Orbital Evolution in Resonance Lock. II. Two Mutually Perturbing Bodies

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Abstract
I investigate the orbital evolution of two mutually perturbing bodies affected by nonconservative forces and locked in a mean motion resonance. This is a generalization of a previous work for the restricted three-body problem. General equations constraining the secular variations of the semimajor axes, eccentricities, and inclinations of both bodies are deduced. For well-separated resonances, specific variations for any orbital element can be computed. The theory is applied to the tidal evolution of natural satellites in resonance lock, where the equations are validated through an example for a specific librating angle. Tidal evolution of the Galilean satellites in their present and possible past resonance configurations is revisited. Some results obtained by Yoder & Peale are reproduced, thus further validating the method.