On-Orbit Operational Range Computation Using Gauss’s Variational Equations with Perturbations

Abstract

Aircraft operational range, the distance an aircraft can travel with a fixed quantity of fuel, is an intuitive measure that provides strategic and tactical insight to the end user. Currently, there is no rigorously defined and derived operational range measure for on-orbit spacecraft operations with which to inform strategic decisions and planning. This paper illustrates how operational range may be computed in the context of orbital motion using optimal control theory and how existing results in reachability set computation may be leveraged. The solution method presented incidentally solves the free-time minimum-impulse full orbit-element transfer problem under perturbations. The derived optimal control policy reproduces known optimal free-time minimum basis maneuvers. The methodology presented is shown to have the capability to exactly capture the minimum-fuel free-time operational range volumes, although numerical solution algorithm errors persist. The approach is validated using known minimum-fuel optimal maneuvers, and numerical examples of on-orbit operational range for low Earth orbits, geostationary transfer orbits, and geostationary Earth orbits are given. Applications to spacecraft operations are detailed.