Recent progress in the computation of collision solutions for Near-Earth Asteroids (NEAs) allows one to identify future possible impacts from asteroids which have already been discovered [Milani et al. 1999]. Some of these asteroids have only been observed for a very short time, so that the uncertainty of their positions on the sky grows rapidly, and very soon they have to be considered lost. In the long run most of these lost asteroids will be recovered serendipitously, but, there is no guarantee that they would be recovered before a possible impact.
Although the best thing would be just to recover a lost potential impactor, it may turn out that the recovery is not feasible with the available telescope resources. The next best thing to do is to make sure that the asteroid is not on a collision course. Even for a lost asteroid, it remains possible to exclude a collision solution with a rather small observational effort.
To do this we need to be able to characterize the footprint on the sky that the asteroid would have if it were on a collision course, and to develop a suitable observational strategy to check whether it is or it is not there. The adoption of this procedure can eliminate a potential threat, and also alleviate a possible public perception that the astronomical community has failed in its obligation of monitoring NEAs, not only for scientific purposes, but also to guarantee the safety of the Earth. This is possible with a small observational effort because the collision at some later time can be thought of as an observation, and in that sense the possible collider has a well determined orbit, as it is typical of asteroids observed at multiple oppositions, so that its position on the sky has a small uncertainty.
The possible impact solutions for all NEAs are announced, and continuously updated, by the NEODyS online information service (http://newton.dm.unipi.it/neodys). For asteroids discovered after the start of operations of NEODyS, the announcement of possible impact solutions can result in quick response by observers, resulting in further observations that reduce the uncertainty region enough to eliminate the impact risk. This sequence of events took place in the recent case of 1999 RM45. In this case within a couple of days of the announcement the impact solutions could be ruled out by new observations. However, a totally different situation occurs in the case of impact solutions found for a lost asteroid. Currently there is only one such asteroid for which a collision with our planet is known to be possible (although unlikely) in the next 50 years: 1998 OX4, for which there are orbits compatible with the observations leading to collisions in 2014, 2038, 2044 and 2046. In the future, thanks to the increasing efficiency of both the telescopic searches and of the computational methods to detect possible impacts, there could be many more examples of this problem.
To explain with the necessary precision the solution we propose, we need to introduce a few concepts, in particular the notion of Virtual Impactor (VI); they are presented in a non-mathematical way in the following subsections. In Sec. 2 we describe the algorithms to detect the VIs and to predict where in the sky we should ``search'' for them; this section is rather mathematical, and is not required to understand the subsequent sections. In Sec. 3 we discuss the first real example of a lost potential impactor, namely asteroid 1998 OX4, and suggest how the VIs associated with it can be ``destroyed''. In Sec. 4 we discuss the general principles and the validation procedures that should apply to a VI ``search and destroy'' campaign.