

.. Aristarchus of Samos Aristarchus or Aristarch (Greek:
Ἀρίσταρχος, Arístarchos; 310 BC – ca. 230
BC) was a Greek astronomer and mathematician, born
on the island of Samos, in Greece. He was the first
person to present an explicit argument for a
heliocentric model of the solar system, placing the
Sun, not the Earth, at the center of the known
universe. He was influenced by the Pythagorean
Philolaus of Kroton, but, in contrast to Philolaus,
he had both identified the central fire with the
Sun, as well as putting other planets in correct
order from the Sun. His astronomical ideas were
rejected in favor of the geocentric theories of
Aristotle and Ptolemy until they were successfully
revived nearly 1800 years later by Copernicus and
extensively developed and built upon by Johannes
Kepler and Isaac Newton. The crater Aristarchus on
the Moon is named in his honor.
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Heliocentrism The only work usually attributed to Aristarchus which has survived to the present time, On the Sizes and Distances of the Sun and Moon, is based on a geocentric world view. It is peculiar and possibly informative that this work reckons the sun's diameter as 2 degrees, rather than the correct value, 1/2 degree. The latter diameter is known from Archimedes to have been Aristarchus's actual value. Though the original text has been lost, a reference in Archimedes' book The Sand Reckoner (Archimedis Syracusani Arenarius & Dimensio Circuli) describes another work by Aristarchus in which he advanced an alternative hypothesis of the heliocentric model. Archimedes wrote: You ['you' being 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 orbit, 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.Aristarchus thus believed the stars to be very far away, and saw this as the reason why there was no visible parallax, that is, an observed movement of the stars relative to each other as the Earth moved around the Sun. The stars are in fact much farther away than the distance that was generally assumed in ancient times, which is why stellar parallax is only detectable with telescopes. The geocentric model, consistent with planetary parallax, was assumed to be an explanation for the unobservability of the parallel phenomenon, stellar parallax. The rejection of the heliocentric view was common, as the following passage from Plutarch suggests (On the Apparent Face in the Orb of the Moon): Cleanthes (a contemporary of Aristarchus and head of the Stoics) thought it was the duty of the Greeks to indict Aristarchus on the charge of impiety for putting in motion the hearth of the universe … 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.The only other astronomer from antiquity who is known by name and who is known to have supported Aristarchus' heliocentric model was Seleucus of Seleucia, a Mesopotamian astronomer who lived a century after Aristarchus.
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 18 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. 1600 A. D. 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. He thus concluded that the diameter of the Sun was about 20 times larger than the diameter of the Moon; which, although wrong, follows logically from his data. It also leads to the conclusion that the Sun's diameter is almost seven times greater than the Earth's; the volume of Aristarchus's Sun would be almost 300 times greater than the Earth. This difference in sizes may have inspired the heliocentric model. Mentioned by Archimedes and by modern scientists for being the first to propose a heliocentric "universe", Aristarchus also proposed an ancient Greek time period, his "Great Year" of 4868 solar years, equalling exactly 270 saroi, each of 18 Callippic years plus 10 and 2/3 degrees. (Syntaxis, book 4 chapter 2.) Its empirical foundation was the 4267 month eclipse cycle, cited by Ptolemy as source of the "Babylonian" month, which was good to a fraction of a second (1 part in several million). It is found on cuneiform tablets from shortly before 200 B. C., though Ptolemy did not attribute its origin to Babylon. (Due to near integral returns in lunar and solar anomaly, eclipses 4267 months apart exceptionally never deviated by more than an hour from a mean of 126007 days plus 1 hour, the value given by Ptolemy at op. cit. Thus, estimation of the length of the month was ensured to have relative accuracy of 1 part in millions.) Embedded in the Great Year was a length of the month agreeing with the Babylonian value to 1 part in tens of millions, decades before Babylon is known to have used it. There are indications that Babylon's month was exactly that of Aristarchus, which if true renders it effectively certain that one party obtained it from the other or from a common source. Aristarchus's lunar conception represents an advance of science in several respects. Previous estimates of the length of the month were in error by 114 seconds (Meton, 432 B. C.) and 22 seconds (Callippus, 330 B. C.). The attribution of a mean motion to such a motion as the moon's was possibly new. The Vatican has preserved two ancient manuscripts with estimates of the length of the year. The only ancient scientist listed for two different values is Aristarchus. It is now widely suspected that these are among the earliest surviving examples of continued fraction expressions. The most obvious interpretations are precisely computable from the manuscript numbers. The results are Aristarchus years of 365 days plus 1/152, and 365 days minus 15/4868, representing the sidereal year and the civil, supposedly tropical year. Both denominators are relatable to Aristarchus, whose summer solstice was 152 years after Meton's and whose Great Year was 4868 years. The difference between the sidereal and tropical years is identical to precession. The former value is accurate within a few seconds. The latter is erroneous by several minutes. Both are close to the values later used by Hipparchus and Ptolemy, and the precession indicated is almost precisely 1 degree per century, a muchtoolow value. Unfortunately, 1 degree per century precession was used by all later astronomers until the Arabs. The correct value in Aristarchus's time was about 1.38 degrees per century.
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