Solar system objects observed in the Sloan Digital Sky Survey commissioning data

We discuss measurements of the properties of ∼ 13,000 asteroids detected in 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 a baseline of ∼ 5 minutes, resulting in typical velocity errors of ∼ 3%. Extensive tests show that the sample is at least 98% complete, with a 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, and D^-4 for 5 km ≲ D ≲ 40 km. As a consequence of this break, the number of asteroids with r* < 21.5 is 10 times smaller than predicted by extrapolating the power-law relation observed for brighter asteroids (r* ≲ 18). The observed counts imply that there are about 670,000 objects with D > 1 km in the asteroid belt, or up to 3 times less than previous estimates. The revised best estimate for the impact rate of the so-called "killer" asteroids (D > 1 km) is about 1 every 500,000 yr, uncertain to within a factor of 2. We predict that by its completion SDSS will obtain about 100,000 near simultaneous five-band measurements for a subset drawn from 340,000 asteroids brighter than r* < 21.5 at opposition. Only about a third of these asteroids have been previously observed, and usually in just one band. The distribution of main-belt asteroids in the four-dimensional SDSS color space is bimodal, and the two groups can be associated with S-(rocky) and C-(carbonaceous) type asteroids. A strong bimodality is also seen in the heliocentric distribution of asteroids: the inner belt is dominated by S-type asteroids centered at R ∼ 2.8 AU, while C-type asteroids, centered at R ∼ 3.2 AU, dominate the outer belt. The median color of each class becomes bluer by about 0.03 mag AU^-1 as the heliocentric distance increases. The observed number ratio of S and C asteroids in a sample with r* < 21.5 is 1.5:1, while in a sample limited by absolute magnitude it changes from 4:1 at 2 AU, to 1:3 at 3.5 AU. In a size-limited sample with D > 1 km, the number ratio of S and C asteroids in the entire main belt is 1:2.3. The colors of Hungarias, Mars crossers, and near-Earth objects, selected by their velocity vectors, are more similar to the C-type than to S-type asteroids. In about 100 deg² of sky along the celestial equator observed twice 2 days apart, we find one plausible Kuiper belt object (KBO) candidate, in agreement with the expected KBO surface density. The colors of the KBO candidate are significantly redder than the asteroid colors, in agreement with colors of known KBOs. We explore the possibility that SDSS data can be used to search for very red, previously uncataloged asteroids observed by 2MASS, by extracting objects without SDSS counterparts. We do not find evidence for a significant population of such objects; their contribution is no more than 10% of the asteroid population.