COMPARISON BETWEEN 2 THEORIES OF ASTEROID PROPER ELEMENTS

A comparison between two theories for the calculation of proper elemen ts is presented in this paper; the first theory, purely analytical, ha s been developed by Milani and Knezevic (1990, 1992, 1994); the second one, a semi-numerical approach, is due to Lemaitre and Morbidelli (19 94). The analytical theory, based on series expansions in eccentricity and inclination, is particularly suitable for low inclination and low eccentricity orbits, while the semi-numerical one is devoted to orbit s with either large eccentricities or large inclinations. The orbits o f the minor planets 3710, 1021, 387, 980, 185 have been computed numer ically for 4.5 Myrs, and the proper elements have been derived with bo th algorithms. The RMS values of the changes with time of the proper e lements are taken as a measure of the instability. The results confirm the theoretical predictions, namely the Milani and Knezevic proper el ements are more stable at low e and I, while the stability of the Lema itre and Morbidelli proper elements depends very little upon eccentric ity and inclination. As a result, the MK elements should be used below about 15 degrees of inclination, and the LM elements should be used a bove about 17 degrees of inclination. The region between 15 degrees an d 17 degrees should be considered as a transition region where both me thods have roughly the same stability; therein the use of both data se ts and the comparison of the results is recommended. The small values of the instabilities confirm that our long term research program, aime d at providing proper elements for the purpose of asteroid family iden tification, has been successful, to the point that reliable proper ele ments are now available for all the regions of the asteroid main belt (and also beyond the main belt, taking into account other available re sults by ourselves and by others).