Date of Award
Master of Science in Astronautical Engineering
Department of Aeronautics and Astronautics
Joshua Hess, PhD.
High-altitude parking orbits could provide resiliency to the military space infrastructure by providing redundancy in key assets, allowing for rapid reconstitution of underperforming satellites. When analyzing trajectories in a high-altitude regime, two-body models of Keplerian motion become less accurate since the gravitational effects of other bodies are no longer negligible. To provide a higher fidelity model of the dynamics in a high-altitude regime, a multiple-body model can be used. In the Earth-Moon system, a spacecraft operating in the high-altitude regime can be modeled with three-body dynamics. With certain simplifying assumptions, the model is called the circular-restricted three-body problem (CR3BP). The CR3BP provides unique dynamics that could be exploited to provide beneficial trajectories unavailable and unobservable in a lower-order model. The tradeoff for using this higher-order model is there is no closed-form analytical solution and the dynamics are chaotic. Methods to search for optimal trajectories within the CR3BP are analyzed to determine viability in rapid mission development. A direct orthogonal collocation pseudospectral method is utilized to generate fuel- and time- optimal trajectories within the CR3BP. These results are compared to benchmarks from two-body dynamics, such as Hohmann transfers. Numerical approaches to finding optimal solutions are highly dependent on initial guesses to converge on candidate optimal solutions. To compound this issue, the chaotic dynamics in the CR3BP mean small variations in the initial conditions could lead to wildly varying trajectories. The results from the current research provide a methodology to establish a framework for rapid mission development in a dynamical environment, which may be essential to maintain space superiority and responsiveness.
DTIC Accession Number
Dahlke, Jacob A., "Optimal Trajectory Generation in a Dynamic Multi-Body Environment using a Pseudospectral Method" (2018). Theses and Dissertations. 1764.