As described above, certain S-, B- and M-class disruptions can leave rubble
piles with highly elongated shapes and fast spin rates. To estimate the
frequency of those particular disruption events near Earth and Venus, we use
the technique of Bottke et al. (1998) and combine a ``map'' of tidal
ellipticity results (described in Richardson et al., 1998) with probability
distributions based on ECO spins, ECO spin axis orientations, ECO close
approaches with Earth and Venus, and ECO encounter velocities with Earth and
Venus. Our results show that a typical ECO should undergo an S-, B-, or
M-class event once every
Myr, comparable to an ECO's collision rate
with Earth and Venus (Richardson et al., 1998). Similarly, this same body
should get an Geographos-like ellipticity (
)
once every
Myr. The most likely disruption candidates have low
e's and i's, consistent with the Geographos's probable orbital history
(i.e., Sec. 3). Since the dynamical lifetime of ECOs against planetary
collision, comminution, or ejection by Jupiter is thought to be on the order
of 10 Myr ([Gladman et al., 1997]), we predict that
% of all ECOs undergo S-,
B- or M-class disruptions (i.e., 10 Myr / 65 Myr), and that
% of all
ECOs (i.e., 10 Myr / 560 Myr) should have shapes (and spins) like Geographos.
The implications of this prediction will be discussed below.