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It is known that most of the craters on the surface of the Moon were createdby the collision of minor bodies of the Solar System. Main Belt Asteroids,which can approach the terrestrial planets as a consequence of different typesof resonance, are actually the main responsible for this phenomenon. Our aim isto investigate the impact distributions on the lunar surface that low-energydynamics can provide. As a first approximation, we exploit the hyberbolicinvariant manifolds associated with the central invariant manifold around theequilibrium point L_2 of the Earth - Moon system within the framework of theCircular Restricted Three - Body Problem. Taking transit trajectories atseveral energy levels, we look for orbits intersecting the surface of the Moonand we attempt to define a relationship between longitude and latitude ofarrival and lunar craters density. Then, we add the gravitational effect of theSun by considering the Bicircular Restricted Four - Body Problem. As furtherexploration, we assume an uniform density of impact on the lunar surface,looking for the regions in the Earth - Moon neighbourhood these collidingtrajectories have to come from. It turns out that low-energy ejecta originatedfrom high-energy impacts are also responsible of the phenomenon we areconsidering.

A Motivating Exploration on Lunar Craters and Low-Energy Dynamics in the Earth -- Moon System