Aas 12-216 a New Numerical Integration Technique in Astrodynamics

This paper describes a new method of numerical integration and compares its efficiency in propagating orbits to existing techniques commonly used in astrodynamics. By using generalized Gaussian quadratures for bandlimited functions, the implicit Runge-Kutta scheme (a collocation method) allows us to use significantly fewer force function evaluations than other integrators. The new method computes the solution on a large time interval, leading to a different approach to force evaluation. In particular, it is sufficient to use a low-fidelity force model for most of the iterations, thus minimizing the use of a high-fidelity force model. Our goal is to develop a numerical integration technique that is faster than current methods in an effort to address the expected increase of the space catalog due to improvements in tracking capabilities.