Dynamical classification of the asteroids in the Hungaria group: The objects affected by the exterior mean-motion resonance 2:3 with Mars

Abstract

In this paper, we perform a dynamical study of the population of Hungaria asteroids, close to the exterior 2:3 mean-motion resonance (MMR) with Mars. The aim of this work is to initiate a catalog of asteroids captured in mean-motion resonances (MMRs) with Mars in the Hungaria region, by first identifying the minor bodies affected by the 2:3 MMR. To achieve our goal, we follow the temporal evolution of massless test particles by 2 Myr in the proximity of the 2:3 resonance considering the gravitational influence of all planets of the Solar System. We present a semi-analytical model to calculate the extension of the resonant region for a population with the dynamical characteristics of the Hungaria asteroids. We show that the resonance can disturb the asteroids in two ways: by capture or by indirect influence. We find 22 asteroids captured inside the 2:3 MMR and 89 asteroids which exhibit temporary librations around this resonance. The predictions of our model are in good agreement with the numerical results, which make it useful for the study of other MMRs in this region. For asteroids without determined synthetic proper elements, we use the results of our numerical simulations to calculate the mean orbital elements, which can be used as a first approximation of the proper elements.