Geoscience Reference
In-Depth Information
Tabl e 9. 3
All numbers of satellite data used in the article
Mean density
(g/cm
3
)
Orbital period
(days)
10
21
10
7
)
Mass (
kg)
Distance (
10.6 10
6
Mars
Phobos
0.99378
1.9
0.31891
S
2.4 10
6
Deimos
2.3459
1.75
1.26244
S
Jupiter
Io
89.32
42.16
3.53
1.769
S
Europa
48.0
67.06
3.01
3.551
S
Ganymede
148.19
107.04
1.94
7.154
S
Callisto
107.59
188.27
1.83
16.689
S
Saturn
Mimas
0.0379
18.552
1.15
0.942
S
Enceladus
0.108
23.802
1.61
1.370
S
Tethys
0.618
29.466
0.96
1.888
S
Dione
1.1
37.740
1.47
2.737
S
Rhea
2.31
52.704
1.23
4.518
S
Titan
134.55
122.183
1.88
15.945
S
Hyperion
0.0055
148.11
0.57
21.277
C
Iapetus
1.81
356.13
1.09
79.330
S
Uranus
Miranda
0.066
12.939
1.2
1.413
S
Ariel
1.35
19.102
1.67
2.520
S
Umbriel
1.17
26.630
1.4
4.144
S
Titania
3.52
43.591
1.71
8.706
S
Oberon
3.01
58.352
1.63
13.463
S
Neptune
Proteus
0.05
11.7647
-
1.122
Triton
21.4
35.476
2.05
5.877
S
Nereid
0.03
551.34
-
360.136
Since Triton is a dominant satellite in Neptune, the spin of Neptune might be
calculated by the satellite alone in a good approximation. If the mass and the
moment of inertia of Triton are subtracted by those of two other biggest satellites
showninTable
9.3
to consider the effect of small satellites, the core density of
Neptune to produce the exact spin period increases to 4.418 from 3.677 g/cm
3
.To
maintain a stable orbit between a planet and a satellite, torque and reaction torque
with respect to CMI should be in the same direction as in Fig.
9.2
. If torque and
reaction torque with respect to CMI is in the opposite direction as in Neptune, the
orbit might be unstable until the torque decreases to zero because orbital angular
accelerations and angular velocities of the planet and its satellite induced by the
torque and the reaction torque are in the opposite directions.
Pluto has a dominant satellite, Charon, to be a binary system. It is easy to find that
Eq.
9.12
predicts the same periods of rotations if masses and densities of two bodies
are equal. Tidal forces of Pluto and Charon might lock their spins synchronous to
their orbital rotation, though the mass of Pluto is about 8 times larger than Charon.
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