Numerical Solution to Vinti’s Problem

Abstract

A practical, calculable solution to Vinti’s problem is offered. Vinti’s problem describes the motion of a satellite orbiting an oblate planet, including the point mass and oblateness terms and differing from the actual geopotential only at the higher harmonics. Vinti’s original solution is extended to cover motion over a rotating Earth. An eccentric-anomaly-like transform removes the singularities in the elliptic integrals, rendering them accessible to numerical calculation. The prediction problem requires the simultaneous solution of two “Kepler’s equations.” Reduction to canonical action angle variables can also be accomplished via numerical techniques. This new realization of Vinti’s solution is free of series expansions that limit accuracy and uses only simple well-understood numerical techniques. Possible use of Vinti’s solution for further efforts is discussed.