Implicit Runge-Kutta Methods for Orbit Propagation

Accurate and ecient orbital propagators are critical for space situational awareness because they drive uncertainty propagation which is necessary for tracking, conjunction analysis, and maneuver detection. We have developed an adaptive, implicit Runge-Kuttabased method for orbit propagation that is superior to existing explicit methods, even before the algorithm is potentially parallelized. Specifically, we demonstrate a significant reduction in the computational cost of propagating objects in low-Earth orbit, geosynchronous orbit, and highly elliptic orbit. The new propagator is applicable to all regimes of space, and additional features include its ability to estimate and control the truncation error, exploit analytic and semi-analytic methods, and provide accurate ephemeris data via built-in interpolation. Finally, we point out the relationship between collocation-based implicit Runge-Kutta and Modified Chebyshev-Picard Iteration.