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Coupled orbital-thermal evolution of Miranda

Miranda has a unusually high inclination ($I=4.338^\circ$), and its surface reveals signs of past endogenic activity. Investigations of the dynamical aspects of its orbital evolution suggest probable resonant processes, in particular with Umbriel, as an explanation for the present high inclination of Miranda. The tidal heating induced by gravitational interactions can lead to the rise of eccentricities and, consequently, to the increased dissipation of energy inside the satellite and higher internal temperatures. We study here the possible increase in eccentricities caused by orbital resonances and the resulting endogenic heating on Miranda taking into account its temperature dependent rheology. The coupled orbital-thermal evolution model was run with different rheological models and the thermal parameters starting form a cold thermal state, in radiative equilibrium with the environment. For the nominal parameters of the evolution scenarios studied, the resonances were not sufficient to rise neither the eccentricities nor the internal temperatures significantly. Lowest dissipation function $Q$ of around 100 and final eccentricity of $e\approx0.02$ were obtained during the resonance 3:1 with Umbriel.