Orbital dynamics at the equilibrium points under velocity perturbations in the CRTBP: Application to the earth-moon system

In this study, we introduce a systematic numerical methodology to analyze the influence of both the angle and the magnitude of velocity perturbations on trajectories emerging from equilibrium points in the Circular Restricted Three Body Problem (CRTBP). The proposed technique enables a comprehensive assessment of the long-term behavior of velocity perturbed trajectories, including collisions, escapes, and persistent motions around the primaries. Through a series of graphical representations and statistical analyses, we identify global dynamical patterns that offer deeper insights into the system's structure. The findings could have significant applications in the early stages of space mission design, particularly in the preliminary phase where potential trajectories are identified using the CRTBP as a reference model. Additionally, the results contribute to the assessment of station-keeping strategies for future missions involving equilibrium points. Finally, we apply the proposed methodology to the Earth-Moon system, identifying multiple global dynamical patterns. A comparison of these patterns provides new insights into the similarities and differences of the global dynamics at the libration points under velocity perturbations.