Newtonian gravitational field theory: Two-body problem

Abstract

The effects of a dual force which appears in a consistent field theory of Newtonian gravitation are explored by a study of the motion of two bodies which interact with each other through the gravitational field. The equations of motion are solved exactly. Among the results obtained, we find that the present theory formulated in accordance with the Special Theory of Relativity leads to the same analytical result for the precession of the perihelion of the orbit as does Einstein's General Theory of Relativity. Another result is that classical particles are endowed with an intrinsic angular momentum of constant magnitude—a helicity of classical origin. Other results, such as the period of revolution, are similar to Kepler's law, except for relativistic corrections. A slight deviation from the planar orbit of classical theory results, and may be observable. This deviation is related to the magnitude of the precession of the perihelion of the orbit. The significance of these results for charged particles, viewed classically or quantum mechanically, are discussed.