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We consider the Earth-Moon planar circular restricted three body problem andpresent a proof of the existence orbits, which approach arbitrarily close toone of the primary masses, and at the same time after each approach they moveaway from the mass to a prescribed distance. In other words the orbitsoscillate between being arbitrarily close to collision and away from it. Weachieve our goal with the use of topological tools combined with rigorousinterval computations. We use the Levi-Civita regularization and validate thatthe dynamics in the regularized coordinates leads to a good topologicalalignment between various sets. We then perform shadowing arguments that thisleads to the required dynamics in the original coordinates of the system.

Oscillatory collision approach in the Earth-Moon restricted three body problem