Pareto-Optimal Earth–Moon Transfers via L1 Inertial Geometry and Inclination Penalty

Low-energy Earth–Moon transfers via the L1 Lagrange point are characterized within the planar Circular Restricted Three-Body Problem (CR3BP). A scan of the Jacobi constant C and injection angle θ0 from a 200 km low Earth orbit yields a sevenpoint Pareto front with total ∆v from 3,853 to 4,050 m/s and time of flight (TOF) from 2.2 to 57.6 days; the optimum saves 104 m/s (2.6%) over the patched-conic baseline. The Pareto trajectories are reconstructed in the Earth-centered inertial (ECI)frame, and the osculating Keplerian elements, specific orbital energy, and angular momentum are computed along each arc. Short-TOF transfers remain quasi-Keplerian, whereas the Pareto-optimal case (TOF = 57.6 d) exhibits sustained eccentricity oscillations in [0.93, 0.96] at constant semi-major axis (a ≈ 165 Mm) and orbital energy (E ≈ −1.2 MJ/kg), with angular momentum exchanged with the Moon during repeated L1 near-passages. The hyperbolic excess velocity at Hill-sphere entry decreases monotonically from 1,023 to 510 m/s, and the approach angle lies in [132◦, 180◦] forall cases, indicating head-on arrivals characteristic of L1-gateway capture. Extension to inclined departures gives an out-of-plane ∆v penalty growing linearly from 30 m/s (Cape Canaveral, 28.5◦) to 108 m/s (polar, 90◦), two to three orders of magnitude belowthe kinematic plane-change cost; inclined departures require TOF above approximately13 days