An eclipse-calibrated periodic lunar model reproduces realistic translunar Lagrangian solutions

Low-energy transfer orbits near the Earth-Moon Lagrangian points are key to cost-effective space missions, yet their design relies on models that oversimplify the Moon’s orbital complexity, especially affecting libration orbits near L2 . Here, using a new lunar model calibrated on the Saros eclipse cycle, known since antiquity, we demonstrate the existence of Saros-periodic dynamical substitutes for L1 , L2 . These orbits reproduce the Lagrangian libration amplitudes computed from JPL ephemerides, unlike previous periodic models, while retaining periodic time dependence useful for orbital computations. The model’s link to specific eclipses occurring at mirror configurations naturally identifies realistic initial conditions consistent with the real Sun-Earth-Moon system. The solar eclipse of 2 August 2027 is near such a configuration, so the model supports maneuver design for decades.