Masses of the Main Asteroid Belt and the Kuiper Belt from the Motions of Planets and Spacecraft

Dynamical mass estimates for the main asteroid belt and the trans-Neptunian Kuiper belt have been found from their gravitational influence on the motion of planets. Discrete rotating models consisting of moving material points have been used to model the total attraction from small or as yet undetected bodies of the belts. The masses of the model belts have been included in the set of parameters being refined and determined and have been obtained by processing more than 800 thousand modern positional observations of planets and spacecraft. We have processed the observations and determined the parameters based on the new EPM2017 version of the IAA RAS planetary ephemerides. The large observed radial extent of the belts (more than 1.2 au for the main belt and more than 8 au for the Kuiper belt) and the concentration of bodies in the Kuiper belt at a distance of about 44 au found from observations have been taken into account in the discrete models. We have also used individual mass estimates for large bodies of the belts as well as for objects that spacecraft have approached and for bodies with satellites. Our mass estimate for the main asteroid belt is $(4.008 \pm 0.029)\cdot 10^{-4} \ m_{\oplus}$ (3$\sigma$). The bulk of the Kuiper belt objects are in the ring zone from 39.4 to 47.8 AU. The estimate of its total mass together with the mass of the 31 largest trans-Neptunian Kuiper belt objects is $(1.97 \pm 0.030)\cdot 10^{-2} \ m_{\oplus}$ (3$\sigma$), which exceeds the mass of the main asteroid belt almost by a factor of 50. The mass of the 31 largest trans-Neptunian objects (TNOs) is only about 40% of the total one.