The classical description of planetary coronae - that region of the atmosphere wherein the fluid flow problem transitions from a collisional to a non-collisional medium - was established by J.W. Chamberlain in 1963. That solution of the non-collisional Boltzmann equation stands as a seminal achievement in the history of Aeronomy, describing the escape of light gases from planetary atmospheres and by direct extension providing a framework by which the evolution of planetary atmospheres could be analytically quantified. This project expands that analytical treatment from a two-body (planet, atom) formalism to a three-body (planet, satellite, atom) formalism. That expansion promises the first realistic description of satellite atmosphere structure and evolution (there are 11 such atmospheres identified in our solar system), as well as a fundamental improvement in the analytical model of the Earth exosphere, since that corona is properly the manifestation of the Sun-Earth-atom three-body problem.