We analyze 1187 observations of about 860 unique candidate Jovian Trojan asteroids listed in the 3rd release of Sloan Digital Sky Survey (SDSS) Moving Object Catalog. The sample is complete at the faint end to r=21.2 mag (apparent brightness) and H=13.8 (absolute brightness, approximately corresponding to 10 km diameter). A subset of 297 detections of previously known Trojans were used to design and optimize a selection method based on observed angular velocity that resulted in the remaining objects. Using a sample of objects with known orbits, we estimate that the candidate sample contamination is about 3%. The well-controlled selection effects, the sample size, depth and accurate five-band UV-IR photometry enabled several new findings and the placement of older results on a firmer statistical footing. We find that there are significantly more asteroids in the leading swarm (L4) than in the trailing swarm (L5): N(L4)/N(L5)=1.6$pm$0.1, independently of limiting objects size. The overall counts normalization suggests that there are about as many Jovians Trojans as there are main-belt asteroids down to the same size limit, in agreement with earlier estimates. We find that Trojan asteroids have a remarkably narrow color distribution (root-mean-scatter of only $sim$0.05 mag) that is significantly different from the color distribution of the main-belt asteroids. The color of Trojan asteroids is correlated with their orbital inclination, in a similar way for both swarms, but appears uncorrelated with the objects size. We extrapolate the results presented here and estimate that Large Synoptic Survey Telescope will determine orbits, accurate colors and measure light curves in six photometric bandpasses for about 100,000 Jovian Trojan asteroids.
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