Empirical method of proper element calculation and identification of asteroid families

Abstract

A search for asteroid families was carried out with the use of a proper element set comprising 649 050 asteroid orbits. Proper elements were calculated by the empirical method. This method uses distributions of orbital elements to calculate secular perturbations. There are two types of secular perturbations: the classical perturbations and the Lidov-Kozai mechanism. The empirical method allows us to distinguish these perturbations in distributions of orbital elements. In this work, amplitudes of inclination and eccentricity oscillations were calculated for both types of perturbations, and thereafter the perturbations were excluded from the osculating elements one after another. The exclusion was made by means of the coordinate transformation formula. The method can be applied for high-inclination and resonant regions. The obtained proper elements are accurate enough to search for asteroid families. As a result, 141 asteroid families were identified in the interval of a semimajor axis 1.8-5.4 au.