This paper explores the application of stochastic continuation methods in the context of mission analysis for spacecraft trajectories around libration points in the planar circular restricted three-body problem. Traditional deterministic approaches have limitations in accounting for uncertainties, requiring a two-step process involving Monte Carlo techniques for assessing the robustness of the deterministic design. This might lead to suboptimal solutions and to a long and time-consuming design process. Stochastic continuation methods, which extend numerical continuation techniques to moments of probability density functions, offer a promising alternative. This paper aims to pioneer the application of stochastic continuation procedures in mission analysis, incorporating and acknowledging the stochastic nature of spacecraft missions from the early design phases. By extending existing frameworks to handle fixed points of stroboscopic or Poincaré mappings, the study focuses on robustifying and enhancing trajectory design by considering uncertainties in the determination of periodic orbits. The proposed approach has the potential to discover new solutions that may remain hidden in deterministic analyses, offering improved mission design outcomes. 

Specifically, this work concentrates on the planar circular restricted three-body problem, assuming uncertainties in both initial conditions and the mass ratio parameter. Stochastic continuation is employed to identify equilibrium points and periodic orbits in this uncertain dynamical system. The generalization of steady states and periodic orbits in uncertain environments is discussed, demonstrating the effectiveness of stochastic continuation in identifying safe operational regions in uncertain astrodynamics problems.