Admissible regions for space debris orbits

The main problem in the orbit determination of the space debris population orbiting our planet is the identification of two or more set of data. The observations of a given object during a passage above an observing station are called a Too Short Arc (TSA): data from a TSA cannot allow for a complete determination of an orbit. Therefore it is not possible to solve the orbit determination problem without solving first the identification problem, finding two or more TSAs belonging to the same physical object and an orbit fitting all the observations. This problem is well known for the determination of orbits of asteroids: we shall show how to apply the methods developed for preliminary orbit determination of heliocentric objects to geocentric objects. We shall focus on the definition of an admissible region for space debris, both in the case of optical observations and radar observations; then we shall outline a strategy to perform a full orbit determination.