Statistics – Computation
Scientific paper
Mar 1990
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990zamp...41..174c&link_type=abstract
Zeitschrift für angewandte Mathematik und Physik (ISSN 0044-2275), vol. 41, March 1990, p. 174-204.
Statistics
Computation
20
Computational Astrophysics, Orbit Perturbation, Orbital Resonances (Celestial Mechanics), Astronomical Models, Earth-Moon System, Equations Of Motion, Fourier Series, Planetary Orbits
Scientific paper
A study is made of the stability of spin-orbit resonances in celestial mechanics, namely the exact commensurabilities between the periods of rotation and revolution of satellites or planets. A mathematical model is developed to describe an approximation of the physical situation, and a set of satellites is selected for which such simplified model provides a good approximation. The Kolmogorov-Arnold-Moser theory is applied 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, makes it possible to prove the stability of the 1:1 resonance.
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