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

We discuss measurements of the properties of similar to 13,000 asteroids de tected in 500 deg(2) of sky in the Sloan Digital Sky Survey (SDSS) commissi oning data. The moving objects are detected in the magnitude range 14 <r* < 21.5, with a baseline of similar to5 minutes, resulting in typical velocity errors of similar to3%. Extensive tests show that the sample is at least 9 8% complete, with a contamination rate of less than 3%. We find that the si ze distribution of asteroids resembles a broken power law, independent of t he heliocentric distance : D-2.3 for 0.4 km less than or similar to D less than or similar to 5 km, and D-4 for 5 km less than or similar to D less th an or similar to 40 km. As a consequence of this break, the number of aster oids with r* <21.5 is 10 times smaller than predicted by extrapolating the power-law relation observed for brighter asteroids (r* <less than or simila r to> 18). The observed counts imply that there are about 670,000 objects w ith D>1 km in the asteroid belt, or up to 3 times less than previous estima tes. 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 fac tor 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 as teroids brighter than r* <21.5 at opposition. Only about a third of these a steroids have been previously observed, and usually in just one band. The d istribution 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-(ca rbonaceous) type asteroids. A strong bimodality is also seen in the helioce ntric distribution of asteroids : the inner belt is dominated by S-type ast eroids centered at R<similar to>2.8 AU, while C-type asteroids, centered at R similar to 3.2 AU, dominate the outer belt. The median color of each cla ss becomes bluer by about 0.03 mag AU(-1) as the heliocentric distance incr eases. 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 aste roids. In about 100 deg(2) of sky along the celestial equator observed twic e 2 days apart, we find one plausible Kuiper belt object (KBO) candidate, i n agreement with the expected KBO surface density. The colors of the KBO ca ndidate are significantly redder than the asteroid colors, in agreement wit h colors of known KBOs. We explore the possibility that SDSS data can be us ed to search for very red, previously uncataloged asteroids observed by 2MA SS, by extracting objects without SDSS counterparts. We do not find evidenc e for a significant population of such objects; their contribution is no mo re than 10% of the asteroid population.