  We offer an analytical study on the dynamics of a two-body problem perturbed
by small post-Newtonian relativistic term. We prove that, while the angular
momentum is not conserved, the motion is planar. We also show that the energy
is subject to small changes due to the relativistic effect. We also offer a
periodic solution to this problem, obtained by a method based of separation of
timescales. We demonstrate that our solution is more general than the method
developed in the book by Brumberg (1991). The practical applicability of this
model may be studies of the long-term evolution of relativistic binaries
(neutron stars or black holes).
