Survey of secular resonances in the asteroid belt

Abstract

Using a recently introduced synthetic method to compute the asteroid secular frequencies (Knežević and Milani 2019), in this paper we survey the locations of secular resonances in the 9 dynamically distinct zones of the asteroid belt. Positions of all resonances up to order four, of a significant fraction of the order six resonances, and of a several order eight ones were determined, plotted in the space of proper elements, and discussed in relation to the local dynamics and to the structure and shape of the nearby asteroid collisional families. Only the resonant combinations with fundamental frequencies of Jupiter and Saturn were considered, with a few special cases involving other planets and largest asteroids. Accuracy of the polynomial fit to determine the frequencies was found to be satisfactory for the purpose of determination of secular resonance positions. This enabled a precise identification of dynamical mechanisms affecting the computation of frequencies (close vicinity of the mean motion resonances and libration in secular resonances), and of the “cycle slips” as a primary technical drawback causing deterioration of the results. For each zone we also presented and discussed a fairly complete sample of recent works dealing with interaction of the secular resonances with asteroid families present in that zone. Finally, a few words were devoted to possibilities for future work.

Keywords

• celestial mechanics
• minor planets
• asteroids: general