  In this paper we propose a notion of stability, that we call $\epsilon
-N$-stability, for systems of particles interacting via Newton's gravitational
potential, and orbiting a much bigger object. For these systems the usual
thermodynamical stability condition, ensuring the possibility to perform the
thermodynamical limit, fails, but one can use as relevant parameter the maximum
number of particles $N$ that guarantees the $\epsilon -N$-stability. With some
judicious but not particularly optimized estimates, borrowed from the classical
theory of equilibrium statistical mechanics, we show that our model has a good
fit with the data observed in the Solar System, and it gives a reasonable
interpretation of some of its global properties.
