Determination of asteroid masses I. (1) Ceres, (2) Pallas and (4) Vesta

The masses of the three largest asteroids: (1) Ceres, (2) Pallas and (4) Ve sta were determined from gravitational perturbations exerted on respectivel y 25, 2, and 26 selected asteroids. These masses were calculated by means o f the least-squares method as weighted means of the values obtained separat ely from the perturbations on single asteroids. Special attention was paid to the selection of the observations of the asteroids. For this purpose, a criterion based on the requirement that the post-selection distribution of the (O - C) residuals should be Gaussian was implemented. The derived masse s are: (4.70 +/- 0.04) x 10(-10) M., (1.21 +/- 0.26) x 10(-10) M., and (1.3 6 +/- 0.05) x 10(-10) M. for (1) Ceres, (2) Pallas and (4) Vesta, respectiv ely. We also show how the fact that a statistically substantial number of pertur bed asteroids is used in the determination of the mass of (1) Ceres and (4) Vesta increases the reliability of their mass determination because effect s like the flaws of the dynamical model and/or the observational biases can cel out. In case of Ceres and Vesta, these effects have a very small influe nce on the final result. The number of acceptable mass determinations of Pa llas is much smaller, but can be increased in the future when the dynamical model is improved. We indicate some promising encounters with Pallas.