Collision solutions in orbital elements space

Using the analytical method introduced by Valsecchi et al. (Proc. IAU Coll. 197, pp. 249-254, 2005), we compute the size of the region in orbital elements space containing collisions solutions. In the linearized approximation the collision region, when projected in the plane of a pair of orbital elements, is the interior of an ellipse, whose size and orientation of axes depend on the orbital elements of the impactor and, if one of the elements of the pair is the semimajor axis, on the time to impact. We analyze and discuss a number of practical cases.