Construction of Invariant Tori for the Spin / Orbit Problem in the Mercury / Sun System
Abstract
The stability of spinorbit 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 onedimensional, timedependent 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 MercurySun system. A connection with the probability of capture in a resonance is also provided.
 Publication:

Celestial Mechanics and Dynamical Astronomy
 Pub Date:
 June 1992
 DOI:
 10.1007/BF00049460
 Bibcode:
 1992CeMDA..53..113C
 Keywords:

 Invariance;
 Mercury (Planet);
 Orbital Resonances (Celestial Mechanics);
 Solar Planetary Interactions;
 Spin Resonance;
 SpinOrbit Interactions;
 Toruses;
 Astronomical Models;
 Hamiltonian Functions;
 Perturbation Theory;
 Astrophysics;
 Spinorbit resonance;
 KAM theory;
 Invariant tori