*Astron. Astrophys. 360, 411-416 (2000)*
## An analytical approximation for the MOID and its consequences
**
C. Bonanno
**
Dipartimento di Matematica, Università di Pisa, via Buonarroti 2, 56100 Pisa, Italy (bonanno@mail.dm.unipi.it)
*Received 13 March 2000 / Accepted 29 May 2000*
**Abstract**
We give an analytical formulation for the approximation of the
*Minimum Orbital Intersection Distance (MOID)* between two
elliptical orbits, and we apply it to the case of the Earth and of an
asteroid. With this formulation we are able to find an algorithm to
compute the variance of the MOID for a given asteroid and we make the
computation in the case of the asteroids whose orbit has been
determined, even if with a great uncertainty, to find cases of
asteroids that have a good probability of having a small MOID even if
their nominal orbit gives a relatively large MOID.
**Key words:** celestial mechanics, stellar
dynamics
minor planets, asteroids
This article contains no SIMBAD objects.
### Contents
© European Southern Observatory (ESO) 2000
Online publication: July 27, 2000
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