Asteroid masses and improvement with Gaia

Context.The ESA astrometric mission Gaia, due for launch in late 2011, will observe a very large number of asteroids ($\thicksim$350 000 brighter than V = 20) with an unprecedented positional precision (at the sub-milliarcsecond level). Aims.Gaia will yield masses of the hundred largest asteroids from gravitational perturbations during close approaches with target asteroids. The objective is to develop a global method to obtain these masses which will use simultaneously all perturbers together with their target asteroids. In this paper, we outline the numerical and statistical methodology and show how to estimate the accuracy. Methods.The method that we use is the variance analysis from the formulation of observed minus calculated position (O-C). We assume a linear relationship between the (O-C) and the fitted parameters which are the initial position and velocity of the asteroids and the masses of perturbers. The matrix giving the partial derivatives with respect to the positions and masses is computed by numerical integration of the variational equations. Results.We show that with Gaia it will be possible to derive more than 100 masses of minor planets 42 of which with a precision better than 10%