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Just as with Venus or Jupiter, we suppose a sphere illuminated at some intensity, in this case the standard intensity above Earth's atmosphere, radiating light back and spreading it over a sphere of radius equal to our distance. So that light gets attenuated by a dimensionless factor, the square of the distance ratio (sphere radius / distance radius), which is just the half the visual angle (in radians) subtended in the sky: 1/2 1/2 degree = 0.0044 radians (at 360/2 degrees per radian). So we expect (1/0.0044)²= 50,000-fold attenuation, which is 12 magnitude factors of 100^1/5, and then further attenuated by losses in the dark rocks. We don;t know how dark they are, nor whether the answer depends on angles of illumination and observation, but if we guess 6-fold loss on average (2.5 magnitudes), then the full Moon "should" look magnitude -27 +12 + 2.5 = -12.5 as observed under clear skies. Notice, however, that with nothing to compare them to, Moon rocks don't look dark from our distance. One could easily imagine the Moon to be made of chalk. "Optical illusion"? Here is a nice experiment to check, attributed to William (alias Friedrich Wilhelm) Herschel, the discoveror of Uranus. He noticed the full moon rising over Table Mountain near Cape Town. Sunlight on the South African rocks contrasted brightly with the adjacent sunlight on Moon rocks. In both cases the sunlight had traversed about the same slant distance through Earth's atmosphere. Conclusion: Moon rocks are lots darker. You can try the same (and so can I) on 30 November  for full moon, or another day when Sun and Moon appear equally high on opposite sides of the sky. Use the wall of your (my) house in place of Table Mountain, or use a piece of gray paper at arm's length (and as control experiment, a bigger piece farther away, supported at the same angle in sunlight.) 

Notice also that we dealt only with the full moon here. Do you suppose a quarter-moon (half the visible disk illumined) sheds half as much light? It doesn't. The intensity of moonlight falls off with surprising abruptness as the Moon's phase advances At 90 degrees (quarter moon) the night is less than a tenth as bright as at full moon (0 degrees). There is a good "Discovery" exercise in this, too, if you like geometry and dare attempt a tricky integration over some trigonometric expressions. The result might help to refine our estimates last week regarding Venus.

 

Plotted from Allen, C.W., Astrophysical Quantities, 3rd edition (1973), p. 143.