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

Giovanni F. Gronchi; Giacomo Tommei

doi:10.3934/dcdsb.2007.7.755

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2007, Volume 7, Issue 4: 755-778. Doi: 10.3934/dcdsb.2007.7.755

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

Giovanni F. Gronchi^1, and
Giacomo Tommei^1,

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

Received: January 31, 2006

Revised: December 31, 2006

Published: October 2007

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Abstract

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.

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Mathematics Subject Classification: Primary: 70F15; Secondary: 70F10.

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