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We prove the presence of chaotic dynamics for the classical two-body Kepler problem with a time-periodic gravitational coefficient oscillating between two fixed values. The set of chaotic solutions we detect is coded by the number of revolutions in each period. The chaotic dynamics is obtained for large period  T  as well as for small angular momentum μ. In particular, we provide an explicit lower bound on  T  and explicit upper bound on μ which guarantee the existence of complex dynamics. We get our results by applying a simple and well-known topological method, the  stretching along the path  technique. Our results are robust with respect to small perturbations of the gravitational coefficient and to the addition of a small friction term.

Chaotic Dynamics of the Kepler Problem with Oscillating Singularity