  We study the dynamics of two bodies moving on elliptic Keplerian orbits
around a fixed center of attraction and interacting only by means of elastic or
inelastic collisions. We show that there exists a bounded invariant region: for
suitable values of the total energy and the total angular momentum (explicitly
computable) the orbits of the bodies remain elliptic, whatever are the number
and the details of the collisions. We show that there exists a bounded
invariant region even in the case of two bodies interacting by short range
potential.
