Maps of secular resonances in the NEO region

Abstract

Context. From numerical simulations, it is known that some secular resonances may affect the motion of near-Earth objects (NEOs). However, the specific location of the secular resonance inside the NEO region is not fully known because the methods previously used to predict their location cannot be applied to highly eccentric orbits or the time when the NEOs cross the orbits of the planets. Aims. In this paper, we aim to map the secular resonances with the planets from Venus to Saturn in the NEO region, while including high eccentricity values as well. Methods. We used an averaged semi-analytical model that can deal with orbit-crossing singularities for the computation of the secular dynamics of NEOs, from which we were able to obtain suitable proper elements and proper frequencies. Then, we computed the proper frequencies over a uniform grid in the proper elements space. Secular resonances can thus be located by the level curves corresponding to the proper frequencies of the planets. Results. We determined the location of the secular resonances with the planets from Venus to Saturn, showing that they appear well within the NEO region. By using full numerical N-body simulations, we also showed that the location predicted by our method is fairly accurate. Finally, we provided some indications about possible dynamical paths inside the NEO region due to the presence of secular resonances.