Qualitative analysis of the anisotropic two-body problem under Seeliger's potential

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 the Seeliger potential. We will show that the set of initial conditions leading to collisions and ejections has positive measure and study the capture and escape solutions in the positive-energy case using the infinity manifold. We will also apply the Melnikov method to show that the flow on the zero-energy manifold of another potential which is the sum of the classical Keplerian potential and the anisotropic Seeliger's potential perturbation is chaotic.