An analytical approximation for the MOID and its consequences

We give an analytical formulation for the approximation of the Minimum Orbi tal Intersection Distance (MOID) between two elliptical orbits, and we appl y it to the case of the Earth and of an asteroid. With this formulation we are able to find an algorithm to compute the variance of the :MOID for a gi ven asteroid and we make the computation in the case of the asteroids whose orbit has been determined, even if with a great uncertainty, to find cases of asteroids that have a good probability of having a small MOID even if t heir nominal orbit gives a relatively large MOID.