rotation and the prime meridian of the satellites (2000)
α0, δ0, T and d have the same meanings as in Table I (epoch 2000 January 1.5, i.e., JD 2451545.0 TCB).
Earth   Moon α0=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
    δ0=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 -1.4 x 10-12d2 +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
  where 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
Mars I Phobos α0=317.68 -0.108T +1.79 sin M1
    δ0=52.90 -0.061T -1.08 cos M1
    W=35.06 +1128.8445850d +8.864T2
    -1.42 sin M1 -0.78 sin M2
  II Deimos α0=316.65 -0.108T +2.98 sin M3
    δ0=53.52 -0.061T -1.78 cos M3
    W=79.41 +285.1618970d -0.520T2
    -2.58 sin M3 +0.19 cos M3
  where M1=169°.51-0°.4357640d, M2=192°.93+1128°.4096700d+8°.864T2, M3=53°.47-0°.0181510d
Jupiter XVI Metis α0=268.05 -0.009T
    δ0=64.49 +0.003T
    W=346.09 +1221.2547301d
  XV Adrastea α0=268.05 -0.009T
    δ0=64.49 +0.003T
    W=33.29 +1206.9986602d
  V Amalthea α0=268.05 -0.009T -0.84 sin J1 +0.01 sin 2J1
    δ0=64.49 +0.003T -0.36 cos J1
    W=231.67 +722.6314560d +0.76 sin J1 -0.01 sin 2J1
  XIV Thebe α0=268.05 -0.009T -2.11 sin J2 +0.04 sin 2J2
    δ0=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
  I Io α0=268.05 -0.009T +0.094 sin J3 +0.024 sin J4
    δ0=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
  II Europa α0=268.08 -0.009T +1.086 sin J4 +0.060 sin J5
    +0.015 sin J6 +0.009 sin J7
    δ0=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)
  III Ganymede α0=268.20 -0.009T -0.037 sin J4 +0.431 sin J5
    +0.091 sin J6
    δ0=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 (b)
    -0.082 sin J6
  IV Callisto α0=268.72 -0.009T -0.068 sin J5 +0.590 sin J6
    +0.010 sin J8
    δ0=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 (c)
    -0.009 sin J8
  where 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
Saturn XVIII Pan α0=40.6 -0.036T
    δ0=83.5 -0.004T
    W=48.8 +626.0440000d
  XV Atlas α0=40.58 -0.036T
    δ0=83.53 -0.004T
    W=137.88 +598.3060000d
  XVI Prometheus α0=40.58 -0.036T
    δ0=83.53 -0.004T
    W=296.14 +587.289000d
  XVII Pandora α0=40.58 -0.036T
    δ0=83.53 -0.004T
    W=162.92 +572.7891000d
  XI Epimetheus α0=40.58 -0.036T -3.153 sin S1 +0.086 sin 2S1
    δ0=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)
  X Janus α0=40.58 -0.036T -1.623 sin S2 +0.023 sin 2S2
    δ0=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)
  I Mimas α0=40.66 -0.036T +13.56 sin S3
    δ0=83.52 -0.004T -1.53 cos S3
    W=337.46 +381.9945550d -13.48 sin S3 -44.85 sin S5 (d)
  II Enceladus α0=40.66 -0.036T
    δ0=83.52 -0.004T
    W=2.82 +262.7318996d (e)
  III Tethys α0=40.66 -0.036T +9.66 sin S4
    δ0=83.52 -0.004T -1.09 cos S4
    W=10.45 +190.6979085d -9.60 sin S4 2.23 sin S5 (f)
  XIII Telesto α0=50.51 -0.036T
    δ0=84.06 -0.004T
    W=56.88 +190.6979332d (j)
  XIV Calypso α0=36.41 -0.036T
    δ0=85.04 -0.004T
    W=153.51 +190.6742373d (j)
  IV Dione α0=40.66 -0.036T
    δ0=83.52 -0.004T
    W=357.00 +131.5349316d (g)
  XII Helene α0=40.85 -0.036T
    δ0=83.34 -0.004T
    W=245.12 +131.6174056d
  V Rhea α0=40.38 -0.036T +3.10 sin S6
    δ0=83.55 -0.004T -0.35 cos S6
    W=235.16 +79.6900478d -3.08 sin S6 (h)
