ASTEROID PROPER ELEMENTS AND THE DYNAMICAL STRUCTURE OF THE ASTEROID MAIN BELT

We have computed proper elements for 12,573 asteroids, including all the ones with orbits accurate enough to be useful for family identification. This was done with an upgraded version of our iterative analytical algorithm, resulting in significantly improved accuracy for most asteroids in the low to moderate inclination and eccentricity region of the main belt (typical instability in the proper e and sin I being less-than-or-equal-to 0.0015 over 5 Myr). This stability has been verified by numerical integrations (within a realistic model) of 35 test cases. In a small percentage of cases, the accuracy of the proper elements computation was degraded by the effects of some resonance, either in mean motion or secular. We have been able to list the resonances responsible for this degradation in almost all the cases, in such a way that these are properly flagged with a ''resonance code.'' This list of resonances, including nine high-degree secular resonances not known before our work, provides a detailed map of the dynamical structure of the asteroid main belt. We investigate the long-term dynamics of some of these secular resonances and find both very large amplitude oscillations of the eccentricity and irregular behavior for asteroids affected by one or more resonances. We show the geometry of these resonances in the proper elements space and their relationship with the asteroid distribution and with the most prominent families. In the second part of the paper, we give a detailed description of the improvements of this version of the proper elements theory with respect to the previously published ones (A. Milani and Z. Knezevic, 1990, Celest. Mech. 49, 347-411; 1992, Icarus 98, 211-232). We discuss the success of some of these improvements in cases which were previously of degraded accuracy, and we also comment on the failure of some attempted improvements. We conjecture that our theory is very close to the fundamental limitations to the accuracy of any analytical theory, which result from the fact that there is an infinite web of resonances and from the occurrence of chaotic motions. Thus we think that further improvements of this theory will only be of local nature and will affect only a fraction of the asteroid population. (C) 1994 Academic Press, Inc.