Although the lighted area of the full moon is only twice as large as that of the moon at first or last quater, the full moon is about nine times brighter. Why?

sequoianoir

When studying the brightness of the Moon, there are three angles which we need to consider: The angle of incidence (the angle at which the light from the Sun hits the {Moon;)} the angle of emergence ( the angle at which light is reflected off the surface of the Moon) and the phase angle (which is the angle between the light from the sun and the light reflected to earth.) When half the Moon is visible (first or last quarter) it is illuminated from the side and very little light is actually reflected in the direction of Earth. Think of it as a convex mirror being viewed from the side (edgeways on) and not from the front, although it is direstly facing the light source. As the Moon gets fuller, the Sun is slowly moving around to a position 'behind' the Earth so all 3 of these angles decrease. Not only does more surface of the Moon get illuminated, more of the light is directed back towards the Earth. This is like the mirror slowly being turned more face on towards you. At the same time the light source is moving from the side to behind you (but not that you are in the way - otherwise you would eclipse it) When the Earth obstructs sun light that would normally fall on the Moon , you have a Lunar eclipse! At full Moon all angles are zero - the maximum visible surface is illuminated and the direction of reflection is 'perfect'. In fact some of the light is reflected back from the Earth and back towards the Moon making it slightly brighter still ! Dec 08 02, 7:12 PM

Bryce

The luner surface is full of craters, mountain walled plains, and other irregularities. These surface features cast long shadows when illuminated obliquely by the sun, as during the first or last quarter. The shadows make the surface appear darker than at full moon when the sun shines directly from above over most of the lunar surface. Note that due to the eccentricity of the moon's orbit around the earth one full moon's brightness is not equal to another's! The distance to the moon varies from as little as 356,400 km to as much as 466,700 km, and accordingly light of a full moon can vary by as much as 30%. Dec 09 02, 1:13 AM