Our estimate that 2% of all rubble pile ECOs should have Geographos-type shapes and spin periods is, at best, only accurate to a factor of several, given the many unknown quantities we are modeling and the relatively unknown shape distribution of the ECO population. Still, the following thought experiment is useful in providing a crude ``reality check''. 1620 Geographos has a mean diameter of 3 km and an absolute magnitude of H = 15.6 (Giorgini et al. 1998). Morrison (1992) estimates there are roughly 100 ECOs with absolute magnitudes brighter than 15.0 (6 and 3 km diameters, respectively, for the dark C's and bright S's). Since 2% of 100 objects is 2 objects, it is perhaps not surprising we have not noticed more Geographos-like asteroids.
Alternatively, one could argue that, given these odds, it was fortunate to have discovered Geographos's shape in the first place, especially when one considers that only 35% of the H < 15.0 ECOs have been been discovered, and relatively few of them have had their shapes determined by delay-Doppler radar (Morrison 1992). It is useful to recall, however, that the known ECO population is biased towards objects which pass near the Earth on low inclination orbits (Jedicke 1996), exactly the class of objects which are favored to undergo tidal disruption. Hence, the discovery of Geographos's shape among a limited sample of ECOs may not be a fluke. We predict, though, that more Geographos-like objects are lurking among the undiscovered ECO population.
Our investigation of Geographos led us to examine a second asteroid, 433 Eros, which shares many of Geographos's distinguishing characteristics. We believe Eros may also be tidally distorted, as we will discuss further below.