To quantify shape changes, we measured the length of each rubble pile's axes after encounter ( ), calculated the axis ratios ( and ), and defined a single-value measure of the remnant's ``ellipticity'' ( ). For reference, our progenitor has and Geographos has a value of .

Sampling a broad set of parameters to map tidal disruption outcomes, Richardson et al. (1998) identified 195 S, B, or M-class events produced with a rubble pile. Fig. 2 shows this set with ellipticity plotted against the fraction of mass shed by the progenitor during tidal disruption.

fig2

We find that, in general, S-class events tend to yield lower ellipticity values; only 2 of the 79 outcomes are likely to have a Geographos-like elongations ( ). The mean value of for the S-class events is 0.22 with standard deviation = 0.14. The near-spherical shapes produced by S-class events are a by-product of gravitational instabilities in the fragment chain which readily agglomerate scattered particles as they recede from the planet.

B-class events do not show a simple trend with respect to ellipticity, though these values tend to increase as the degree of mass shedding decreases. We find that 5 of 40 outcomes have Geographos-like values. The mean value of for all 40 B-class events is 0.45 (), very close to the starting ellipticity of 0.43.

M-class events are most effective at increasing and creating Geographos-like shapes, probably because tidal torques must first stretch and/or spin-up the rubble pile before particles or clumps can be ejected near the ends of the body. Fig. 2 shows 23 of 76 M-class events with Geographos-like values. Overall, the 76 outcomes have a mean with . Thus, getting a Geographos-like ellipticity from a M-class disruption is less than a 1 event, decent odds if such disruptions (and progenitors) are common.