Um estudo da evolução orbital dos satélites de Urano atribuída ao efeito de maré - Gomes, Gabriel de Oliveira [UNESP] (2017)
Almost all studies so far performed related to possible events capable of elevating Miranda's inclination to its present value and explain the relatively active surface of Ariel are based on passage through some mean motion resonances (MMR) between two satellites. For Miranda's inclination, it is claimed that an entrapment in a 3 : 1 resonance between Miranda and Umbriel would have been responsible for an increase in Miranda's inclination, where escape from such resonance occurs when chaotic behavior during the resonance ensues. For Ariel's present surface, studies show that a 5 : 3 resonance between Ariel and Umbriel would have been responsible for increasing Ariel's eccentricity, causing intense processes of energy dissipation resulting on Ariel's present resurfacing. In this work, we revisit these two problems from a new point of view taking the classical newtonian formalism, but in a tridimensional case and considering that, during the resonances, tidal interactions act on Miranda, Ariel and Umbriel. Since the 5 : 3 resonance between Ariel and Umbriel was probably the last encountered by the system (Peale, 1988), rstly the 3 : 1 resonance between Miranda and Umbriel is studied in order to obtain reasonable initial conditions to study the 5 : 3 resonance between Ariel and Umbriel. Finally, it is shown that, for both resonances, the initial conditions are an important aspect to be analyzed, since the system is very sensitive concerning alterations on the initial conditions