Consider the Restricted Planar Elliptic Three Body Problem. This problem models the Sun-Jupiter-Asteroid dynamics. For eccentricity of Jupiter \(e_0\) small enough, we show that there exists a family of probability measures supported at the \(3 : 1\) mean motion resonance such that the push forward under the associated Hamiltonian flow has the following property. At the timescale \(te_0^{-2}\), the distribution of the Jacobi constant of the Asteroid weakly converges to an Ito diffusion process on the line as \(e_0\to 0\). This resonance corresponds to the biggest of the Kirkwood gap on the Asteroid belt in the Solar System. This is a joint work with V. Kaloshin, P. Martin and P. Roldan. Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027)