Issue D. Production Rate of Geographos-Shaped Objects

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 $\sim 65$ 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 ( $\varepsilon_{{\rm rem}} > 0.60$) once every $\sim 560$ 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 $\sim 15$% of all ECOs undergo S-, B- or M-class disruptions (i.e., 10 Myr / 65 Myr), and that $\sim 2$% 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.