HIPPARCOS minor planets: first step towards the link between the HIPPARCOS and the dynamical reference frames.

Abstract

The observations of minor planets are of particular interest for determining a possible rotation between the Hipparcos and the dynamical reference frames. In order to evaluate these unknowns, Hipparcos data are compared to the values calculated from the equations of motion. The satellite's observations are related to intermediate reference frames called Reference Great Circle (RGC). In the case of a minor planet only the abscissa along a given RGC can be observed. The associated equations of condition involve in addition the orbital elements and dynamical parameters (such as masses of minor planets, etc.). For the minor planets, the accuracy of the satellite observations is quite better than the ground-based one. So, an improved determination of the unknowns under study can be expected. In this paper, the problem of the stability of a classical least squares solution is studied. Due to correlations, the system of normal equations is highly ill-conditioned. A statistical methodology is being constructed for a better determination of the parameters of interest. It is tested on the preliminary Hipparcos data. Singular value analysis and principal components regression are performed.