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We discuss measurements of the properties of about 10,000 asteroids detectedin 500 deg2 of sky in the Sloan Digital Sky Survey (SDSS) commissioning data.The moving objects are detected in the magnitude range 14 < r < 21.5, with abaseline of 5 minutes. Extensive tests show that the sample is at least 98%complete, with the contamination rate of less than 3%.  We find that the size distribution of asteroids resembles a broken power-law,independent of the heliocentric distance: D^{-2.3} for 0.4 km < D < 5 km, andD^{-4} for 5 km < D < 40 km. As a consequence of this break, the number ofasteroids with r < 21.5 is ten times smaller than predicted by extrapolatingthe power-law relation observed for brighter asteroids (r < 18). The observedcounts imply that there are about 530,000 objects with D>1 km in the asteroidbelt, or about four times less than previous estimates.  The distribution of main belt asteroids in the 4-dimensional SDSS color spaceis bimodal, and the two groups can be associated with S (rocky) and C(carbonaceous) asteroids. A strong bimodality is also seen in the heliocentricdistribution of asteroids and suggests the existence of two distinct belts: theinner rocky belt, about 1 AU wide (FWHM) and centered at R~2.8 AU, and theouter carbonaceous belt, about 0.5 AU wide and centered at R~3.2 AU. The colorsof Hungarias, Mars crossers, and near-Earth objects are more similar to theC-type than to S-type asteroids, suggesting that they originate in the outerbelt. (abridged).Comment: 89 pages, 31 figures, submitted to A

Solar System Objects Observed in the Sloan Digital Sky Survey Commissioning Data