Riemann’s generalization of equations of motion in prolate spheroidal coordinates

Abstract

One of the most profound and prominent fact of nature today is that all astronomical bodies in the universe are spheroidal in geometry. It is also an established fact that Riemannian geometry is more general than the well-known Euclidean geometry. Therefore in this paper, we derived the generalized equations of motion in prolate spheroidal coordinate system using Riemannian geometry and the golden metric tensor. Our results pave way for application in the proper description of the motion of prolate bodies.