Perihelion Precession in the Special Relativistic Two-Body Problem
  The classical two-body system with Lorentz-invariant Coulomb interaction V=-k/rho is solved in 3+1 dimensions using the manifestly covariant Hamiltonian mechanics of Stueckelberg. Particular solutions for the reduced motion are obtained which correspond to bound attractive, unbound attractive, and repulsive scattering motion. A lack of perihelion precession is found in the bound attractive orbit, and the semi-classical hydrogen spectrum subsequently contains no fine structure corrections. It is argued that this prediction is indicative of the correct classical special relativistic two-body theory for the limit of no magnetic interaction. 
M. A. Trump and W. C. Schieve