(To do this they needed to know the size of the Earth too, which Eratosthenes figured out to within a few percent.) They achieved this and much more by working carefully with the geometry of right-angle triangles and circles, and using trigonometry (or its precursors.) The classical Greeks were expert geometers, and used eclipses, both lunar and solar, to figure out how big the Moon is and how far away. And since the Moon eclipses the Sun periodically by blocking its light, the Sun must be further than the Moon. But in fact, almost everyone in the nighttime half of the Earth can see the full Moon at the same time, so it must be much further away than a couple of Earth diameters. If the Moon were close, only a small fraction of us could see it at any one time, as shown in the figure at right. Even the highest clouds, up to 10 miles high, can only be seen by those within a couple of hundred miles or so. With our global society, it’s clear that neither can be, because they can be seen everywhere around the world. Historically, many peoples thought they were quite close. But in fact (except at new moon) about half the Earth can see it at a time. If the Moon were close to Earth, then at any one time it would only be visible over a small part of the Earth, as indicated in light blue.
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