Implementation of Gauss-Jackson Integration for Orbit Propagation

The Gauss-Jackson multi-step predictor-corrector method is widely used in numerical in-tegration problems for astrodynamics and dynamical astronomy. The U.S. space surveil-lance centers have used an eighth-order Gauss-Jackson algorithm since the 1960s. In this paper, we explain the algorithm including a derivation from first principals and its relation to other multi-step integration methods. We also study its applicability to satellite orbits in-cluding its accuracy and stability