Dynamical evolution of the Uranian satellite system I. From the 5/3 Ariel-Umbriel mean motion resonance to the present
arxiv(2024)
摘要
Mutual gravitational interactions between the five major Uranian satellites
raise small quasi-periodic fluctuations on their orbital elements. At the same
time, tidal interactions between the satellites and the planet induce a slow
outward drift of the orbits, while damping the eccentricities and the
inclinations. In this paper, we revisit the current and near past evolution of
this system using a N-body integrator, including spin evolution and tidal
dissipation with the weak friction model. We update the secular eigenmodes of
the system and show that it is unlikely that any of the main satellites were
recently captured into a high obliquity Cassini state. We rather expect that
the Uranian satellites are in a low obliquity Cassini state and compute their
values. We also show that the current eccentricities of the satellites are not
forced, and estimate the free eccentricities and inclinations. We constrain the
quality factor of Uranus to be Q_U = (8.6 ± 2.9)×10^3, and that of the
satellites to be Q_S ∼ 500. We find that the system most likely
encountered the 5/3 mean motion resonance between Ariel and Umbriel in the
past, at about (0.7±0.2) Gyr ago. We additionally determine the
eccentricities and inclinations of all satellites just after the resonance
passage that comply with the current system. We finally show that, from the
crossing of the 5/3 MMR to the present, the evolution of the system is mostly
peaceful and dominated by tides raised on Uranus by the satellites.
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