Determination of asteroid masses

The masses of the three largest asteroids: (1) Ceres, (2) Pallas and (4) Vesta were determined from gravitational perturbations exerted on respectively 25, 2, and 26 selected asteroids. These masses were calculated by means of the leastsquares method as weighted means of the values obtained separately 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 masses are: (4.70 ± 0.04) × 10−10 M , (1.21 ± 0.26) × 10−10 M , and (1.36 ± 0.05) × 10−10 M for (1) Ceres, (2) Pallas and (4) Vesta, respectively. We also show how the fact that a statistically substantial number of perturbed asteroids is used in the determination of the mass of (1) Ceres and (4) Vesta increases the reliability of their mass determination because effects like the flaws of the dynamical model and/or the observational biases cancel out. In case of Ceres and Vesta, these effects have a very small influence on the final result. The number of acceptable mass determinations of Pallas is much smaller, but can be increased in the future when the dynamical model is improved. We indicate some promising encounters with Pallas.