Determination of the area and mass distribution of orbital debris fragments

An important factor in modeling the orbital debris environment is the loss rate of debris due to atmospheric drag and lunisolar perturbations. An accurate knowledge of the area-to-mass ratio of debris fragments is required to calculate the effects of atmospheric drag. It is shown here that the orbital elements as a function of time can be used to invert any propagation algorithm to yield the area-to-mass ratio of an orbiting object. From these calculations and the observed radar cross-section of the object, the mass can be calculated to an accuracy of about 30 percent. It is shown that the mass is related to the effective cross-section area by a power-law relation, but for a given area the mass distribution is very broad. An expression is given for the cumulative mass distribution.