09/13/2021 – Ephemeris – The Greeks knew the size and shape of the Earth and estimated the distance to the Moon a long time ago

This is Bob Moler with Ephemeris for Monday, September 13th. Today the Sun will be up for 12 hours and 37 minutes, setting at 7:56, and it will rise tomorrow at 7:20. The Moon, at first quarter today, will set at 11:57 this evening.

The Ancient Greeks used lunar eclipses to determine that Earth is a sphere, and worked on determining the distance to the Moon. From ancient times, the Greeks knew that an eclipse of the Moon was caused by the Earth’s shadow falling on the Moon. Since the Earth’s shadow was always circular, no matter where the Moon was in the sky during an eclipse, the Earth must be a sphere since that’s the only three-dimensional body that always casts a circular shadow. They also used the size of the Earth’s shadow to estimate the distance to the Moon. The lunar distance, on average, is 60.8 times the Earth’s radius away. The first estimates were about one third of that. Hipparchus in the 2nd century BC got much closer. It got even better from there.

The astronomical event times given are for the Traverse City/Interlochen area of Michigan (EDT, UT – 4 hr). They may be different for your location.

Addendum

Partial Lunar Eclipse showing circular arc of the Earth’s shadow. Taken 04:15 UT August 17, 1970. Credit: the author.

The size of the Earth was unknown until Eratosthenes did in 240 BC. He came up with the circumference of the Earth to a fairly high degree. The Circumference is equal to the radius of a sphere or circle by 2πr.