Effects of Linear Secular Resonances in the Region of Semimajor Axes Smaller Than 2 AU

Abstract

A semianalytical model is developed to study the effects of linear secular resonances located by P. Michel and Ch. Froeschlé (Icarus128,230–240, 1997) for semimajor axesa< 2 AU, where many near-Earth objects are found. We present examples illustrating the perturbative effects caused by the secular resonances with the inner and the outer planets and by the overlapping of some of these resonances. The results show that in the neighborhood of the terrestrial planets, the resonances involving the characteristic frequencies of those planets become much more effective than the ones associated with the outer planets. They provide a transport mechanism from quasi-stable regions to planet-crossing ones and can cause significant inclination changes. Moreover, the interaction of two resonances can lead to large-scale chaos. These results confirm previous numerical studies of real objects and fictitious particles and show that the close approaches to planets are not the only sources of perturbation in this region. Therefore, the study of the orbital evolution of small bodies in this region must take into account the possible occurrence and effects of secular resonances.