  The Trojan asteroids orbit about the Lagrangian points of Jupiter and the
residence times about their present location are very long for most of them. If
these bodies originated in the outer Solar System, they should be mainly
composed of water ice, but, in contrast with comets, all the volatiles close to
the surface would have been lost long ago. Irrespective of the rotation period,
and hence the surface temperature and ice sublimation rate, a dust layer exists
always on the surface. We show that the timescale for resurfacing the entire
surface of the Trojan asteroids is similar to that of the flattening of the red
spectrum of the new dust by solar-proton irradiation. This, if the cut-off
radius of the size distribution of the impacting objects is between 1mm and 1m
and its slope is -3, for the entire size-range. Therefore, the surfaces of most
Trojan asteroids should be composed mainly of unirradiated dust.
