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

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 themajor 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 contemplated according to a simple geometrical and dynamical interpretation in Keplerian language by means of the usual relations characterizing elliptic elements along ahypothetic Keplerian motion.Appropriate choices for the terms appearing in the proposed Hamiltonian lead to recovering the analogues of some well-known, classical radial intermediaries (those introduced by Deprit and the one built by Alfriend and Coffey), but also certain new ones derived by Ferrándiz for the Main Problem in the Theory of Artificial Satellites of the Earth. In any case, the results are also applicable to problems dealing with orbital motion of other planetary satellites.The generality of this pattern leads to asystematic obtaining of solutions to the considered intermediaries: special choices of the Hamiltonian yield the correspondinganalytical solution to the respective intermediary problem.