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Aristarchus of Samos
Statue of Aristarchus of Samos at the Aristotle University of Thessaloniki
Born	c. 310 BC Samos
Died	c. 230 BC (aged around 80) Alexandria, Ptolemaic Kingdom
Nationality	Greek
Occupations	Scholar Mathematician Astronomer

Aristarchus of Samos (/ˌærəˈstɑːrkəs/; Ancient Greek: Ἀρίσταρχος ὁ Σάμιος, Aristarkhos ho Samios; c. 310 – c. 230 BC) was an ancient Greek astronomer and mathematician who presented the first known heliocentric model that placed the Sun at the center of the universe, with the Earth revolving around the Sun once a year and rotating about its axis once a day. He also supported the theory of Anaxagoras according to which the Sun was just another star.

He likely moved to Alexandria, and he was a student of Strato of Lampsacus, who later became the third head of the Peripatetic School in Greece. According to Ptolemy, he observed the summer solstice of 280 BC. Along with his contributions to the heliocentric model, as reported by Vitruvius, he created two separate sundials: one that is a flat disc; and one hemispherical.

Aristarchus was influenced by the concept presented by Philolaus of Croton (c. 470 – 385 BC) of a fire at the center of the universe, but Aristarchus identified the "central fire" with the Sun and he arranged the other planets in their correct order of distance around the Sun.

Like Anaxagoras before him, Aristarchus suspected that the stars were just other bodies like the Sun, albeit farther away from Earth. His astronomical ideas were often rejected in favor of the geocentric theories of Aristotle and Ptolemy. Nicolaus Copernicus knew that Aristarchus had a 'moving Earth' theory, although it is unlikely that Copernicus was aware that it was a heliocentric theory.

Aristarchus estimated the sizes of the Sun and Moon as compared to Earth's size. He also estimated the distances from the Earth to the Sun and Moon. He is considered one of the greatest astronomers of antiquity along with Hipparchus.

Heliocentrism

The original text has been lost, but a reference in a book by Archimedes, entitled The Sand Reckoner (Archimedis Syracusani Arenarius & Dimensio Circuli), describes a work in which Aristarchus advanced the heliocentric model as an alternative hypothesis to geocentrism:

You are now aware that the "universe" is the name given by most astronomers to the sphere the centre of which is the centre of the earth, while its radius is equal to the straight line between the centre of the sun and the centre of the earth. This is the common account (τὰ γραφόμενα) 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 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.

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 considered 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 promulgated.

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 of the demonstration 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 (unreal) 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 that was believed 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.

Distance to the Sun

The only known work attributed to Aristarchus, On the Sizes and Distances of the Sun and Moon, is based on a geocentric worldview. Historically, it has 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 half a degree, which is much closer to the average value of 32' or 0.53 degrees. The discrepancy may come from a misinterpretation of which unit of measure was meant by a Greek term in the text of Aristarchus.

Aristarchus claimed that at half moon (first or last quarter moon), the angle between the Sun and Moon was 87°. He may 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 (which is about three arcminutes of accuracy). Aristarchus is known to have studied light and vision as well.

Using correct geometry, but the insufficiently accurate 87° datum, Aristarchus concluded that the Sun was between 18 and 20 times farther away from the Earth than the Moon. (The correct value of this angle is close to 89° 50', and the Sun's distance is approximately 400 times that of the Moon.) The implicit inaccurate 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.

Size of the Moon and Sun

In On the Sizes and Distances of the Sun and Moon, Aristarchus discusses the size of the Moon and Sun in relation to the Earth. In order to achieve these measurements and subsequent calculations, he used several key notes made while observing a lunar eclipse. The first of these consisted of the time that it took for the Earth's shadow to fully encompass the Moon, along with how long the Moon remained within the shadow. This was used to estimate the angular radius of the shadow. From there, using the width of the cone that was created by the shadow in relation to the Moon, he determined that it was twice the diameter of the Moon at the full, non-central eclipse. In addition to this, Aristarchus estimated that the length of the shadow extended around 2.4 times the distance of the Moon from the Earth.

