Dynamical systems associated to a Newtonian-type potential plus a perturbing potential containing a small real parameter model a large class of concrete astronomical situations, among which satellite orbits have a place of choice. We investigate such models using a combination between block-diagonalization technique and the usual reduction procedure. Within the so-called "main problem of space dynamics", we use this method to study the stability of relative equilibria. The test points out certain nonlinearly stable orbits, and proves to be inconclusive for the remaining relative equilibria. The latter ones are investigated via linearization; all of them prove linear instability. As a main result, all nonlinearly stable relative equilibria remain stable under perturbations that preserve the conserved momentum.
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- Satellite Orbits: Stability