3.4 Positive Detections

So far we have discussed negative observations, but we need to discuss the consequences of a positive observation in one of the skyprints defined by some VI, even if this is unlikely to happen. It is clear that in the unfortunate event that a detection were to occur either inside or close to some VI skyprint a more serious confirmation process would become necessary. It would be essential to ascertain the correct identification of the object, at first by using its apparent motion, and then by continuing the observations over several nights. Let us assume that this confirmation procedure would be successful, and that the real asteroid was indeed very close (in the initial conditions space) to the VI.

To assess the possible consequences, we have simulated an observation only 5 seconds to the East in right ascension from the nominal prediction for the 2046 VI on February 23, 2001 (and with the same declination). As it can be see from Figure 3, this is well inside the skyprint. Using the VI orbit from the last column of Table 1 as initial guess, we have applied differential corrections and found a new nominal orbit with a close approach at 0.008 AU in January 2046. By applying the Newton's method of Sec. 2.4 we have found a VI at $\Delta \sigma =1.29$and with stretching 0.0045, which implies a probability of impact roughly 1/300.

We have also checked that this conclusion would be robust with respect to the statistical model of the observation errors, by the following procedure. We have removed from the fit the observation in 1998 resulting in the largest residual (more than 2 arcsec in R.A., to be compared with an overall RMS of 0.529 arcsec; it is indeed reasonable to consider it as an outlier). But, with the 2001 skyprint observation, the best fit solution still has a close approach in 2046 at 0.006 AU, and a VI at $\Delta \sigma=0.84$, with essentially the same probability of impact.

We can conclude from this unpleasant experiment that, if the real asteroid was to be found in one of the skyprints described above, the probability of impact would immediately increase to worrisome values. On the other hand, the asteroid would not be lost anymore, and it could be followed up to further refine the orbit; in the worst case, if the impact was confirmed by further observations, there would be plenty of time to plan for deflection.