The orbits of 4583 main belt asteroids are integrated orbits for 57 ye
ars and searched for asteroid-asteroid encounters from which it may be
possible to determine the masses of 23 of the largest asteroids (diam
eter greater than or equal to 200 km) and 11 smaller asteroids. The se
arch is conducted using a scattering formula which serves as a useful
filter for identifying encounters that can lead to a mass determinatio
n. A total of 460 such encounters were found. The ten most useful of t
hese encounters are examined in detail. The results show that, to make
a reliable mass determination, the mean distance of the perturbed ast
eroid must be known to within a few times 10(-8) AU. An observing prog
ram targeting the asteroids listed here would have a substantial impac
t on our knowledge of asteroid masses and densities. (C) 1996 American
Astronomical Society.