Implementation of Gauss-Jackson Integration for Orbit Propagation

This paper focuses on the Gauss-Jackson algorithm for numerical integration, which particularly suited to the computation of orbits. Other multistep integration methods for first and second order ordinary differential equations are discussed as well. Accompanying it is code for computing the coefficients. This publication is posted with the permission of the American Astronautical Society.The Gauss-Jackson multi-step predictor-corrector method is widely used in numerical integration problems for astrodynamics and dynamical astronomy. The U.S. space surveillance 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 including its accuracy and stability