How was the distance to the Moon measured?

Building on how Eratosthenes measured the Earth's diameter, ancient Greeks also tackled measuring the Earth-Moon distance. This required comparing the moon's distance to the Earth's diameter or some other terrestrial measurement. The video discusses three methods, focusing on Aristarchus's approach using lunar eclipses.

Aristarchus, known for proposing the heliocentric system, devised a method based on observing how the Moon enters the Earth's shadow during a lunar eclipse. By overlaying circles on a photograph of a partial lunar eclipse, it's observed that the Earth's shadow is approximately 2.5 times larger than the Moon's diameter. Ancient astronomers had to make these comparisons directly in the sky, which was challenging for accuracy.

Another method to determine the size ratio involved observing the phases of a lunar eclipse. By measuring the duration of the Moon entering the shadow (T1) and the duration of being fully within the shadow (T2), it was found that T2 is about 1.5 times T1. This observation implies that the diameter of the Earth's shadow is 2.5 times larger than the Moon's diameter, consistent with the initial photo observation.

The Earth's shadow is conical because the Sun is much larger than the Earth. The width of the Earth's shadow at the Moon's position during an eclipse is smaller than the Earth's actual diameter. A total solar eclipse provides a crucial clue: the Moon perfectly covers the Sun, and its shadow collapses to a point on Earth. This indicates that the Earth's shadow also narrows by the diameter of the Moon at that distance, making the Earth's diameter 3.5 times larger than the Moon's diameter.

To find the Earth-Moon distance, the angular size of the Moon is measured using a simple tool: a rod with a diopter and a movable cylinder. By adjusting the cylinder's distance until it just covers the Moon, a proportional relationship is established. In the experiment, the distance from the eye to the cylinder was 1600mm for a 14mm cylinder, meaning the distance to the Moon is 114 times the Moon's diameter. Dividing this by 3.5 (the Earth's diameter to Moon's diameter ratio) yields a distance of 33 Earth diameters, close to the modern average of 30 Earth diameters.