Sensitivity Analysis of Separation Time Along Weak Stability Boundary Transfers

Abstract: This study analyzes the sensitivity of the dynamics around Weak Stability Boundary Transfers (WSBT) in the elliptical restricted three-body problem. With WSBTs increasing popularity for cislunar transfers, understanding its inherently chaotic dynamics becomes pivotal for guiding and navigating cooperative spacecrafts as well as detecting non-cooperative objects. We introduce the notion of separation time to gauge the deviation of a point near a nominal WSBT from the trajectory's vicinity. Employing the Cauchy-Green tensor to identify stretching directions in position and velocity, the separation time, along with the Finite-Time Lyapunov Exponent are studied within a ball of state uncertainty scaled to typical orbit determination performances.