Table 1
Parameters and dynamical timescales of some satellites and their host planets in the Solar System.
| Satellite | rM | a∕rM | τ | η | Planet | ε | T |
|---|---|---|---|---|---|---|---|
| The Moon | 9.7 Req | 6.23 | 139 yr | 532 | The Earth | 23.4° | 73 700 yr |
| Deimos | 13.0 Req | 0.53 | 260 yr | 1.22 × 10−4 | Mars | 25.2° | 0.154 Myr |
| Callisto | 36.3 Req | 0.73 | 1269 yr | 1.46 | Jupiter | 3.1° | 1.40 Myr |
| Titan | 41.7 Req | 0.49 | 4501 yr | 12.4 | Saturn | 26.7° | 6.74 Myr |
| Iapetus | 54.8 Req | 1.08 | 2982 yr | 6.45 × 10−2 } | |||
| Oberon | 65.0 Req | 0.34 | 25 674 yr | 7.27 | Uranus | 97.9° | 165 Myr |
| TNO | 1038 au | − | 209 Gyr | 0 | Solar System | 61.7° | ∞ |
Notes. See text for the definition of the parameters. The J2 used in Eq. (6) is enhanced by the contribution of inner satellites if there are any (Tremaine et al. 2009), thus the difference of rM and τ between Titan and Iapetus. The parameter λ appearing in Eq. (29) is not well known for the giant planets, so the values of T given here are only approximate. We used λ = 0.25, 0.23, and 0.23 for Jupiter, Saturn, and Uranus, respectively. The line ‘TNO’ refers to the motion of a trans-Neptunian object perturbed by the quadrupolarperturbations from the planets and from the galactic tides (Saillenfest et al. 2019a); in this case, ε is the tilt of the galactic plane with respect to the invariable plane of the Solar System (Murray 1989; Souami & Souchay 2012), and the other parameters are 
and 
, where μi and ai are the gravitational parameters and semi-major axes of the planets of the Solar System, and
is a constant incompassing the mass distribution within the Galaxy (Fouchard 2004).
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