Table 1
Physical parameters and mean orbital elements of the Uranian moon system used in the numerical simulations.
| Miranda | Ariel | Umbriel | Titania | Oberon | |
|---|---|---|---|---|---|
| mi (mU) | 7.4552178 × 10−7 | 1.4405272 × 10−5 | 1.4686589 × 10−5 | 3.9169073 × 10−5 | 3.5437548 × 10−5 |
| (Ri RU) | 9.3900 × 10−3 | 2.2736 × 10−2 | 2.2876 × 10−2 | 3.0866 × 10−2 | 2.9790 × 10−2 |
| ζi | 0.327 | 0.320 | 0.342 | 0.326 | 0.310 |
| k2,i | 0.03 | 0.15 | 0.03 | 0.03 | 0.03 |
| Qi | 10 000 | ∈ [50, 400] | 1000 | 1000 | 10 00 |
| QU,i | 10 000 | Eq. (12) | 10 000 | 10 000 or Eq. (12) | 10 000 |
| ai (RU) | 5.080715 | 7.470167 | 10.406589 | 17.069604 | 22.827536 |
| ei | 0.00135 | 0.00122 | 0.00394 | 0.00123 | 0.00140 |
| Ii (deg) | 4.4072 | 0.0167 | 0.0796 | 0.1129 | 0.1478 |
| ϖi (deg) | 108.8614 | 253.4145 | 184.7195 | 49.7581 | 95.0536 |
| Ωi (deg) | 304.5699 | 113.0462 | 39.3105 | 190.7227 | 244.4884 |
Notes. Masses mi and radii Ri are from Jacobson (2014) and references therein contained; normalized moments of inertia ζi are taken from Gomes & Correia (2024a), where for Uranus ζU = 0.225; tidal Love numbers k2,i and quality factors Qi of the satellites, as well as constant (i.e., non-resonance-locking) quality factors QU,i of the planet at the frequency of the i-th satellite, are assigned suitable values for the purpose of the present parametric study (see Sects. 2.3 and 2.4), with k2,U = 0.3 for Uranus (Stixrude et al. 2021); Ariel is always assumed in resonance locking according to Eq. (12), whereas Titania is or is not depending on the type of resonant encounter (two-body or three-body, see Sects. 3 and 4). Semimajor axes, eccentricities, and inclinations are from Gomes & Correia (2024a), whereas longitudes of pericenter and ascending node were obtained by averaging the JPL ephemerides at J2000 epoch (Jacobson 2014; see Sect. 2.5).
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