To Explain the World: The Discovery of Modern Science

by Steven Weinberg

Hipparchus made astronomical observations in Alexandria from 161 BC to 146 BC, and then continued until 127 BC, perhaps on the island of Rhodes. Almost all his writings have been lost; we know about his astronomical work chiefly from the testimony of Claudius Ptolemy, three centuries later. One of his calculations was based on the observation of an eclipse of the Sun, now known to have occurred on March 14, 189 BC. In this eclipse the disk of the Sun was totally hidden at Alexandria, but only four-fifths hidden on the Hellespont (the modern Dardanelles, between Asia and Europe). Since the apparent diameters of the Moon and Sun are very nearly equal, and were measured by Hipparchus to be about 33' (minutes of arc) or 0.55°, Hipparchus could conclude that the direction to the Moon as seen from the Hellespont and from Alexandria differed by one-fifth of 0.55°, or 0.11°. From observations of the Sun Hipparchus knew the latitudes of the Hellespont and Alexandria, and he knew the location of the Moon in the sky at the time of the eclipse, so he was able to work out the distance to the Moon as a multiple of the radius of the Earth. Considering the changes during a lunar month of the apparent size of the Moon, Hipparchus concluded that the distance from the Earth to the Moon varies from 71 to 83 Earth radii. The average distance is actually about 60 Earth radii.