RESIDENT SPACE OBJECT PROPER ORBITAL ELEMENTS

Proper elements are obtained as a result of the elimination of short and long periodic perturbations from their instantaneous, osculating counterparts, and therefore represent a kind of average characteristic of motion. Projected into proper element space, asteroids tend to cluster around special values of the orbital elements leading to their unique classification into dynamical families. Proper elements thus appear to have application to a number of underpinning areas of SSA, including the dynamical taxonomy of resident space objects and the association of debris from breakup into its parent satellite. Here, we work out a preliminary theory of proper orbital elements in the circumterrestrial context. We recover a classical solution of Cook (1966) on frozen orbits and adopted it in a semi-analytical computation of geocentric proper eccentricity. These quasi integrals were found to be nearly constant on decadal timescales for high altitude LEO satellites.