Aristarchus and the Diameter of the Moon

Many people are familiar with Eratosthenes' discovery of the circumference of the Earth using vertical sticks and geometry, but a lesser-known and equally fascinating ancient measurement is that of Aristarchus and the Diameter of the Moon. Aristarchus was a Greek astronomer who was actually more renowned than Eratosthenes was during their respective time periods. He wrote a text known as On the Sizes and Distances, where he discussed the sizes of the Sun and Moon using measurements available to him at the time. While his calculation of the Sun's size is inaccurate (primarily due to his severe underestimation of the size and distance of the Sun), his estimated size of the Moon relative to the Earth was only about 20% off. While that sounds very large, it's essential to consider that, for a time when the size of the Earth was still groundbreaking work and telescopes hadn't yet been invented, his estimate is both clever and accurate.

Visualization of the moon relative to the Earth's Umbra.

Aristarchus began by observing that the Moon takes about 1 hour to cross a distance equal to its own diameter-- about 1 hour. During a total lunar eclipse, he noted that the moon spends around three hours within the Earth's shadow (Umbra). He reasoned that if the moon fit into the Shadow cast by the Earth three times, then the diameter of the Earth is approximately three times that of the moon's, which is close to the estimate that we know today. This led him to believe that Moon's diameter is about one-third that of Earth’s, which translates to a modernized figure in the ballpark of 4,000 km. The actual value is roughly 3,474 km, making his estimate impressively close by ancient standards.

In an era when leading scientists debated whether the Earth itself moved, this calculation was nothing short of revolutionary. It was a clear demonstration that the universe could be measured and understood. His insights were actually entirely overlooked in ancient times. Still, they now stand as early evidence of a profound shift in our understanding of the Cosmos: From myth to measurement, from assumption to inquiry, his quiet estimate of the Moon’s size was a glimpse into the future of astronomy.