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We discuss the applicability of the Melnikov and Landau-Teller theories inobtaining semi-analytical estimates of the speed of chaotic diffusion insystems driven by the separatrix-like stochastic layers of a resonancebelonging to the `second fundamental model' (SFM)\cite{henrard1983second}.Stemming from the analytic solution for the SFM in terms of Weierstrasselliptic functions, we introduce stochastic Melnikov and Landau-Teller modelsallowing to locally approximate chaotic diffusion as a sequence of uncorrelated`jumps' observed in the time series yielding the slow evolution of an ensembleof trajectories in the space of the adiabatic actions of the system. Such jumpsoccur in steps of one per homoclinic loop. We show how a semi-analyticaldetermination of the probability distribution of the size of the jumps can bearrived at by the Melnikov and Landau-Teller approximate theories. Computingalso the mean time required per homoclinic loop, we arrive at estimates of thechaotic diffusion coefficient in such systems. As a concrete example, we referto the long-term diffusion of a small object (e.g. Earth navigation satelliteor space debris) within the chaotic layers of the so-called $2g+h$ lunisolarresonance, which is of the SFM type. After a suitable normal form reduction ofthe Hamiltonian, we compute estimates of the speed of diffusion of theseobjects, which compare well with the results of numerical experiments.

Semi-analytical estimates for the chaotic diffusion in the Second Fundamental Model of Resonance. Application to Earth's navigation satellites