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In the third century BCE, the Greek astronomer Aristarchus of Samos estimated the distance to the moon using geometry after measuring the length of Earth's shadow during a lunar eclipse.

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Additional insights we found via 3Blue1Brown

  1. By equating the ratio between the durations of a lunar eclipse and a lunar month with a ratio between the length of the Earth's shadow and the circumference of the moon's orbit, which depended on the orbital radius, Aristarchus calculated the distance to the moon.

  2. In his "On the Sizes and Distances of the Sun and Moon," Aristarchus estimated the distance to the sun and the sizes of both the star and Earth's moon.

  3. About a century after Aristarchus's deduction of the Earth-moon distance with a lunar eclipse, Hipparchus used trigonometry and data obtained during a solar eclipse to largely validate the calculation.

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