Are Main-Belt Asteroids a Sufficient Source for the Earth-Approaching Asteroids?

Abstract

This paper predicts the size distribution of the Earth-approaching asteroids with diameterd= 10 m to 10 km, assuming they originate as the fragments of main-belt asteroids with a cumulative size distribution proportional tod−2.5and that they have self-similar fragmentation properties. The resulting distribution is dominated by “fast-track” bodies originating from parent asteroids with orbits close to the 3:1 mean-motion resonance with Jupiter. Because the dynamical lifetimes of these Earth approachers are shorter than their collisional lifetimes, their size distribution is nearly proportional tod−3.0, the production distribution in the main belt. This prediction, however, is at odds with the Spacewatch observations. The observed distribution is relatively flat ford> ∼100 m, and relatively steep ford< ∼100 m, so that the number of Earth approachers withd∼ 10 m to 0.3 km is overestimated. If these populations are predominantly of main-belt origin, then the size distribution in the main belt is not a simple power law. A nonuniform size distribution with wave-like oscillations, possibly caused by a cutoff at small sizes, would lead to Earth approachers with a size distribution in better agreement with the observations. If such wave-like oscillations are realistic, then the main belt is sufficient to supply the observed number of Earth approachers throughout the observed size range.