Restricted Three Body Problem

The restricted three-body problem (R3BP) models the motion of a small body under the gravitational influence of two larger bodies, a fundamental problem in astrodynamics with applications in spacecraft trajectory design. Current research focuses on leveraging machine learning, particularly deep generative models like variational autoencoders and diffusion models, to efficiently explore the vast solution space of R3BP, including the discovery of periodic orbits and optimal control strategies. These data-driven approaches, complemented by techniques like Koopman theory for system linearization and particle swarm optimization for initial orbit determination, aim to improve the speed and accuracy of spacecraft mission planning and enhance our understanding of complex orbital dynamics. The resulting advancements have significant implications for optimizing fuel consumption, reducing mission time, and enabling more ambitious space exploration endeavors.