Estimations of masses of the largest asteroids and the main asteroid belt from ranging to planets, Mars orbiters and landers

Perturbations from asteroids affect significantly the orbits of the inner planets and should be taken into account when high-accuracy planetary ephemerides are constructed. On the other hand, from analysis of these perturbations by processing available precise measurements of radar ranging to the Viking, Pathfinder, Mars Global Surveyor, Odyssey spacecraft and planets (1961-2003) it appears possible to derive values of some physical parameters of the asteroids. Masses of the some large asteroids have been determined individually from data above (in GM_i/GM_⊙\cdot 10^-12): (1) Ceres 474.9 ±2.0 (2) Pallas 103.6 ±2.0 (3) Juno 14.2 ±0.6 (4) Vesta 135.8 ±2.0 (7) Iris 5.2 ±0.8 (324) Bamberga 5.1 ±0.8 Masses of the other most significant about 300 asteroids have been derived from their latest published diameters, making use of the corresponding densities. The diameters are based on IRAS, MSX infrared data, as well as observations of occultations of stars by minor planets and radar observations. The mean dendensities for C,S,M taxonomy classes have been estimated while processing the observations. The total contribution of all remaining small asteroids is modeled as an acceleration caused by a solid ring in the ecliptic plane. Two parameters that characterize the ring (its mass and radius) are included in the set of solution parameters. As the result the total mass of the main asteroid belt including the 300 asteroids mentioned above and the asteroid ring was obtained: M_belt = (15 ± 1) \cdot 10^-10 M_⊙. A expression for estimating the total number of minor planets in any unit interval of absolute magnitude H was derived and compared with the observed distributions of the asteroids (72688 numbered, 160313 unnumbered) and with the distribution of the SAM model by Tedesco et al.