Periodic, Transition and Escape Trajectories for 3D-Kepler 2-Body Problem of Classical Electrodynamics

Abstract

In a previous paper we studied the Kepler problem for the extended Synge’s 2-body problem of classical electrodynamics. We have used the radiation terms introduced in our previous papers and prove an existence–uniqueness of a periodic orbit in polar coordinates which confirmed the Bohr's hypothesis of the existence of the stationary states in the frame of classical electrodynamics. Our main aim here is to show the existence of trajectories of transition оf the particle orbiting the nucleus from one stationary state to another excited state. We also prove the existence of escape trajectories. This is made by a choice of suitable function space and applying fixed point method.