A few simple observations about the moon's eclipses can lead us to an important result concerning the force of gravity.
The moon's size is very nearly ½°, that is to say the from the of the to the is ½° - Fig. 39 - and during an eclipse of the sun the moon's only just the earth's surface. We know this because the patch of total darkness cast by the moon's shadow is only a few miles wide. When an eclipse of the moon occurs though, in Fig. 40, the earth's is much than the moon and the moon is for some time. By measuring this time it is easily worked out that the earth's shadow is 2½ moon wide where the moon it and that the earth itself is therefore 3½ moon diameters across.This, combined with the ½° angle, enables us to work out by geometry that the moon is about 60 times the earth's radius away from the earth.

(Fom: Physics, by David Bryan, Hodder & Stoughton, 1971)