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 Issue A&A Volume 431, Number 2, February IV 2005 729 - 746 Celestial mechanics and astrometry http://dx.doi.org/10.1051/0004-6361:20041737

A&A 431, 729-746 (2005)
DOI: 10.1051/0004-6361:20041737

## Multiple solutions for asteroid orbits: Computational procedure and applications

A. Milani1, M. E. Sansaturio2, G. Tommei1, O. Arratia2 and S. R. Chesley3

1  Dipartimento di Matematica, Università di Pisa, via Buonarroti 2, 56127 Pisa, Italy
e-mail: [milani;tommei]@mail.dm.unipi.it
2  E.T.S. de Ingenieros Industriales, University of Valladolid Paseo del Cauce 47011 Valladolid, Spain
e-mail: [meusan;oscarr]@eis.uva.es
3  Jet Propulsion Laboratory, 4800 Oak Grove Drive, CA-91109 Pasadena, USA
e-mail: steve.chesley@jpl.nasa.gov

(Received 27 July 2004 / Accepted 20 October 2004)

Abstract
We describe the Multiple Solutions Method, a one-dimensional sampling of the six-dimensional orbital confidence region that is widely applicable in the field of asteroid orbit determination. In many situations there is one predominant direction of uncertainty in an orbit determination or orbital prediction, i.e., a "weak" direction. The idea is to record Multiple Solutions by following this, typically curved, weak direction, or Line Of Variations (LOV). In this paper we describe the method and give new insights into the mathematics behind this tool. We pay particular attention to the problem of how to ensure that the coordinate systems are properly scaled so that the weak direction really reflects the intrinsic direction of greatest uncertainty. We also describe how the multiple solutions can be used even in the absence of a nominal orbit solution, which substantially broadens the realm of applications. There are numerous applications for multiple solutions; we discuss a few problems in asteroid orbit determination and prediction where we have had good success with the method. In particular, we show that multiple solutions can be used effectively for potential impact monitoring, preliminary orbit determination, asteroid identification, and for the recovery of lost asteroids.

Key words: minor planets, asteroids -- celestial mechanics -- astrometry -- surveys