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Determination of Initial Eigenorbits for Asteroids

Published online by Cambridge University Press:  12 April 2016

Karri Muinonen ,
Andrea Milani  and
Edward Bowell
Karri Muinonen
Affiliation:
Observatory, University of Helsinki, Helsinki, Finland
Andrea Milani
Affiliation:
Department of Mathematics, University of Pisa, Pisa, Italy
Edward Bowell
Affiliation:
Lowell Observatory, Flagstaff, Arizona, USA

Abstract

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We consider initial determination of asteroid orbits in the case of small numbers of observations and short observational arcs. For asteroids having long arcs, we can assess the orbital uncertainties with the help of the covariance matrix that, in the phase space of the orbital elements, defines a set of probability ellipsoids. In initial orbit determination, because of the nonlinear characteristics and multiple solutions of the inversion problem, we cannot readily use the covariance matrix to estimate the orbital uncertainties. However, by computing the eigenvalues and eigenvectors of the formal correlation matrix (that is, by deriving the eigenorbits), we can discern the most indeterminate orbital elements. Here we solve the eigenproblem for 17 single-apparition asteroids.

Type
Solar System Dynamics
Information
International Astronomical Union Colloquium , Volume 165: Dynamics and Astrometry of Natural and Artificial Celestial Bodies , 1997 , pp. 191 - 198
Copyright
Copyright © Kluwer 1997

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