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When an asteroid has a few observations over a short time span theinformation contained in the observational arc could be so little that a fullorbit determination may be not possible. One of the methods developed in recentyears to overcome this problem is based on the systematic ranging and combinedwith the Admissible Region theory to constrain the poorly-determinedtopocentric range and range-rate. The result is a set of orbits compatible withthe observations, the Manifold Of Variations, a 2-dimensional compact manifoldparametrized over the Admissible Region. Such a set of orbits represents theasteroid confidence region and is used for short-term hazard predictions. Inthis paper we review the Manifold Of Variations method and make a detailedanalysis of the related probabilistic formalism.

The Manifold Of Variations: hazard assessment for short-term impactors