  VI Titan α0=36.41 -0.036T +2.66 sin S7
    δ0=83.94 -0.004T -0.30 cos S7
    W=189.64 +22.5769768d -2.64 sin S7
  VIII Iapetus α0=318.16 -3.949T
    δ0=75.03 -1.143T
    W=350.20 +4.5379572d (i)
  IX Phoebe α0=355.00
    δ0=68.70
    W=304.70 +930.8338720d
  where 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
Uranus VI Cordelia α0=257.31 -0.15 sin U1
    δ0=-15.18 +0.14 cos U1
    W=127.69 -1074.5205730d -0.04 sin U1
  VII Ophelia α0=257.31 -0.09 sin U2
    δ0=-15.18 +0.09 cos U2
    W=130.35 -956.4068150d -0.03 sin U2
  VIII Bianca α0=257.31 -0.16 sin U3
    δ0=-15.18 +0.16 cos U3
    W=105.46 -828.3914760d -0.04 sin U3
  IX Cressida α0=257.31 -0.04 sin U4
    δ0=-15.18 +0.04 cos U4
    W=59.16 -776.5816320d -0.01 sin U4
  X Desdemona α0=257.31 -0.17 sin U5
    δ0=-15.18 +0.16 cos U5
    W=95.08 -760.0531690d -0.04 sin U5
  XI Juliet α0=257.31 -0.06 sin U6
    δ0=-15.18 +0.06 cos U6
    W=302.56 -730.1253660d -0.02 sin U6
  XII Portia α0=257.31 -0.09 sin U7
    δ0=-15.18 +0.09 cos U7
    W=25.03 -701.4865870d -0.02 sin U7
  XIII Rosalind α0=257.31 -0.29 sin U8
    δ0=-15.18 +0.28 cos U8
    W=314.90 -644.6311260d -0.08 sin U8
  XIV Belinda α0=257.31 -0.03 sin U9
    δ0=-15.18 +0.03 cos U9
    W=297.46 -577.3628170d -0.01 sin U9
  XV Puck α0=257.31 -0.33 sin U10
    δ0=-15.18 +0.31 cos U10
    W=91.24 -472.5450690d -0.09 sin U10
  V Miranda α0=257.43 +4.41 sin U11 -0.04 sin 2U11
    δ0=-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
  I Ariel α0=257.43 +0.29 sin U13
    δ0=-15.10 +0.28 cos U13
    W=156.22 -142.8356681d +0.05 sin U12 0.08 sin U13
  II Umbriel α0=257.43 +0.21 sin U14
    δ0=-15.10 +0.20 cos U14
    W=108.05 -86.8688923d -0.09 sin U12 +0.06 sin U14
  III Titania α0=257.43 +0.29 sin U15
    δ0=-15.10 +0.28 cos U15
    W=77.74 -41.3514316d +0.08 sin U15
  IV Oberon α0=257.43 +0.16 sin U16
    δ0=-15.10 +0.16 cos U16
    W=6.77 -26.7394932d +0.04 sin U16
  where 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
Neptune III Naiad α0=299.36 +0.70 sin N -6.49 sin N1 +0.25 sin 2N1
    δ0=43.36 -0.51 cos N -4.75 cos 2N1 +0.09 cos 2N1
    W=254.06 +1222.8441209d -0.48 sin N +4.40 sin N1 -0.27 sin 2N1
  IV Thalassa α0=299.36 +0.70 sin N -0.28 sin N2
    δ0=43.45 -0.51 cos N -0.21 cos N2
    W=102.06 +1155.7555612d -0.48 sin N +0.19 sin N2
  V Despina α0=299.36 +0.70 sin N -0.09 sin N3
    δ0=43.45 -0.51 cos N -0.07 cos N3
    W=306.51 +1075.7341562d -0.49 sin N +0.06 sin N3
  VI Galatea α0=299.36 +0.70 sin N -0.07 sin N4
    δ0=43.43 -0.51 cos N -0.05 cos N4
    W=258.09 +839.6597686d -0.48 sin N +0.05 sin N4
  VII Larissa α0=299.36 +0.70 sin N -0.27 sin N5
    δ0=43.41 -0.51 cos N -0.20 cos N5
    W=179.41 +649.0534470d -0.48 sin N +0.19 sin N5
  VIII Proteus α0=299.27 +0.70 sin N -0.05 sin N6
    δ0=42.91 -0.51 cos N -0.04 cos N6
    W=93.38 +320.7654228d -0.48 sin N +0.04 sin N6
  I Triton α0=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
    δ0=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
  where N=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
Pluto I Charon α0=313.02
    δ0=9.09
    W=56.77 -56.3623195d
(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.
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".