ON 3D-KEPLER TWO BODY PROBLEM OF CLASSICAL ELECTRODYNAMICS WITH RADIATION TERMS

The Kepler problem for two charged particles in classical electrodynamics is planar and it has been studied in our previous papers. The main goal of the present paper is to derive equations of motion of the three-dimensional Kepler problem in spherical coordinates. We solve the obtained nonlinear differential equations by introducing appropriate functional spaces for the derivatives of the unknown functions using the fixed point method for periodic operators. The obtained solution has periodically changing radius, unbounded polar angle and periodically changing latitude. We show that the electron has an orbit in the framework of classical electrodynamics. This confirms our previous results concerning two-body problem in an internal frame of reference (in Cartesian coordinates) for the existence of periodic orbits of the two-body problem. It is known that the quantum mechanics postulates only discrete stationary states and orbitals.