A mathematical model representing the statistical properties of sets of orbits

With the fast growth of the number of the objects orbiting around our planet, the statistical description of their orbits has become more and more important. In this paper we discuss a general approach to this problem and we present a new expression for the spatial density function related to some chosen set of orbit. In a simple case in which the statistical distribution of the RAAN and of the argument of the perigee are considered to be constant the new expression given is shown to be coincident with Dennis formulas. Some applications to LEO and GEO are shown at the end.