Motions of asteroids at the Kirkwood gaps II. On teh 5:2, 7:3, and 2:1 resonances with Jupiter

Abstract

The behavior of asteroids at the 5:2, 7:3, and 2:1 resonances with Jupiter is studied in the scheme of the elliptical restricted three-body problem. Following the previous study of Yoshikawa (1990, Icarus, 87, 78–102), the motions of asteroids are investigated by using semianalytical and numerical methods. In semianalytical models, the effect of the inclination of asteroids is taken into account. In numerical integrations, however, only planar cases are treated, but large parameter regions are investigated. The results are summarized as follows: (1) in the 5:2 resonance, the eccentricities of orbits of asteroids change greatly in most of the resonance region, (2) in the 7:3 resonance, the eccentricities of asteroids change greatly mainly in the central part of the resonance region, and (3) in the 2:1 resonance, the eccentricities of asteroids do not change greatly in most of the resonance region. This result for the 2:1 resonance is in agreement with Lemaître and Henrard (1990, Icarus 83, 391–409). Considering these results and the result of Yoshikawa (1990), we can say that the origin of the Kirkwood gaps at the 3:1 and 5:2 resonances can be explained by the scenario of collision with major planets, which was first proposed by Wisdom (1982, Astron. J. 87, 577–593). However, within the restriction of our study, the results obtained here do not support this scenario for the gaps at the 7:3 and 2:1 resonances. In order to reveal the formation mechanism of these gaps, we should study more general cases, that is, the motions of asteroids in three-dimensional space under the perturbation of several planets.