| Abstract: |
| Within an unperturbed central-body gravitational field, Keplerian orbital elements provide both a coordinate representation and an intuitive geometric description, enabling clear visualization of orbit properties and intuitive design of spaceflight solutions. In contrast, for the Circular Restricted Three-Body Problem (CR3BP), no compact and expressive parameterization exists that plays an analogous role to Keplerian elements or other two-body coordinate sets. This limitation creates a disconnect between commonly used state representations and salient orbit features that are readily observable yet not rigorously encoded. Topological data analysis (TDA) offers a promising pathway to bridge this gap by augmenting coordinate descriptions with topological, potentially geometry-aware, signatures and distance metrics that capture the intrinsic shape of orbits. Such representations may enable a more faithful characterization of nonlinear dynamical behavior and provide a principled basis for comparing underlying structures and signals linked to orbit motion. Extending these ideas across models of varying fidelity, as well as to observational sensor data streams, opens new opportunities for enhanced space domain awareness and orbit motion inference in cislunar environments. |
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