A Time Regularization Scheme for Spacecraft Trajectories Subject to Multi-Body Gravity

• Published in: The Journal of the astronautical sciences Vol. 70; no. 2
• Main Authors: Leith, James, Russell, Ryan P.
• Format: Journal Article
• Language: English
• Published: New York Springer US 21.03.2023
• Subjects: Aerospace Technology and Astronautics; Engineering; Mathematical Applications in the Physical Sciences; Original Article; Space Exploration and Astronautics; Space Sciences (including Extraterrestrial Physics; Spacecraft trajectory design; Time regularization; Sundman transformation; Step size regulator; Spacecraft trajectory optimization; Flyby tour
• ISSN: 2195-0571; 2195-0571
• DOI: 10.1007/s40295-023-00364-0

A time regularization scheme is introduced that facilitates trajectory optimization in multi-body regimes. The time transformation function allows for fixed-step propagation, while eliminating the need for multiple models in patched conic approaches, and mitigating the risk of stepping over unplanned flybys. The scheme is motivated by Sundman’s two-body regularization, but accounts for multiple bodies using their spheres of influence and a Heaviside approximation. The transformation enables efficient discretization of the many types of motion that exist in multi-body regimes. The new formulation is analyzed in several restricted three-body dynamical problems, which serve as proxy models that capture the dominant features of N -body ephemeris models within the solar system. The parameters embedded in the transformation are tuned, and its performance is compared against several existing regularizations on a diverse set of examples including periodic orbits in the Earth–Moon and Saturn-Enceladus systems, a low-thrust Earth–Moon spiral, and a low-altitude Jupiter-Europa flyby. The transformation is shown to be robust to the differing conditions, outperforming the benchmarks over wide ranges of the tuning parameters. The results of the numerical experiments are used to justify a set of recommendations for parameter selection in general multi-body applications. The regularization is finally demonstrated on ephemeris-modeled Saturn system trajectories that include unplanned flybys and traverse all three levels of the sun-planet-moon solar system hierarchy.