  We consider Earth satellite orbits in the range of semi-major axes where the
perturbing effects of Earth's oblateness and lunisolar gravity are of
comparable order. This range covers the medium-Earth orbits (MEO) of the Global
Navigation Satellite Systems and the geosynchronous orbits (GEO) of the
communication satellites. We recall a secular and quadrupolar model, based on
the Milankovitch vector formulation of perturbation theory, which governs the
long-term orbital evolution subject to the predominant gravitational
interactions. We study the global dynamics of this two-and-a-half
degrees-of-freedom Hamiltonian system by means of the fast Lyapunov indicator
(FLI), used in a statistical sense. Specifically, we characterize the degree of
chaoticity of the action space using angle-averaged normalized FLI maps,
thereby overcoming the angle dependencies of the conventional stability maps.
Emphasis is placed upon the phase-space structures near secular resonances,
which are of first importance to the space debris community. We confirm and
quantify the transition from order to chaos in MEO, stemming from the critical
inclinations, and find that highly inclined GEO orbits are particularly
unstable. Despite their reputed normality, Earth satellite orbits can possess
an extraordinarily rich spectrum of dynamical behaviors, and, from a
mathematical perspective, have all the complications that make them very
interesting candidates for testing the modern tools of chaos theory.
