The original text has been lost, but a reference in Archimedes' book The Sand Reckoner describes a work in which he advanced the heliocentric model as an alternative hypothesis to geocentrism: Aristarchus suspected the stars were other suns that are very far away, and that in consequence there was no observable parallax, that is, a movement of the stars relative to each other as the Earth moves around the Sun. Since stellar parallax is only detectable with telescopes, his accurate speculation was unprovable at the time. It is a common misconception that the heliocentric view was held as sacrilegious by the contemporaries of Aristarchus. Lucio Russo traces this to Gilles Ménage's printing of a passage from Plutarch's On the Apparent Face in the Orb of the Moon, in which Aristarchus jokes with Cleanthes, who is head of the Stoics, a sun worshipper, and opposed to heliocentrism. In the manuscript of Plutarch's text, Aristarchus says Cleanthes should be charged with impiety. Ménage's version, published shortly after the trials of Galileo and Giordano Bruno, transposes an accusative and nominative so that it is Aristarchus who is purported to be impious. The resulting misconception of an isolated and persecuted Aristarchus is still transmitted today. According to Plutarch, while Aristarchus postulated heliocentrism only as a hypothesis, Seleucus of Seleucia, a Hellenistic astronomer who lived a century after Aristarchus, maintained it as a definite opinion and gave a demonstration of it but no full record has been found. In his Naturalis Historia, Pliny the Elder later wondered whether errors in the predictions about the heavens could be attributed to a displacement of the Earth from its central position. Pliny and Seneca referred to the retrograde motion of some planets as an apparent phenomenon, which is an implication of heliocentrism rather than geocentrism. Still, no stellar parallax was observed, and Plato, Aristotle, and Ptolemy preferred the geocentric model, which was held as true throughout the Middle Ages. The heliocentric theory was revived by Copernicus, after which Johannes Kepler described planetary motions with greater accuracy with his three laws. Isaac Newton later gave a theoretical explanation based on laws of gravitational attraction and dynamics. After realizing that the sun was much larger than the earth and the other planets, Aristarchus concluded that planets revolved around the sun. But this brilliant insight, it turned out, "was too much for the philosophers of the time to swallow and astronomy had to wait 2000 years more to find the right path."
The only known 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 two 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 the text of Aristarchus. Aristarchus claimed that at half moon, the angle between the Sun and Moon was 87°. He might have proposed 87° as a lower bound, since gauging the lunar terminator's deviation from linearity to one degree of accuracy is beyond the unaided human ocular limit. 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 implicit false solar parallax of slightly under three degrees was used by astronomers up to and including Tycho Brahe, c. 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; thus, the diameter of the Sun was calculated to be between 18 and 20 times the diameter of the Moon.
