Abstract
In this paper, we study the two-body problem that describes the motion of two-point masses in an anisotropic space under the influence of a Newtonian force-law with two relativistic correction terms. We will show that the set of initial conditions leading to collisions and ejections and leading to escapes and captures have positive measure. Using the infinity manifold, we study capture and escape solutions in the zero-energy case. We also show that the flow on the zero energy manifold of a two-body problem given by the sum of the Newtonian potential and three anisotropic perturbations (corresponding to three relativistic correction terms) is chaotic.
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