Physics
Scientific paper
Sep 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981cemec..25...65b&link_type=abstract
Celestial Mechanics, vol. 25, Sept. 1981, p. 65-78. Research supported by the California Institute of Technology;
Physics
3
Natural Satellites, Orbit Perturbation, Orbital Resonances (Celestial Mechanics), Planetary Orbits, Solar System, Spin Resonance, Equations Of Motion, Equilibrium Equations, Libration, Orbital Elements, Spin Dynamics, Titan
Scientific paper
On the basis of the strong mathematical and physical parallels between orbit-orbit and spin-orbit resonances, the dynamics of mutual orbit perturbations between two satellites about a massive planet are examined, exploiting an approach previously adopted in the study of spin-orbit coupling. Resonances are found to exist when the mean orbital periods are commensurable with respect to some rotating axis, which condition also involves the apsidal and nodal motions of both satellites. In any resonant state the satellites are effectively trapped in separate potential wells, and a single variable is found to describe the simultaneous librations of both satellites. The librations in longitude are 180 deg out-of-phase, with fixed amplitude ratio that depends only on their relative masses and semimajor axes. The theory is applicable to Saturn's resonant pairs Titan-Hyperion and Mimas-Tethys, and in these cases the calculated libration periods are in reasonably good agreement with the observed periods.
Anderson John D.
Blitzer Leon
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