Aristarchus of Samos was a Greek astronomer of the early Hellenistic period, active at Alexandria approximately 280–260 BC. He had been a student of the Peripatetic Strato of Lampsacus and was associated with the early generation of scholars at the Mouseion of Alexandria. His substantial mathematical and astronomical work appears to have been considerable; one substantial treatise of his survives in full (On the Sizes and Distances of the Sun and Moon), one substantive astronomical claim survives at second hand through Archimedes, and the rest of his work is lost.
The substantive claim that has given Aristarchus his modern importance is the heliocentric hypothesis — the proposal that the Earth orbits the Sun rather than the Sun orbiting the Earth.
The Archimedes attestation
The only primary source for Aristarchus’s heliocentric proposal is a single passage from Archimedes’s Sand-Reckoner, a mathematical treatise written approximately 230 BC at Syracuse. Archimedes opens the Sand-Reckoner with a statement of the mathematical problem he intends to solve (computing an upper bound on the number of sand-grains that would fill a sphere the size of the cosmos), and in setting up the problem he attributes a specific astronomical model to Aristarchus:
Aristarchus of Samos brought out a book consisting of certain hypotheses, in which it appears, as a consequence of the assumptions made, that the universe is many times greater than that now so called. His hypotheses are that the fixed stars and the Sun remain unmoved, that the Earth revolves about the Sun in 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 centre 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 centre of the sphere bears to its surface.
The Archimedes passage substantively contains the full classical heliocentric model: Sun at the centre, Earth in orbit, fixed stars at distance, the dimensional argument required to explain why no stellar parallax is observed despite the Earth’s annual motion (the stars must be at greater distance than was generally believed). Copernicus would substantively recover precisely the same set of claims in 1543; Tycho Brahe and Kepler would substantively refine them; Galileo’s telescopic observations would substantively confirm them; the substantive modern Solar System model is the same model Aristarchus had proposed.
Why it was rejected
The Greek astronomical mainstream — most importantly Hipparchus in the 2nd century BC and Claudius Ptolemy in the 2nd century AD — rejected the Aristarchian heliocentric model on substantively empirical and substantively dynamical grounds.
The empirical objection was stellar parallax. If the Earth moves through a annual orbit, the apparent positions of the fixed stars must shift detectably as the Earth changes its viewing baseline by the orbital diameter. No such shift had been measured (and indeed none would be measured until 1838, by Bessel observing 61 Cygni). The Hipparchian-Ptolemaic response was the obvious one: if there is no observable parallax, either the Earth is not moving or the stars are at substantively greater distance than is geometrically plausible. The substantive Ptolemaic verdict was the former.
The dynamical objection came from substantively Aristotelian physics. A moving Earth required the body of the planet to be physically moving through space at velocities; if so, objects on the Earth’s surface should not behave as if stationary; arrows shot straight up should fall to the west; clouds should appear to drift eastward. None of these effects was observed. The substantive Aristotelian-Ptolemaic explanation was that the Earth was substantively stationary at the centre of the cosmos.
The substantive objection from the Hellenistic religious-philosophical mainstream was a third one. The Stoic philosopher Cleanthes of Assos (the head of the Stoic school after Zeno) substantively argued that Aristarchus should be substantively prosecuted on charges of impiety for substantively displacing the Earth from its cosmological centre. No prosecution appears to have been undertaken, but the substantive theological-philosophical hostility to the heliocentric proposal was.
The eighteen-century gap
The substantive astronomical mainstream of the Hellenistic, Roman, and Islamic periods rejected the Aristarchian model. The geocentric Ptolemaic system substantively dominated European and Islamic astronomy from approximately 150 AD to 1543 AD — approximately 1,400 years.
The substantive revival came with Nicolaus Copernicus’s De revolutionibus orbium coelestium (1543), which substantively re-proposed the Aristarchian model with mathematical detail and appeal to the Hellenistic precedent. Copernicus’s preface explicitly cites Aristarchus by name. Galileo’s telescopic observations of 1610 substantively confirmed the model empirically (the phases of Venus and the moons of Jupiter were substantively incompatible with Ptolemaic geocentrism); Tycho’s 1572 supernova and the 1577 comet had substantively undermined the substantively Aristotelian cosmology that geocentrism depended on; Kepler’s three laws (1609–1619) substantively quantified the model into the substantive shape it still has.
The stellar parallax that had been the Hipparchian-Ptolemaic objection was substantively observed for the first time by Friedrich Bessel in 1838 — about 2,100 years after Aristarchus had predicted it would be observable in principle if substantively refined enough instruments could be built.
What survives
Aristarchus’s substantive surviving treatise On the Sizes and Distances of the Sun and Moon uses substantively pure geometry (no observational astronomy beyond a single estimated solar angular separation) to substantively derive a substantively wrong but substantively methodologically sound estimate of the relative distances and sizes of the Sun and Moon. The substantive figure he derived (the Sun roughly 19 times further than the Moon) is substantively about a twentieth of the actual ratio (the actual ratio is about 390), but the substantive geometric method is substantively correct.
The substantively heliocentric work survives only through Archimedes. The original Aristarchian treatise was lost in late antiquity, probably during the substantive transitions that produced the parallel collapse of the library and lecture-hall infrastructure of Alexandria.