Speaker: Davide Guzzetti, Department of Aerospace Engineering, Auburn. 

 

Title: Orbit Shapes in the Three-Body Problem: Importance and Applications  

 

Abstract: Within an unperturbed central-body gravitational field, Keplerian orbital elements form a coordinate set that is also an effective and intuitive topological description, amenable to the visualization of orbit properties and the design of space flight solutions. Unfortunately, a compact and elegant topological description for all orbits in the Circular Restricted Three-Body Problem (CR3BP), akin to the widely used Keplerian orbital elements, or alternative two-body-problem coordinate sets, is not currently available. As a result, there exists a disconnect between coordinate sets and topological features that may render orbit uniqueness within CR3BP dynamics. Tools from topological data analysis offer the opportunity to bridge this disconnect by further equipping coordinate sets with additional elements—signatures and distance metrics—that precisely represent orbit topology. Our current work explores the possibility of developing a comprehensive and dependable representation of dynamical structures within gravitational multi-body environments at all levels of fidelity, one that is derived from the study of persistence of topology generators, such as loops and voids. Synergistically, our work introduces spatial computing interfaces as a new paradigm for trajectory design. In particular, we explore the challenges of mapping user-drawn curves in virtual reality to feasible spacecraft trajectories in the Earth-Moon system. Such new modalities in human-computer interactions could enhance the interface between human insight and algorithmic processes. More effective visual steering strategies are particularly beneficial for trajectory designers who have temporary, limited access to the solution space of a dynamical system, like in the case of CR3BP dynamics.