On the dynamical evolution of the Atens and the Apollos

Abstract

In this investigation we compare the dynamical evolution of the two groups of Earth crossing asteroids namely the Atens which move—grosso modo—inside the orbit of the Earth and the Apollos which move outside the Earths orbit. The main goal of this study was to compute the encounters of these asteroids with the Earth, respectively the collision probabilities. We also briefly analyzed their qualitative behavior over one million years and computed the mixing of the two groups. The approach to achieve these results was a purely numerical one: we used extensive numerical integrations in the framework of a dynamical model of the planetary system (consisting of the Sun and the planets Venus through Saturn). Other interesting features of the dynamics of Apollos and Atens are confirmed in our study—e.g. the temporary capture into the 1 : 1 mean motion resonance with the Earth. Close encounters with the inner planets (primarily with the Earth and with Venus) are the major events which change the orbit of such an asteroid, but the Kozai resonances and the secular resonances have to be taken into account to understand the dynamical evolution over longer time intervals. The results of collision probabilities with the Earth are in good agreement with statistically derived results by other authors: approximately 20 (50 for smaller objects) collisions for each Aten and 10 collisions for each Apollo per 1 billion years.