Hidden Mass in the Asteroid Belt

Abstract The total mass of the asteroid belt is estimated from an analysis of the motions of the major planets by processing high precision measurements of ranging to the landers Viking-1, Viking-2, and Pathfinder (1976–1997). Modeling of the perturbing accelerations of the major planets accounts for individual contributions of 300 minor planets; the total contribution of all remaining small asteroids is modeled as an acceleration caused by a solid ring in the ecliptic plane. Mass M ring of the ring and its radius R are considered as solve-for parameters. Masses of the 300 perturbing asteroids have been derived from their published radii based mainly on measured fluxes of radiation, making use of the corresponding densities. This set of asteroids is grouped into three classes in accordance with physical properties and then corrections to the mean density for each class are estimated in the process of treating the observations. In this way an improved system of masses of the perturbing asteroids has been derived. The estimate M ring ≈(5±1)×10 −10 M ⊙ is obtained ( M ⊙ is the solar mass) whose value is about one mass of Ceres. For the mean radius of the ring we have R ≈2.80 AU with 3% uncertainty. Then the total mass M belt of the main asteroid belt (including the 300 asteroids mentioned above) may be derived: M belt ≈(18±2)×10 −10 M ⊙ . The value M belt includes masses of the asteroids which are already discovered, and the total mass of a large number of small asteroids—most of which cannot be observed from the Earth. The second component M ring is the hidden mass in the asteroid belt as evaluated from its dynamical impact onto the motion of the major planets. Two parameters of a theoretical distribution of the number of asteroids over their masses are evaluated by fitting to the improved set of masses of the 300 asteroids (assuming that there is no observational selection effect in this set). This distribution is extrapolated to the whole interval of asteroid masses and as a result the independent estimate M belt ≈18×10 −10 M ⊙ is obtained which is in excellent agreement with the dynamical finding given above. These results make it possible to predict the total number of minor planets in any unit interval of absolute magnitude H . Such predictions are compared with the observed distribution; the comparison shows that at present only about 10% of the asteroids with absolute magnitude H

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