Determination of Masses of Ceres and Vesta from Their Perturbations on Four Asteroids

Masses of 1 Ceres and 4 Vesta were determined simultaneously from observations of four asteroids: 197 Arete, 203 Pompeja, 348 May, and 486 Cremona. We collected 785 observations of these four asteroids covering the observation interval 1879--1995; in this period the asteroids approached several times Ceres and Vesta closer than to 0.1 a.u. We applied the recurrent power series method to integrate numerically equations of motion of the four asteroids, including the perturbations caused by the nine major planets and by the four biggest asteroids: Ceres, Pallas, Vesta, and Hygiea. Twenty six normal equations, corresponding to 1536 observational equations, have been solved by means of the least squares method to determine the masses of Ceres and Vesta along with corrections to the orbital elements of Arete, Pompeja, May, and Cremona. Thus we found the masses of Ceres and Vesta in the solar unit mass equal to (4.622 pm 0.071) times 10^{-10} and (1.396 pm 0.043) times 10^{-10}, respectively.