Effect of Coordinate Switching on Simulation Accuracy of Translunar Trajectories

Abstract

This thesis focuses on the effect of round-off error in the accurate simulation of translunar trajectories. The three-body dynamics can be posed in either an Earth-centered (EC) or Moon-centered (MC) frame. In this study, multiple translunar trajectories were simulated to determine if there is an optimal switch point from an EC to MC frame that minimizes round-off error. A high fidelity baseline simulation was first created, and the entire trajectory was propagated in EC. Comparison trajectories were then simulated at lower precision using both EC and MC frames. The trajectory was propagated first in EC and then switched to MC at a preselected switch point. By testing a range of switch points, it was determined that switching to the MC frame during the first 10\% of the trajectory led to significantly higher round-off errors. For any later switch points, there was little sensitivity in the round-off error. There was, however, some correlation to switch points located at the radii of well established gravitational spheres of the Moon. The importance of round-off error in simulation of translunar trajectories is also demonstrated by calculation of the Lyapunov exponents along the trajectory.