Accuracy limit of modern ephemerides imposed by the uncertainties in asteroid masses

¹ Jet Propulsion Laboratory, California Institute of Technology, JPL 301-150, Pasadena, CA 91109, USA
² Institut de Mécanique céleste et de calculs des éphémérides, 77 Av. Denfert-Rochereau, 75014 Paris, France

Corresponding author: A. Fienga, fienga@bdl.fr

Received: 19 November 2001
Accepted: 20 December 2001

Abstract

Accuracy limits in the ephemerides of the four inner planets, imposed by uncertainties in the masses of the asteroids, are investigated and illustrated. We consider present-day knowledge of the asteroid masses (determined by the IRAS survey, direct dynamical determinations, ground-based photometry, occultations, etc.), and we model the distribution of those masses. This distribution is then used in a Monte Carlo study, repeatedly adjusting the ephemerides to fit the observational data, each time using a different, but equally-likely, set of asteroid masses. The differences in the resulting ephemerides are shown. If the full inherent weighting of the highly accurate ranging data is used, stretching over more than two decades, the orbits become distorted in right ascension and declination – as much as 5 kilometers or more. If the ranging is de-weighted to a level equivalent to the other two coordinates (1–2 mas, determined by VLBI), then a reasonable ephemeris results, showing uncertainties of 2–3 kilometers. It is also possible to produce an ephemeris which will extrapolate a year or so into the future at the sub-kilometer level (as is often required for spacecraft navigation). This can be done by fully-weighting only the recent observational data. However, the ephemeris farther from the fitting interval is seen to deteriorate rapidly.