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Table 1

Parameters and dynamical timescales of some satellites and their host planets in the Solar System.

Satellite rM arM 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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