Description of this file is at bottom
Included: p 0 1 2 3 4 5 6 7 9
(Neptune is under 'N'; it has trig terms, which the other major planets lack)
Included: E 10
Included: M 28 29
Included: J 47 48 49 50 11 12 13 14
Included: S 51 52 53 54 15 16 17 18 19 20 22 40
Included: U 23 24 25 26 27 55 56 57 58 59 60 61 62 63 64 23 24 25 26 27
Included: N 8 71 70 68 69 67 66 30
Included: P 31 108 109
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) retrograde
a0= 272.76
d0= 67.16
W=160.20-1.4813688d (b)
W2=160.20-85.7142857d (k)
Obj: 3 (Earth.. for reference only; see comment (m))
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
W= 67.1+877.900d (System I)
W2= 43.3+870.270d (System II)
W3= 284.95+870.5366420d (d) (System III)
Obj: 6 (Saturn)
a0= 40.589-0.036T
d0= 83.537-0.004T
W= 227.90+844.3d (System I)
W2= 104.90+812d (System II)
W3= 38.90+810.7939024d (d) (System III)
Obj: 7 (Uranus) retrograde
a0= 257.311
d0=-15.175
W= 203.81-501.1600928d (d)
(See Neptune under 'N'; it has trig terms)
Obj: 9 (Pluto) retrograde
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: 10 (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: 28 (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: 29 (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: 50 (Metis)
XVI Metis a0=268.05 -0.009T
d0=64.49 +0.003T
W=346.09 +1221.2547301d
Obj: 49 (Adrastea)
XV Adrastea a0=268.05 -0.009T
d0=64.49 +0.003T
W=33.29 +1206.9986602d
Obj: 47 (Amalthea)
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: 48 (Thebe)
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: 11 (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: 12 (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: 13 (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: 14 (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: 54 (Pan)
Saturn XVIII Pan a0=40.6 -0.036T
d0=83.5 -0.004T
W=48.8 +626.0440000d
Obj: 51 (Atlas)
XV Atlas a0=40.58 -0.036T
d0=83.53 -0.004T
W=137.88 +598.3060000d
Obj: 52 (Prometheus)
XVI Prometheus a0=40.58 -0.036T
d0=83.53 -0.004T
W=296.14 +587.289000d
Obj: 53 (Pandora)
XVII Pandora a0=40.58 -0.036T
d0=83.53 -0.004T
W=162.92 +572.7891000d
# Obj: ...no code for Epimetheus or Janus yet
# 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)
# 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: 15 (Mimas)
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: 16 (enceladus)
II Enceladus a0=40.66 -0.036T
d0=83.52 -0.004T
W=2.82 +262.7318996d (e)
Obj: 17 (tethys)
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: ...Telesto and Calypso have no codes yet
# XIII Telesto a0=50.51 -0.036T
# d0=84.06 -0.004T
# W=56.88 +190.6979332d (j)
# XIV Calypso a0=36.41 -0.036T
# d0=85.04 -0.004T
# W=153.51 +190.69792373d (j)
Obj: 18 (dione)
IV Dione a0=40.66 -0.036T
d0=83.52 -0.004T
W=357.00 +131.5349316d (g)
#Obj: ... Helene has no code yet
# XII Helene a0=40.85 -0.036T
# d0=83.34 -0.004T
# W=245.12 +131.6174056d
Obj: 19 (rhea)
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: 20 (Titan)
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: 22 (Iapetus)
VIII Iapetus a0=318.16 -3.949T
d0=75.03 -1.143T
W=350.20 +4.5379572d (i)
Obj: 40 (Phoebe)
IX Phoebe a0=356.90
d0=77.80
W=178.58 +931.639d
Planet: U
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
Obj: 55 (Cordelia) retrograde
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: 56 (Ophelia) retrograde
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: 57 (Bianca) retrograde
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: 58 (Cressida) retrograde
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: 59 (Desdemona) retrograde
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: 60 (Juliet) retrograde
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: 61 (Portia) retrograde
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: 62 (Rosalind) retrograde
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: 63 (Belinda) retrograde
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: 64 (Puck) retrograde
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: 23 (Ariel) retrograde
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: 24 (Umbriel) retrograde
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: 25 (Titania) retrograde
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: 26 (Oberon) retrograde
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: 27 (Miranda) retrograde
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: 71 (Naiad)
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: 70 (Thalassa)
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: 68 (Despina)
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: 69 (Galatea)
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: 67 (Larissa)
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: 66 (Proteus)
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: 30 (Triton) retrograde
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: 31 (Charon) retrograde
a0= 312.993
d0= 6.163
W= 237.305-56.3625225d (e)
Pluto I Charon a0=312.993
d0=6.163
W=57.305 -56.3625225d
Obj: 108 (Hydra/Pluto III) retrograde (n)
Pluto I Hydra a0=312.993
d0=6.163
W=126.81 -9.422837d
Obj: 109 (Nix/Pluto III) retrograde (n)
Pluto I Nix 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
8 Feb 2008 version
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.
At some point, the 'Included' lines will be used to do quick error
checking and can help the code skip ahead to get the right data for an
object. Right now, though, it's ignored.
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/
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.
For the nonce, one can edit this file and in the Venus section,
change "W" to "W2" and "W2" to "W". Right now, Guide is ignoring the
W2 line; if you make this change, it'll show everything with System
II longitudes. The planet will appear to rotate once every 4.2 days.
(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