# Aristarchus of Samos

The Greek astronomer Aristarchus of Samos (ca. 310-230 B.C.) hypothesized that the earth revolves yearly about the sun and daily rotates about its own axis. He attempted to determine the relative sizes and distances of the sun, moon, and earth.

Born on the island of Samos, Aristarchus studied at Athens in the Lyceum under Straton of Lampsacus, who was the head of the Peripatetic school from 288/287 to 270/269 B.C.

## Heliocentric System

Though Aristarchus is known to have written on problems of vision, light, and color, his primary work was in astronomy, specifically on the interrelations of the sun, moon, and earth. With respect to their relative positions he pointed out that, mathematically, one can imagine the earth rotating about the sun as easily as the sun about the earth; all that is required is a vastly increased radius of the sphere of the fixed stars and the daily rotation of the earth about its own axis rather than the rotation of the sphere of the fixed stars. Though all serious astronomers in antiquity and the Middle Ages would have realized the mathematical equivalence of the geocentric and heliocentric hypotheses (and many do refer to it), arguments from physics compelled them to accept geocentricity, as Aristarchus himself does in his sole surviving book. Only with the abandonment of Aristotelian physics could the heliocentric hypothesis attain credibility.

Following many predecessors in the 6th to 4th century (Cleostratus, Meton, Eudoxus, and Callippus), Aristarchus tried to fix a "Great Year"—a period in which integer numbers of days, solar years, and the various kinds of months would occur exactly. His Great Year of 2,434 solar years contains 45 exeligmi, and each exeligmus contains three periods in which the period-relation holds: 223 synodic months = 239 anomalistic months = 242 draconic months. Neither the exeligmus nor its third (both Babylonian period-relations) contains an integer number of years, though the exeligmus has an integer number of days. The 45 exeligmi of Aristarchus's Great Year are based on the following period-relations: 30,105 synodic months = 32,265 anomalistic months = 32,670 draconic months = 32,539 sidereal months = 889,020 days = 2,434 solar years.

## Relative Sizes of the Sun and Moon

In his treatise On the Sizes and Distances of the Sun and Moon, using Euclid's laws of proportions, Aristarchus seeks to define the limits of the ratios of the sizes and distances of the sun, moon, and earth to each other. He uses the situation of a lunar eclipse, assuming that the diameters of the sun and moon are each 2° and the diameter of the disk of the cone of the earth's shadow at the distance of the moon is 4°; thus he uses a diameter of both sun and moon that is about four times what it should be (in another lost work he gave a more correct value of 0:30°) and ignores the variation in the distance and apparent diameter of the moon.

He arrives at the conclusions that the distance of the sun from the earth is between 18 and 20 times that of the moon from the earth, that the diameter of the sun is between 19/3 and 43/6 times the diameter of the earth and the diameter of the earth between 108/43 and 60/19 times the diameter of the moon, and that the diameter of the moon is between 1/30 and 2/45 of the distance of the moon from the earth. Though these results are not correct, their limitations are largely imposed by the state of the mathematics available to Aristarchus, though the erroneous estimate of the moon's diameter contributes. The method was more fully developed and fruitfully applied by Hipparchus a century later.