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P. Farinella (University of Trieste, Trieste, Italy)
The research on asteroids' dynamics has been focussed for years on proper elements and on the main resonances (i.e. on the regions characterized by the most regular or the most chaotic behavior). Current research is conversely focussed on the slow changes of orbital elements that may occur on time-scales of several million years. Slow changes of eccentricity and inclination are driven by weak resonances, which are almost densely located throughout the entire belt: high order mean motion resonances with Jupiter, mean motion resonances with Mars, three--body resonances. The slow motion of semi-major axis is caused by the so--called Yarkowsky force, that results from the thermal re--emission of rotating bodies. Both these phenomena are essential to understand several properties of asteroids' distribution: the depletion of the outer belt, the dispersion of some asteroid families, the origin of Mars--crossing asteroids and NEAs.
On the observational side, a lot of effort is being payed to discover Near Earth asteroids. Recent modeling of the unbiased distribution of NEAs, however, show that we are still far from achieving the Spaceguard goal of finding 90 A more tight collaboration between observers and theoreticians would be welcome in order to optimize the search strategies. Finally, it would be very important to perform a new PLS--type deep search of the asteroid belt, using the new technologies (large telescopes, mosaic CCDs) in order to better determine the luminosity function of main belt asteroids. This would provide new informations on the size distribution of the asteroids at small sizes and on the collisional evolution of the belt as a whole.