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.