We determine the distance to the open cluster NGC 2264 using a statistical analysis of cluster member inclinations. We derive distance-dependent values of sin i (where i is the inclination angle) for 97 stars in NGC 2264 from the rotation periods, luminosities, effective temperatures, and projected equatorial rotation velocities, v sin i, measured for these stars. We have measured 96 of the v sin i values in our sample by analyzing high-resolution spectra with a cross-correlation technique. We model the observed distribution of sin i for the cluster by assuming that member stars have random axial orientations and by adopting prescriptions for the measurement errors in our sample. By adjusting the distance assumed in the observed sin i distribution until it matches the modeled distribution, we obtain a best-fit distance for the cluster. We find the data to be consistent with a distance to NGC 2264 of 913 pc. Quantitative tests of our analysis reveals uncertainties of 40 and 110 pc due to sampling and systematic effects, respectively. This distance estimate suggests a revised age for the cluster of 1.5 Myrs, although more detailed investigations of the full cluster membership are required to draw strong conclusions.
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