Implementation of Gauss-Jackson Integration for Orbit Propagation
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Implementation of Gauss-Jackson Integration for Orbit Propagation 1 Matthew M. Berry' and Liam M. Healy3 Abstract 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.
Introduction Determination and prediction of orbits requires an orbit propagator that finds the phase space state of a satellite at one time based on its state at another time. This function has traditionally been performed by an analytical computation such as Hamiltonian normalization (general perturbations). While numerical integration (special perturbations) can provide a wider range of force models, until recent years the computation time required made it prohibitive for routine use in space surveillance. With greatly increased computation speeds now widely available, the daily processing of 10,000 or more satellites routinely tracked by space surveillance centers can conceivably be based on numerical integration, and a significant fraction of this number are processed numerically now. The Gauss-Jackson integrator [1] is a fixed-step predictor-corrector method. The Gauss-Jackson software used in space surveillance originated in the 1960s as part IBased on paper AAS 01-426 presented at the AAS/AIAA Astrodynamics Specialists Conference, Quebec City, Canada, July 30-August 2, 2001. 2Astrodynamics Engineer, Analytical Graphics Inc., 220 Valley Creek Blvd., Exton, PA 19341. E-mail: [email protected]. This work was completed while the first author was a Graduate Assistant in the Department of Aerospace and Ocean Engineering at Virginia Tech and an employee of the Naval Research Laboratory. 3Research Physicist, Naval Research Laboratory, Code 8233, Washington, DC 20375-5355. E-mail: [email protected].
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of the Advanced Orbit/Estimation Subsystem (AOES) [2]. Over the years, AOES has given rise to a family of astrodynamics applications used in the various space surveillance centers whose integrators are essentially unchanged, including a system known as SpecialK [3]. SpecialK has been used by Naval Network and Space Operations Command for special perturbations catalog maintenance for the last six years. Another member of the family is Astrodynamics Support Workstation (ASW) [4], used in Cheyenne Mountain to support the special perturbations catalog and in support of conjunction assessment for NASA. We have chosen to use SpecialK as the implementation on which to focus, but our analysis has broad applicability to all Gauss-Jackson integrators, including the one in ASW. This paper presents a study of the theory upon which the integrator is based, how it is implemented, and its accuracy and stability. Afte
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