On the Sizes and Distances of the Sun and Moon
Peri Megethon kai Apostematon Heliou kai Selenes
By measuring the angle between the sun and the moon at the moment of exact half-moon, the relative distances and sizes of the sun and moon compared to the earth can be calculated through pure geometry, and the resulting figures gave Aristarchus grounds to propose that the earth orbits the sun rather than the reverse.
- geometric measurement of sun and moon distances
- the only complete surviving Aristarchus treatise
- a flawed measurement but sound method
- grounds for the earliest known heliocentric hypothesis
- heliocentrism preserved only through Archimedes's testimony
Aristarchus of Samos's On the Sizes and Distances of the Sun and Moon, the only one of his works to survive complete, uses the geometry of a right triangle formed by the earth, sun, and moon at the exact moment of half-moon to calculate the ratio of the sun's distance to the moon's distance. His measured angle was badly off due to the difficulty of pinpointing exact half-moon by naked eye, but his conclusion that the sun is dramatically larger than the earth is credited by later sources, chiefly Archimedes in the Sand-Reckoner, as the reasoning that led Aristarchus to propose, roughly eighteen centuries before Copernicus, a heliocentric universe.
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