Shaping of Earth-Crossing Asteroids by Tidal Forces

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 with 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, bound together only by gravity (rubble pile). We used an N-body code to determine the amount of elongation that they acquire in a tidal encounter as a function of impact parameter and velocity with respect to Earth. The model enjoys a similarity relation that allows detailed geometric and energetic features of the tidal distortion to be scaled from one asteroid size to another. The maximum elongation of tidally distorted asteroids exceeds that of any observed NEA including Geographos, so tidal encounters appear to adequately explain the high degree of elongation shown by these objects.