Precession of nearly circular orbits in the Newtonian 2-body problem perturbed by constant positive curvature

We generalize the reduced Newtonian 2-body problem by embedding it in a space of constant positive curvature. Using perturbation theory, we demonstrate analytically that a nearly circular orbit will precess with a frequency proportional to the square root of its size. Using computer simulation, we confirm this behavior numerically by directly integrating the equations of motion. This work is part of a larger study of the nonlinear dynamics of the 2-body problem in a spherical universe and was supported by NSF Grant No. DMR-0243811 and The College of Wooster.