Elliptical Hill's problem (large and small impact parameters)

Abstract

This paper gives analytical formulas to express the changes in orbital elements due to a close encounter between two particles of a ring or between two small satellites of a planet. The study is performed in the frame of the Hill's problem, extended to fully take into account the eccentricities. The Lie's transform method is used to average the Hamiltonian, particularized to two types of encounters: the ones with small impact distance (coorbitals) and those with a large one (shepherds).