Brouwer’s satellite solution redux

Abstract

Brouwer’s solution to the artificial satellite problem is revisited. We show that the complete Hamiltonian reduction is rather achieved in the plain Poincaré’s style, through a single canonical transformation, than using a sequence of partial reductions based on von Zeipel’s alternative for dealing with perturbed degenerate Hamiltonian systems. Beyond the theoretical interest of the new approach as regards the complete reduction of perturbed Keplerian motion, we also show that a solution based on a single set of corrections may yield computational benefits in the implementation of an analytic orbit propagator.