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How did Hipparchus use a solar eclipse to estimate the Moon’s distance?

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Engraving of six astronomers, with Hipparchus seated at center and, from left to right, Galileo, Johannes Hevelius, Tycho Brahe, Nicolaus Copernicus, and Ptolemy standing, each holding scientific instruments. — Hipparchus “Six astronomers,” the frontispiece of *Astronomica Institutio* (1692) by Jan Luyts, engraving after drawing by Gerard Hoet. Hipparchus is seated at center with from left to right: Galileo, Johannes Hevelius, Tycho Brahe, Nicolaus Copernicus, and Ptolemy.

Hipparchus estimated the Moon’s distance by utilizing an observation of a solar eclipse that was total near the Hellespont but only partial at Alexandria.1

He attributed the difference in the appearance of the eclipse between these two locations entirely to the Moon’s parallax—the apparent displacement of an object when viewed from different vantage points. By assuming the Sun was indefinitely far away (similar to the stars), he used this parallax to calculate that the mean distance of the Moon from Earth was 77 times Earth’s radius.1