Reachability Analysis to Track Non-cooperative Satellite in Cislunar Regime

Space Domain Awareness (SDA) architectures must adapt to overcome the challenges present in cislunar space. Dynamical systems theory provides tools which may be leveraged to address some of the many challenges associated with cislunar space. The PSS is an analysis tool used to reduce dimensionality and help study the properties of the system flow. Invariant manifolds have been combined with the PSS to prescribe trajectories through various cislunar regimes by other researchers. In this work, the PSS and the invariant manifolds are used to pose a set of boundary value problems which define the \(\Delta \textbf{v}\) from a nominal \(L_2\) Lyapunov orbit through the PSS. By approximating the solutions through the PSS, the admissible controls onto these highways are approximated. One viable use for this formulation of a reduced reachable set will allow an SDA operator to intelligently task sensors to regain custody of a maneuver spacecraft. This paper examine uses concepts of a admissible region to intelligently reduce the reachability set for maneuver spacecraft and studies the efficacy for multiple maneuver windows and the affects of various user set parameters.