Mathematics – Probability
Scientific paper
Oct 1990
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990icar...87..249m&link_type=abstract
Icarus (ISSN 0019-1035), vol. 87, Oct. 1990, p. 249-264.
Mathematics
Probability
21
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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