Start with the few knowns. We know, as did the Ancient Greeks, that the Moon travels around the Earth at a constant speed—about 29 days per revolution. The diameter of the Earth is also known to be about 12,875 kilometers, or 8,000 miles. By tracking the movement of the Earth’s shadow across the Moon, Greek astronomers found that the Earth’s shadow was roughly 2.5 times the apparent size of the Moon and lasted roughly three hours from the first to last signs of the shadow.
From these measurements, it was simple geometry that allowed Aristarchus (circa 270 B.C.) to determined that the Moon was around 60 Earth radii away (about 386,243 km or 240,000 miles). This is quite close to the currently accepted figure of 60.3 radii.
You can follow Aristarchus’ method in your own backyard if you have a clear view of a Lunar eclipse. Track the movement of the Earth’s shadow on the Moon by drawing the changes and time the eclipse. Use your measurements to determine the Moon’s distance.
