The size of the Moon
In one of Aristarchus' books that did survive, he laid out the earliest known attempted calculations of the sizes and distances to the Sun and Moon.
From solar eclipses, where the Moon passes in front of the Sun, they realised that the Sun was further away. Aristarchus estimated that the size of the Moon was approximately one-third that of the Earth, based on the careful timing of lunar eclipses. He was surprisingly accurate in determining the ratio of the size of the Earth to the Moon. (the Moon has a diameter 0.27 times that of Earth).
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