The Instability of the Central Configuration Caused By Resonance Perturbation

Abstract

The gravitation interaction between particles is taken into account in central configuration model. After that, the resonance perturbation of the particle of the central configuration by distant satellite is considered in the restricted 3-body problem approach. A shift between simple mean motion resonances and parametric resonance zones is derived. This shift depends upon mass satellite and central configuration properties. Unexpectedly, the resonance structure depends only on particle density and number of particles in the central configuration, but not depends on particles mass. Then, the system of few non-interacted planar central configurations is considered. The resonance structure, which follows from parametric instability, is more abundant than for simple mean motion resonance case. The areas of parametric instability restrict stable central configuration, placed in exact commensurability, from both sides. The possible application to the planetary ring structure is discussed.