Black Hole Orbital Mechanics

Abstract [(Paper Linked)]

In this report, we derive the four types of orbits that appears in the Kepler problem. We start from the Two-body problem that we transform into a One-body problem with reduced mass. We then dig into orbits in the Schwarszchild metric where we derive the geodesics and equation of motion. We provide two proofs of the conservation laws in which we find values for the energy and angular momentum . We derive the relativistic potential as well as the location of stable and unstable circular orbits, the innermost stable circular orbit and the limit of bounded orbits. Finally, we explore briefly the radial infall motion and we describe in details the derivation of the perihelion advance/relativistic precession.