The Secular Resonances in the Solar System

Abstract

In the last three years new studies on secular resonances have been done. The second-order and fourth-degree secular perturbation theory of Milani and Kneževic allowed to point out the effect of mean motion resonances on the location of the linear and non linear secular resonances. Moreover this theory improved the knowledge of the exact location of the g = g 6 (i.e. v 6) resonance at low inclination. Morbidelli and Henrard revisited the semi-numerical method of Williams, taking into account the quadratic terms in the perturbing masses. They computed not only the location of secular resonances, but also provided a global description of the resonant dynamics in the main secular resonances namely g = g 5 (i.e. v 5), g = g 6 (i.e. v 6) and s = s 6 (i.e. v 16). The resonant proper element algorithm developed by Morbidelli allows to identify the dynamical nature of resonant objects, and is a powerful tool to study the mechanisms of meteorite transport to the inner Solar System. Purely numerical experiments have been done, which show : (i) the complexity of the dynamics when two resonances overlap; (ii) the efficiency of successive crossings of non linear resonances in pumping up the inclination of small bodies; (iii) the efficiency of the secular resonance v 6 as a source of meteorites up to 2.4 AU.