In case a lost asteroid is Earth-crossing, there might be one (or
more) of the virtual asteroids associated with it for which an actual
collision is possible. Then there is a small nearby region filled
with collision orbits still compatible with the observations. We call
a virtual asteroid with an orbit in this region a *Virtual
Impactor* (VI).

In practice, let us suppose that some time after the discovery
apparition the orbit undergoes a close approach to the Earth; the *Modified Target Plane* (MTP) for that encounter is the plane
perpendicular to the geocentric velocity at closest approach
[Milani and Valsecchi 1999]. For some initial condition in the confidence region
in element space there is a point on the MTP representing the close
approach of the corresponding orbit. If some of the points on the MTP
are inside the cross section of the Earth, these correspond to VIs.

For this paper, we have modified the procedure to find potential collisions described recently in [Milani et al. 1999, Sec. 3]. Here we find VIs in the following way:

- 1.
- We sample the set of possible orbits by computing a large number
(typically of the order of a thousand) orbital solutions equally
spaced along the ``weak direction'' [Milani 1999]--the longest axis
of the ellipsoid approximating the confidence region in element
space--at an epoch close to observations.
- 2.
- We then propagate each of these virtual asteroid orbits until
some specified future epoch (currently we stop at 2050), and note
cases which pass near the Earth.
- 3.
- We perform detailed MTP analyses on these notable cases, and compute in an iterative manner the nearby orbital solution along the weak direction on the MTP that approaches most closely to the Earth; if the approach is to within the radius of the Earth, we have found a VI.

In the neighborhood of a VI there is a small region of the element
space containing other collision solutions; this we call a *Virtual Impactor Region* (VIR). To exclude the possibility of an
impact (at a given encounter) we need not only to perform negative
observations of the VI, but of all the orbits belonging to the VIR.