Capture probabilities for secondary resonances

Mathematics – Probability

Scientific paper

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Librational Motion, Orbit Perturbation, Orbital Resonances (Celestial Mechanics), Pendulums, Capture Effect, Degrees Of Freedom, Miranda, Orbital Mechanics, Solar System, Umbriel

Scientific paper

A perturbed pendulum model is used to analyze secondary resonances, and it is shown that a self-similarity between secondary and primary resonances exists. Henrard's (1982) theory is used to obtain formulas for the capture probability into secondary resonances. The tidal evolution of Miranda and Umbriel is considered as an example, and significant probabilities of capture into secondary resonances are found.

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