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On the uncertainty of the minimal distance between two confocal Keplerian orbits
We introduce a regularization for the minimal distance maps, giving the
locally minimal values of the distance between two points on two confocal
Keplerian orbits. This allows to define a meaningful uncertainty for the
minimal distance also when orbit crossings are possible, and it is useful to
detect the possibility of collisions or close approaches between two celestial
bodies moving approximatively on these orbits, with important consequences in
the study of their dynamics. An application to the orbit of a recently
discovered near-Earth asteroid is also given.