The Asteroid Identification Problem: I. Recovery of Lost Asteroids☆

Abstract When an asteroid is lost, the observers need to know the portion of the celestial sphere where it could be recovered at a given time. This region is an image of the region, in the space of orbital elements, where the orbit is compatible with the previous observations. The map between these two regions is nonlinear; therefore the classical linear approximation can fail. Indeed it fails by a large amount when both these regions are large, which is precisely when an asteroid has been observed only over a short arc and/or it has been lost for a long time. The recovery, and identification, of asteroids long lost is very difficult if the only available prediction is a single point corresponding to the least squares solution, which could be very far from the real state; thus the availability of an efficient algorithm to bound the recovery region is essential, also to decide if the recovery is worth the effort. This paper proposes three new algorithms to better approximate the recovery region based upon approximations going beyond linearization. It gives the results of tests based upon asteroids which have been recovered by chance and could have been found in the recovery region computed by the new algorithms. Free software is available now, by means of which the new algorithms can be tested, and eventually adopted, by the observers and by the ephemerides computation centers.