New Methods of Celestial Mechanics

Indexed in: Scopus

The book attempts to explain the main features of celestial mechanics using a new and unique technique. Its emphasis, in terms of applications, is on the Solar System, including its most peculiar ...
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Resonances

Pp. 79-102 (24)

Jan Vrbik

Abstract

Resonances occur when period of the perturbing force is commensurable with the perturbed body’s orbital motion (2/1 resonance corresponds to a perturbing force whose one cycle is completed in two orbits of the perturbed body; two cycles are completed during one orbit in the case of 1/2 resonance, etc.). They constitute a rather special (and difficult) category of time-dependent perturbations, as we demonstrate using several examples of an asteroid perturbed by Jupiter’s gravitational pull. We start with the 1/1 resonance, which has some unique features, not shared by other resonances.

Affiliation:

Department of Mathematics Brock University Canada.