Abstract
The stability of spin-orbit resonances, namely commensurabilities between the periods of rotation and revolution of an oblate satellite orbiting around a primary body, is investigated using perturbation theory. We reduce the system to a model described by a one-dimensional, time-dependent Hamiltonian function. By means of KAM theory we rigorously construct bidimensional invariant surfaces, which separate the three dimensional phase space. In particular with a suitable choice of the rotation numbers of the invariant tori we are able to trap the periodic orbit associated with a given resonance in a finite region of the phase space. This technique is applied to the Mercury-Sun system. A connection with the probability of capture in a resonance is also provided.
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Celletti, A., Falcolini, C. Construction of invariant tori for the spin-orbit problem in the mercury-sun system. Celestial Mech Dyn Astr 53, 113–127 (1992). https://doi.org/10.1007/BF00049460
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DOI: https://doi.org/10.1007/BF00049460