On the universality of orbital theory for satellite motion perturbed by gravitational harmonics

Abstract

The author's approach to perturbation analysis for a satellite orbiting in a general gravitational field, concisely formulated by the use of a particular system of spherical polar coördinates, was conceived as applying only to elliptic orbits. However, the formulation extends, with surprising ease, to hyperbolic orbits. No change is required in the manner in which some perturbations are applied to the orbital elements and others to the coördinates, though it becomes purely conventional to describe the coördinate perturbations as ‘short-periodic’.