Analysis of resonances in the spinorbit problem in Celestial Mechanics: The synchronous resonance (Part I)
Abstract
We study the stability of spinorbit resonances in Celestial Mechanics, namely the exact commensurabilities between the periods of rotation and revolution of satellites or planets. We introduce a mathematical model describing an approximation of the physical situation and we select a set of satellites for which such simplified model provides a good approximation. Applying the KolmogorovArnoldMoser theory we are able to construct invariant surfaces trapping the synchronous resonance from above and below. The existence of such surfaces, established for the natural values of the physical and orbital parameters, allows to prove the stability of the 1∶1 resonance. Furthermore we try to construct KAM tori with frequencies as close as possible to one so to trap the synchronous resonance in a finer region.
 Publication:

Zeitschrift Angewandte Mathematik und Physik
 Pub Date:
 March 1990
 DOI:
 10.1007/BF00945107
 Bibcode:
 1990ZaMP...41..174C
 Keywords:

 Computational Astrophysics;
 Orbit Perturbation;
 Orbital Resonances (Celestial Mechanics);
 Astronomical Models;
 EarthMoon System;
 Equations Of Motion;
 Fourier Series;
 Planetary Orbits;
 Astrophysics