Most of the craters on the surface of the Moon were created by the collision of minor bodies of the Solar System, in particular asteroids coming from the Main Belt as a consequence of different types of resonance. Our aim is to investigate the dynamics of such asteroids, paying special attention on the hyperbolic invariant manifolds associated with the equilibrium point L2 of the Earth – Moon system within the framework of the Circular Restricted Three – Body Problem. We analyze how different distributions of initial conditions for transit trajectories and the value considered for the relative Earth – Moon distance can vary the probability of a lunar impact. Then, we add the gravitational effect of the Sun by means of the Bicircular Restricted Four – Body Problem, showing that the initial phase associated with the Sun and the ratio between the Earth – Moon – Sun distance and the Earth – Moon one can affect the collision pattern in terms of lunar longitude and latitude.