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The Restricted 3-Body Problem models the motion of a body of negligible massunder the gravitational influence of two massive bodies called the primaries.If one assumes that the primaries perform circular motions and that all threebodies are coplanar, one has the Restricted Planar Circular 3-Body Problem(RPC3BP). In rotating coordinates, it can be modeled by a two degrees offreedom Hamiltonian, which has five critical points called the Lagrange pointsL1,.., L5.  The Lagrange point L3 is a saddle-center critical point which is collinearwith the primaries and beyond the largest of the two. In this paper, we obtainan asymptotic formula for the distance between the stable and unstablemanifolds of L3 for small values of the mass ratio $0<\mu\ll 1$. In particularwe show that L3 cannot have (one round) homoclinic orbits.  If the ratio between the masses of the primaries $\mu$ is small, thehyperbolic eigenvalues of L3 are weaker, by a factor of order $\sqrt\mu$, thanthe elliptic ones. This rapidly rotating dynamics makes the distance betweenmanifolds exponentially small with respect to $\sqrt\mu$. Thus, classicalperturbative methods (i.e the Melnikov-Poincar\'e method) can not be applied.  The obtention of this asymptotic formula relies on the results obtained inthe prequel paper on the complex singularities of the homoclinic of a certainaveraged equation and on the associated inner equation.  In this second paper, we relate the solutions of the inner equation to theanalytic continuation of the parameterizations of the invariant manifolds of L3via complex matching techniques. We complete the proof of the asymptoticformula for their distance showing that its dominant term is the one given bythe analysis of the inner equation.

Breakdown of homoclinic orbits to L3 in the RPC3BP (II). An asymptotic formula