# American Institute of Mathematical Sciences

June  2007, 7(4): 755-778. doi: 10.3934/dcdsb.2007.7.755

## On the uncertainty of the minimal distance between two confocal Keplerian orbits

 1 Dipartimento di Matematica, Universitá di Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy, Italy

Received  February 2006 Revised  January 2007 Published  March 2007

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.
Citation: Giovanni F. Gronchi, Giacomo Tommei. On the uncertainty of the minimal distance between two confocal Keplerian orbits. Discrete and Continuous Dynamical Systems - B, 2007, 7 (4) : 755-778. doi: 10.3934/dcdsb.2007.7.755
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