Using these calculations, along with his estimated distances of the Sun from the Earth and Moon from the Earth, he created a triangle. Employing geometry similar to that he had already used for the distances, he was able to determine that the diameter of the Moon is roughly one-third of the Earth's diameter. In order to estimate the size of the Sun, Aristarchus considered the proportion of the Sun's distance to Earth in comparison to the Moon's distance from Earth, which was found to be roughly 18 to 20 times the length. Therefore, the size of the Sun is around 19 times wider than the Moon, making it approximately six times wider than the Earth's diameter.

Legacy

The lunar crater Aristarchus, the minor planet 3999 Aristarchus, and the telescope Aristarchos are named after him.

See also

• Aristarchus's inequality
• Eratosthenes (c. 276 – c. 194/195 BC), a Greek mathematician who calculated the circumference of the Earth and also the distance from the Earth to the Sun.
• Hipparchus (c. 190 – c. 120 BC), a Greek mathematician who measured the radii of the Sun and the Moon as well as their distances from the Earth.
• Posidonius (c. 135 – c. 51 BC), a Greek astronomer and mathematician who calculated the circumference of the Earth.

References

1. "Aristarchus of Samos: Mathematician and astronomer". World History. 8 September 2015. Archived from the original on 7 May 2018. Retrieved 29 November 2018.
3. Huxley, George (30 May 1964). "Aristarchus of Samos and Graeco-Babylonian Astronomy". Greek, Roman, and Byzantine Studies. 5 (2): 123–131. ISSN 2159-3159.
4. Sidoli, Nathan Camillo (22 December 2015). "Aristarchus (1), of Samos, Greek astronomer, mathematician, 3rd century BC". Oxford Classical Dictionary. doi:10.1093/acrefore/9780199381135.013.737. ISBN 978-0-19-938113-5. Retrieved December 7, 2021.
5. Draper, John William (2007) . "History of the Conflict Between Religion and Science". In Joshi, S. T. (ed.). The Agnostic Reader. Prometheus. pp. 172–173. ISBN 978-1-59102-533-7.
6. ^ Owen Gingerich, "Did Copernicus Owe a Debt to Aristarchus?", Journal for the History of Astronomy, vol. 16, no. 1 (February 1985), pp. 37–42. "There is no question but that Aristarchus had the priority of the heliocentric idea. Yet there is no evidence that Copernicus owed him anything.(!9) As far as we can tell both the idea and its justification were found independently by Copernicus."
7. The Greek mathematician and astronomer Aristarchus of Samos proposed such a system during the third century BC (Dreyer 1953, pp. 135–48). In an early unpublished manuscript of De Revolutionibus (which still survives in the Jagiellonian Library in Kraków), Copernicus wrote that "It is credible that... Philolaus believed in the mobility of the Earth and some even say that Aristarchus was of that opinion", a passage that was removed from the published edition, a decision described by Owen Gingerich as "eminently sensible" "from an editorial viewpoint". Philolaus was not a heliocentrist, as he thought that both the Earth and the Sun moved around a central fire. Gingerich says that there is no evidence that Copernicus was aware of the few clear references to Aristarchus's heliocentrism in ancient texts (as distinct from one other unclear and confusing one), especially Archimedes's The Sand-Reckoner (which was not in print until the year after Copernicus died), and that it would have been in his interest to mention them had he known of them, before concluding that he developed his idea and its justification independently of Aristarchus.
