Construction of invariant tori for the spin-orbit problem in the mercury-sun system |
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Authors: | Alessandra Celletti Corrado Falcolini |
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Institution: | (1) Dipt. di Matematica Pura e Applicata, Universitd di L'Aquila, Coppito, 67100 (L'Aquila), Italy;(2) Dipt. di Matematica, II Università di Roma, 00100 Roma, Italy |
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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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Keywords: | Spin-orbit resonance KAM theory Invariant tori |
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