Canonical elements and Keplerian-like solutions for intermediary orbits of satellites of an oblate planet (Q1311634)

Within the framework of the canonical formalism in the extended phase space, a general Hamiltonian is investigated that covers a wide class of radial intermediaries accounting for the major secular effects due to a planet's oblateness perturbations. An analytical, closed-form solution for this generic Hamiltonian is developed in terms of elementary functions via the corresponding Hamilton-Jacobi equation. The analytical solution so obtained can be comtemplated according to a simple geometrical and dynamical interpretation in Keplerian language by means of the usual relations characterizing elliptic elements along a hypothetic Keplerian motion.