Dynamical behavior of asteroids near resonance: the 4:1 gap and the 7:2 group

Abstract

A comparative study of the evolution of the Sun–Jupiter–Asteroid system near the 4:1 and 7:2 resonances is performed by means of two techniques that proceed differently from the Hamiltonian corresponding to the planar restricted elliptic three-body problem. One technique is based on the classical Schubart averaging while the other is based on a mapping method in which the perturbing part of the Hamiltonian is expanded and the resulting terms are ordered according to a weight function that depends on the powers of eccentricities and the coefficients of the terms. For the mapping method the effect of Saturn on the asteroidal evolution is introduced and the degree of chaos is estimated by means of the Lyapunov time. Both methods are shown to lead to similar results and can be considered a suitable tool for describing the evolution of asteroids in the Kirkwood gap and the group corresponding to the 4:1 and 7:2 Jovian resonances, respectively.