Application of a Dirac Delta Disintegration Technique to the Statistics of Orbiting Objects

In many problems related to the description of the debris environment it is mandatory to be able to deal with orbital dynamics from a statistical point of view. This allows one to compute debris spatial densities, to evaluate collision probabilities and to improve the processing of the data received from observational campaigns. In this paper we use a novel technique based on the mathematical manipulation of Dirac’s delta functions and we show how this is a powerful new tool in dealing with orbital mechanics from a statistical point of view. The methodology is applied to derive some analytical expressions for the density functions associated with the velocity distribution of orbiting objects.