  Within the theory of General Relativity, we study the solution and range of
applicability of the standard geodesic deviation equation in highly symmetric
spacetimes. In the Schwarzschild spacetime, the solution is used to model
satellite orbit constellations and their deviations around a spherically
symmetric Earth model. We investigate the spatial shape and orbital elements of
perturbations of circular reference curves. In particular, we reconsider the
deviation equation in Newtonian gravity and then determine relativistic effects
within the theory of General Relativity by comparison. The deviation of nearby
satellite orbits, as constructed from exact solutions of the underlying
geodesic equation, is compared to the solution of the geodesic deviation
equation to assess the accuracy of the latter. Furthermore, we comment on the
so-called Shirokov effect in the Schwarzschild spacetime and limitations of the
first order deviation approach.
