Table of contents |

2 Size of the Moon 3 Distance to the Sun |

The only work of Aristarchus which has survived to the present time, *On the Sizes and Distances of the Sun and Moon*, is based on a geocentric worldview. We know through citations, however, that Aristarchus wrote another book in which he advanced an alternative hypothesis of the heliocentric model.Archimedes wrote:

- "You King Gelon are aware the 'universe' is the name given by most astronomers to the sphere the centre of which is the center of the Earth, while its radius is equal to the straight line between the center of the Sun and the center of the Earth. This is the common account as you have heard from astronomers. But Aristarchus has brought out a book consisting of certain hypotheses, wherein it appears, as a consequence of the assumptions made, that the universe is many times greater than the 'universe' just mentioned. His hypotheses are that the fixed stars and the Sun remain unmoved, that the Earth revolves about the Sun on the circumference of a circle, the Sun lying in the middle of the orbit, and that the sphere of fixed stars, situated about the same center as the Sun, is so great that the circle in which he supposes the Earth to revolve bears such a proportion to the distance of the fixed stars as the center of the sphere bears to its surface."

- "[Cleanthes, a contemporary of Aristarchus] thought it was the duty of the Greeks to indict Aristarchus of Samos on the charge of impiety for putting in motion the Hearth of the universe [i.e. the earth], . . . supposing the heaven to remain at rest and the earth to revolve in an oblique circle, while it rotates, at the same time, about its own axis."

Aristarchus observed the Moon moving through the Earth's shadow during a lunar eclipse. He estimated that the diameter of the Earth was 3 times the Moon's diameter. Using Eratosthenes' calculation that the Earth was 42,000 km in circumference, he concluded that the Moon was 14,000 km in circumference. The Moon has a circumference of about 10,916 km.

Aristarchus argued that the Sun, Moon, and Earth form a near right triangle at the moment of first or last quarter moon. He estimated that the angle was 87°. Using correct geometry, but inaccurate observational data, Aristarchus concluded that the Sun was 20 times farther away than the Moon. The Sun is actually about 390 times farther away. He pointed out that the Moon and Sun have nearly equal apparent angular sizes and therefore their diameters must be in proportion to their distances from Earth. He thus concluded that the Sun was 20 times larger than the Moon. This is also incorrect, although logical.