Lunar crescent visibility
We report the results of five Moonwatches, in which more than 2000 observers throughout North America attempted to sight the thin lunar crescent. For each Moonwatch we were able to determine the position of the Lunar Date Line (LDL), the line along which a normal observer has a 50% probability of spotting the Moon. The observational LDLs were then compared with predicted LDLs derived from crescent visibility prediction algorithms. We find that ancient and medieval rules are higly unreliable. More recent empirical criteria, based on the relative altitude and azimuth of the Moon at the time of sunset, have a reasonable accuracy, with the best specific formulation being due to Yallop. The modern theoretical model by Schaefer (based on the physiology of the human eye and the local observing conditions) is found to have the least systematic error, the least average error, and the least maximum error of all models tested. Analysis of the observations also provided information about atmospheric, optical and human factors that affect the observations. We show that observational lunar calendars have a natural bias to begin early.