Asteroid Orbits with Gaia: Inversion and Prediction

Details Asteroid Orbits with Gaia: Inversion and Prediction Asteroid Orbits with Gaia: Inversion and Prediction

Jan 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005esasp.576..223m&link_type=abstract

"Proceedings of the Gaia Symposium "The Three-Dimensional Universe with Gaia" (ESA SP-576). Held at the Observatoire de Paris-Me

Statistics

Computation

7

Gaia, Asteroids, Neos, Asteroid Orbit Computation, Asteroid Identification, Inverse Problems

Scientific paper

We present numerical methods for the inversion of forthcoming Gaia astrometry for asteroid orbital-element probability density functions. In the initial orbit computation for two or more observations, the statistical ranging technique (Ranging) allows a Monte Carlo (MC) sampling of the phase space of the orbital elements. In assessing the rapidly improving orbits in what we call the phase-transition regime, we sample the phase-space volumes of variation with the help of local linear approximations along the lines of variation (VOV sampling). For extensively observed asteroids, the standard linear approximation based on nonlinear least squares provides the differentially corrected orbital elements and their covariance matrices based on partial derivatives. We offer a short theoretical treatment of the linking and identification problems, that is, the problems of linking different observation sets and cross-identifying objects in the sets. Here we describe the general concepts of the socalled address comparison techniques that entail a onedimensional discretization for phase spaces of arbitrary dimension. We summarize the current state of the Fortran95 software developed for the Gaia orbital inverse and linking problems and, in a companion article, apply the methods to simulated Gaia astrometry.

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