  We discuss the applicability of the Melnikov and Landau-Teller theories in
obtaining semi-analytical estimates of the speed of chaotic diffusion in
systems driven by the separatrix-like stochastic layers of a resonance
belonging to the `second fundamental model' (SFM)\cite{henrard1983second}.
Stemming from the analytic solution for the SFM in terms of Weierstrass
elliptic functions, we introduce stochastic Melnikov and Landau-Teller models
allowing to locally approximate chaotic diffusion as a sequence of uncorrelated
`jumps' observed in the time series yielding the slow evolution of an ensemble
of trajectories in the space of the adiabatic actions of the system. Such jumps
occur in steps of one per homoclinic loop. We show how a semi-analytical
determination of the probability distribution of the size of the jumps can be
arrived at by the Melnikov and Landau-Teller approximate theories. Computing
also the mean time required per homoclinic loop, we arrive at estimates of the
chaotic diffusion coefficient in such systems. As a concrete example, we refer
to the long-term diffusion of a small object (e.g. Earth navigation satellite
or space debris) within the chaotic layers of the so-called $2g+h$ lunisolar
resonance, which is of the SFM type. After a suitable normal form reduction of
the Hamiltonian, we compute estimates of the speed of diffusion of these
objects, which compare well with the results of numerical experiments.
