Abstract: 

The Restricted Planar Circular Three-Body Problem models the motion of a body of negligible mass under the gravitational influence of two massive bodies moving in circular orbits. It can be modeled as a two-degrees-of-freedom Hamiltonian system with five fixed points: \(L_1,…,L_5\).

We explore the family of periodic orbits surrounding \(L_3\) and prove that each orbit possesses two-dimensional stable and unstable manifolds that intersect transversally. By the Smale-Birkhoff homoclinic theorem, this implies the existence of chaotic motions, specifically  Smale’s horseshoes, sufficiently close to \(L_3\). Furthermore, we identify a generic unfolding of a quadratic homoclinic tangency, which gives rise to Newhouse domains.