ASTEROID LONG-PERIODIC PERTURBATIONS - DERIVATION OF PROPER ELEMENTS AND ASSESSMENT OF THEIR ACCURACY

The procedure of elimination of asteriod long-periodic perturbations and derivation of their proper elements, according to the analytical theory of asteroid secular perturbations by Yuasa (1973), is described in detail. An indirect method to determine the accuracy of proper elements is introduced, and estimates are obtained for the four lowest-numbered members of the largest Hirayama families - Flora, Koronis, Eos, and Themis. A significant improvement of the accuracy was found, especially for the proper eccentricity, in comparison with the results coming both from the previously available linear theory, and the first-order solution. For Koronis and Eos, the accuracy of the derived proper elements was found to be close to the 10(-3) level, usually considered as necessary for a reliable identification of families. For Themis, the accuracy of the proper eccentricity was some-what lower, due to the proximity of the 2:1 mean motion resonance with Jupiter. In the region of Flora the analytical theory failed to provide reliable proper elements, because of the small divisors appearing in the terms of first order and fourth degree and in the forced terms. These divisors correspond to secular resonances defined by combinations of up to four fundamental frequencies.