Forces between electric charges in motion: Rutherford scattering,   circular Keplerian orbits, action-at-a-distance and Newton's third law in   relativistic classical electrodynamics
  Standard formulae of classical electromagnetism for the forces between electric charges in motion derived from retarded potentials are compared with those obtained from a recently developed relativistic classical electrodynamic theory with an instantaneous inter-charge force. Problems discussed include small angle Rutherford scattering, Jackson's recent `torque paradox' and circular Keplerian orbits. Results consistent with special relativity are obtained only with an instantaneous interaction. The impossiblity of stable circular motion with retarded fields in either classical electromagnetism or Newtonian gravitation is demonstrated. 
J.H.Field