Measuring the Moon Puzzle

In H. G. Wells' novel The First Men on the Moon, the first astronauts find supremely intelligent insects living in caves beneath the surface. Martin Gardner imagines that they would have a system of weights and measures, also supremely intelligent, in which the standard unit of distance, the “loonie”, was adopted because the moon’s surface area, expressed in square loonies, is exactly equal to the moon’s volume in cubic loonies. The moon’s diameter is 2,100 miles. How long is a loonie?

Hint: The volume of a sphere is 4/3 times the radius cubed. (Euclid XII, 18)

The Answer

This portrait of the moon was assembled from 17 images captured by the Galileo orbiter on December 7, 1992..The distinct bright ray crater at the bottom of the image is the Tycho impact basin. The dark areas are lava rock filled impact basins: Oceanus Procellarum (on the left), Mare Imbrium (center left), Mare Serenitatis and Mare Tranquillitatis (center), and Mare Crisium (near the right edge). These images are acquired through a Violet, 756 nm (red) ,and 968 nm (infrared) filter. The color is 'enhanced' in the sense that the CCD camera is sensitive to near infrared wavelengths of light beyond human vision. Photo courtesy of NASA.