The Monotonicity of the Apsidal Angle Using the Theory of Potential Oscillators

Abstract

In a central force system the angle between two successive passages of a body through pericenters is called the apsidal angle. In this paper we prove that for central forces of the form $$f(r)\sim \lambda r^{-\,(\alpha +1)}$$ with $$\alpha <2$$ the apsidal angle is a monotonous function of the energy, or equivalently of the orbital eccentricity.