Near-Earth asteroids (NEAs) that have been imaged by Earth-based radar
have conspicuously elliptical or potato shapes. If they are ''rubble
piles'' rather than single chunks of competent material, their shapes
may be fossil remnants of past close gravitational tidal encounters wi
th Earth and other planets. The NEAs are removed from the steady-state
population by hitting Earth or being pumped by close encounters with
it into orbits that are strongly perturbed by Jupiter. Cross sections
for tidal encounters exceed those for direct collision with Earth, so
a sizable fraction of the NEOs have passed within the tidal radius of
Earth. We model the asteroids as agglomerations of spherical rocks, bo
und together only by gravity (rubble pile). We used an N-body code to
determine the amount of elongation that they acquire in a tidal encoun
ter as a function of impact parameter and velocity with respect to Ear
th. The model enjoys a similarity relation that allows detailed geomet
ric and energetic features of the tidal distortion to be scaled from o
ne asteroid size to another. The maximum elongation of tidally distort
ed asteroids exceeds that of any observed NEA including Geographos, so
tidal encounters appear to adequately explain the high degree of elon
gation shown by these objects. (C) 1996 American Astronomical Society.