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We present lightcurves of the afterglow of GRB050502A, including very earlydata at t-t_{GRB} < 60s. The lightcurve is composed of unfiltered ROTSE-IIIboptical observations from 44s to 6h post-burst, R-band MDM observations from1.6 to 8.4h post-burst, and PAIRITEL J H K_s observations from 0.6 to 2.6hpost-burst. The optical lightcurve is fit by a broken power law, wheret^{alpha} steepens from alpha = -1.13 +- 0.02 to alpha = -1.44 +- 0.02 at\~5700s. This steepening is consistent with the evolution expected for thepassage of the cooling frequency nu_c through the optical band. Even in ourearliest observation at 44s post-burst, there is no evidence that the opticalflux is brighter than a backward extrapolation of the later power law wouldsuggest. The observed decay indices and spectral index are consistent witheither an ISM or a Wind fireball model, but slightly favor the ISMinterpretation. The expected spectral index in the ISM interpretation isconsistent within 1 sigma with the observed spectral index beta = -0.8 +- 0.1;the Wind interpretation would imply a slightly (~2 sigma) shallower spectralindex than observed. A small amount of dust extinction at the source redshiftcould steepen an intrinsic spectrum sufficiently to account for the observedvalue of beta. In this picture, the early optical decay, with the peak at orbelow 4.7e14 Hz at 44s, requires very small electron and magnetic energypartitions from the fireball.Comment: 22 pages, including 3 tables and 1 figure, Accepted by Ap

Optical Light Curve and Cooling Break of GRB 050502A