INTERRELATING ASTEROID SIZE, ALBEDO, AND MAGNITUDE DISTRIBUTIONS

Given the cumulative distributions of asteroid absolute magnitudes and geometric albedos, we derive the corresponding cumulative size distri bution. The inversion problem entails a one-dimensional integral equat ion whose kernel is not separable from the unknown size distribution. Assuming the size and geometric albedo to be independent, the size dis tribution enters the well-known Fredholm integral equation of the firs t kind. We solve the integral equation analytically for discretely dis tributed geometric albedos. As an application, we then compute the siz e distribution of Earth-crossing asteroids assuming the population has light-scattering properties similar to C- and S-class asteroids. If t he assumed proportion of brighter asteroids is increased, the total nu mber of asteroids larger than a given size is decreased. The size dist ribution is rather insensitive to the geometric albedos assigned to th e C- and S-class asteroids.