Orbital covariance eigenproblem for asteroids and comets

We compute eigenvalues and eigenvectors for the orbital covariances of asteroids and comets. Orbital elements and their covariances are usually determined from astrometric observations in a least-squares sense. In the phase space of orbital elements, the covariances describe a hyperellipsoid centred on the least-squares orbit. The shape and orientation of the hyperellipsoid can be studied by diagonalizing the covariances. Intriguing first results are obtained for the lost asteroid (719) Albert and the newly discovered comet C/1995 O1 Hale-Bopp.