  The non-linearities of the dynamics of Earth artificial satellites are
encapsulated by two formal integrals that are customarily computed by
perturbation methods. Standard procedures begin with a Hamiltonian
simplification that removes non-essential short-period terms from the
Geopotential, and follow with the removal of both short- and long-period terms
by means of two different canonical transformations that can be carried out in
either order. We depart from the tradition and proceed by standard
normalization to show that the Hamiltonian simplification part is dispensable.
Decoupling first the motion of the orbital plane from the in-plane motion
reveals as a feasible strategy to reach higher orders of the perturbation
solution, which, besides, permits an efficient evaluation of the long series
that comprise the analytical solution.
