Effects of general relativistic post-Newtonian approximations on the configuration space properties of elliptical orbital trajectories

Post-Newtonian approximations have been successful in describing various astronomical phenomena that classical Newtonian gravity could not. One such phenomenon is the precession of the periapsis of elliptical orbits. Einstein originally solved the problem in 1916 and since then others have been applying the technique to numerous complex systems. However, not much attention has been given to studying the changes in the configuration space when switching from Newtonian to post-Newtonian mechanics. Here, we compare the sizes and topologies of the configuration spaces of both these approaches and further explore the likelihood of planetary collisions in other star systems when configuration space expansion due to general relativity is taken into account.