Periodic Solution of Two-Body Problem of Classical Electrodynamics with Radiation Terms

Abstract

The present paper is an improved version of a previous one, where we have proved an existence-uniqueness of periodic motion of two-body problem of classical electrodynamics. The system of equation of motion obtained is of a neutral type with respect to the unknown velocities with both retarded and advanced arguments depending on the unknown trajectories. We use an operator introduced in a previous our paper. Its fixed point is a periodic solution of the problem in question. An existence-uniqueness of a periodic solution means an existence of closed orbits. But this means that Bohr-Sommerfeld stationary states are a consequence of classical electrodynamics. Radiation terms are chosen such so as not to disturb the stability of the hydrogen atom.