Length of the lunar crescent

Observations of the crescent moon are studied to determine why the illuminated portion does not extend to a 180-deg arc. The observations are discussed in terms of optical aids, seeing effects, and cusp brightness to examine possible explanations. Hapke's (1984) model is employed to measure lunar surface brightnesses for the present observations and those of Danjon (1932, 1936). The crescent tends to get narrower and dimmer as the moon gets closer to the sun; a model is proposed in which the visible arc length varies as a function of a particular sun-moon angle. Scatter is also predicted for the model which depends on the varying observer sensitivity and other effects. The predictions of the model are found to match all the observational data effectively. An important conclusion is that the crescent moon will be invisible when the moon is within 7 degrees of the sun.