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

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