How many Earth-approaching asteroids are there?

Abstract

The discovery process of Earth-approaching asteroids is formulated as a periodic sampling problem from an urn with replacement. It presumes as unchanging number of such objects over recent historical times, a fixed limiting magnitude/angular speed combination for detection probability, and allows for the possibility of the lack of detection or the lack of sufficient observations to refine an orbit at the first noticed apparition. While simple, the model is sufficiently powerful to show that an estimate of the number of Earth-approaching minor planets is impossible. This conclusion is insensitive to uncertainties in perturbing influences, celestial mechanics, or a model for the distribution of the orbital element sets of these minor planets.