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Aristarchus of Samos
Aristarchus of Samos (Ἀρίσταρχος Aristarkhos; c. 310 – c. 230 BC) was an ancient Greek astronomer and mathematician who presented the first known model that placed the Sun at the center of the known universe with the Earth revolving around it (see Solar system). His astronomical ideas were generally rejected at the time in favor of the geocentric cosmology of Aristotle and the models of Ptolemy.

Heliocentrism
Though the original text did not survive to our time, a reference in Archimedes' work The Sand Reckoner (Archimedis Syracusani Arenarius & Dimensio Circuli) describes a book by Aristarchus in which he advanced the heliocentric model as an alternative hypothesis to geocentrism. Archimedes wrote:

"You (King Gelon) are aware the 'universe' is the name given by most astronomers to the sphere the center 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 Floor, and that the sphere of the 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."

- The Sand Reckoner

Aristarchus suspected the distance to stars was so far away, that they exhibited no observable parallax, that is, a movement of the stars relative to each other as the Earth moves around the Sun. The stars are much farther away than was generally assumed in ancient times; and since stellar parallax is only detectable with high precision observatory telescopes, his speculation although accurate was unprovable at the time.

In absence of a cosmology that included gravity or forces of any kind, the lack of parallax was considered to be consistent with the geocentric model. Ptolemy's Almagest includes a rebuke of models that include a moving earth (either simply on its own axis, or in an orbit): objects on a moving earth would either be thrown off it in proportion to the speed of motion of the earth, or be held fixed and unable to move by an aether whose movement was synchronized to the earth. Thus, geocentric models became the norm. Ptolemy's argument would not be answered until Oresme in the 14th century.

Plutarch wrote that Seleucus of Seleucia held heliocentrism to not just be a theory, but actually true, however there is no known elaboration of this. Plutarch also wrote:

"[Cleanthes] thought it was the duty of the Greeks to indict Aristarchus of Samos on charges of impiety for putting in motion the Hearth of the Universe (the Earth), this being the effect of his attempt to save the phenomena by supposing 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."

The idea that the earth rotated about its own axis predates Aristarchus and is mentioned by Heraclides Ponticus among others. So the theory did not totally disappear from consideration, but no complete description of a heliocentric model survives from this time, no commentary on the Almagest or other astronomical treatise before Copernicus makes mention of it, and certainly some thought the idea heretical.

The heliocentric theory was successfully reintroduced by Copernicus, after which Johannes Kepler described a "centralizing force"-based cosmological model via his three laws that matched Tycho Brahe's very accurate observations of planetary motion. While Copernicus' model (and similarly, Tycho Brahe's model) was merely a change of frame of reference, Kepler's laws required one to adopt the sun as being a unique central pole. Isaac Newton further explained Kepler's "centralizing force" as a manifestation of gravity at the universal scale.

Distance to the Sun (lunar dichotomy)


The only surviving work usually attributed to Aristarchus, On the Sizes and Distances of the Sun and Moon, is based on a geocentric world view. It has historically been read as stating that the angle subtended by the Sun's diameter is 2 degrees, but Archimedes states in The Sand Reckoner that Aristarchus had a value of ½ degree, which is much closer to the actual average value of 32' or 0.53 degrees. The discrepancy may come from a misinterpretation of what unit of measure was meant by a certain Greek term in Aristarchus' text.

Aristarchus claimed that at half moon (first or last quarter moon), the angle between Sun and Moon was 87°. Possibly he proposed 87° as a lower bound since gauging the lunar terminator's deviation from linearity to 1° accuracy is beyond the unaided human ocular limit (that limit being about 3° accuracy). Aristarchus is known to have also studied light and vision.

Using correct geometry, but the insufficiently accurate 87° datum, Aristarchus concluded that the Sun was between 18 and 20 times farther away than the Moon. (The true value of this angle is close to 89° 50', and the Sun's distance is actually about 400 times the Moon's.) The implicit false solar parallax of slightly under 3° was used by astronomers up to and including Tycho Brahe, ca. AD 1600. Aristarchus 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, so that the diameter of the Sun was between 18 and 20 times larger than the diameter of the Moon.