Chaotic amplification in the relativistic restricted three-body problem

The relativistic equations of motion for the restricted three-body problem are derived in the first post-Newtonian approximation. These equations are integrated numerically for seven different trajectories in the earth-moon orbital system. Four of the trajectories are determined to be chaotic and three are not chaotic. Each post-Newtonian trajectory is compared to its Newtonian counterpart. It is found that the difference between Newtonian and post-Newtonian trajectories for the restricted three-body problem is greater for chaotic trajectories than it is for trajectories that are not chaotic. Finally, the possibility of using this Chaotic Amplification Effect as a novel test of general relativity is discussed.