8. For a (less recent) contrary view that Copernicus did know about Aristarchus's heliocentric theory see: George Kish (1978). A Source Book in Geography. Harvard University Press. pp. 51–52. ISBN 978-0-674-82270-2. Copernicus himself admitted that the theory was attributed to Aristarchus, though this does not seem to be generally known... Here, however, there is no question of the Earth revolving around the sun, and there is no mention of Aristarchus. But it is a curious fact that Copernicus did mention the theory of Aristarchus in a passage which he later suppressed: The Philolaus-Aristarchus passage is then given in untranslated Latin, without further comment. This is then followed by quoting in full Archimedes's passage about Aristarchus's heliocentric theory from 'The Sand Reckoner' (using its alternative title Arenarius)', seemingly without mentioning that The Sand Reckoner was not in print until a year after Copernicus's death (unless this is mentioned in a passage not shown by Google Books.).
9. Heath, Thomas (1913), p. 302. The italics and parenthetical comments are as they appear in Thomas Little Heath's original. From Arenarius, 4–5. In the original: "κατέχεις δέ, διότι καλείται κόσμος ὑπὸ μὲν τῶν πλείστων ἀστρολόγων ἁ σφαῖρα, ἇς ἐστι κέντρον μὲν τὸ τᾶς γᾶς κέντρον, ἁ δὲ ἐκ τοῦ κέντρου ἴσα τᾷ εὐθείᾳ τᾷ μεταξὺ τοῦ κέντρου τοῦ ἁλίου καὶ τοῦ κέντρου τᾶς γᾶς. ταῦτα γάρ ἐντι τὰ γραφόμενα, ὡς παρὰ τῶν ἀστρολόγων διάκουσας. ̓Αρίσταρχος δὲ ό Σάμιος ὑποθεσίων τινων ἐξέδωκεν γραφάς, ἐν αἷς ἐκ τῶν ὑποκειμένων συμβαίνει τὸν κόσμον πολλαπλάσιον εἶμεν τοῦ νῦν εἰρημένου. ὑποτιθέται γὰρ τὰ μὲν ἀπλανέα τῶν ἄστρων καὶ τὸν ἅλιον μένειν ἀκίνητον, τὰν δὲ γᾶν περιφερέσθαι περὶ τὸν ἅλιον κατὰ κύκλου περιφέρειαν, ὅς ἐστιν ἐν μέσῳ τῷ δρόμῳ κείμενος, τὰν δὲ τῶν ἀπλανέων ἄστρων σφαῖραν περὶ τὸ αὐτὸ κἐντρον τῷ ἁλίῳ κειμέναν τῷ μεγέθει ταλικαύταν εἶμεν, ὥστε τὸν κύκλον, καθ’ ὃν τὰν γᾶν ὑποτιθέται περιφερέσθαι, τοιαύταν ἔχειν ἀναλογίαν ποτὶ τὰν τῶν ἀπλανέων ἀποστασίαν, οἵαν ἔχει τὸ κέντρον τᾶς σφαίρας ποτὶ τὰν επιφάνειαν." Heath mentions a proposal of Theodor Bergk that the word "δρόμῳ" ("orbit") may originally have been "ὀυρανῷ" ("heaven", thus correcting a grammatical incongruity) so that instead of " lying in the middle of the orbit" we would have " lying in the middle of the heaven".
10. Louis Strous. "Who discovered that the Sun was a star?". solar-center.stanford.edu. Retrieved 13 July 2014.
11. ^ Russo, Lucio (2013). The Forgotten Revolution: How Science Was Born in 300 BC and Why it Had to Be Reborn. Translated by Levy, Silvio. Springer Science & Business Media. p. 82, fn.106. ISBN 978-3642189043. Retrieved 13 June 2017.; Russo, Lucio; Medaglia, Silvio M. (1996). "Sulla presunta accusa di empietà ad Aristarco di Samo". Quaderni Urbinati di Cultura Classica (in Italian). New Series, Vol. 53 (2). Fabrizio Serra Editore: 113–121. doi:10.2307/20547344. JSTOR 20547344.
12. Plutarch. "De facie quae in orbe lunae apparet, Section 6". Perseus Digital Library. Tufts University. Retrieved 13 June 2017.
13. Plutarch, Platonicae quaestiones, VIII, i
14. Neugebauer, O. (1975). A History of Ancient Mathematical Astronomy. Studies in the History of Mathematics and Physical Sciences. Vol. 1. Springer-Verlag. pp. 697–698.
15. Naturalis historia, II, 70
16. Naturales quaestiones, VII, xxv, 6–7
17. Joseph A. Angelo (2014). Encyclopedia of Space and Astronomy. Infobase Publishing. p. 153. ISBN 978-1-4381-1018-9.
18. Rawlins, D. (2008). "Aristarchos Unbound: Ancient Vision The Hellenistic Heliocentrists' Colossal Universe-Scale Historians' Colossal Inversion of Great & Phony Ancients History-of-Astronomy and the Moon in Retrograde!" (PDF). Dio: The International Journal of Scientific History. 14: 19.
19. Greek Mathematical Works, Loeb Classical Library, Harvard University, 1939–1941, edited by Ivor Thomas, volume 2 (1941), pp. 6–7
20. Heath, 1913, pp. 299–300; Thomas, 1942, pp. 2–3.
21. A video on reconstruction of Aristarchus' method, in Turkish without subtitles.
22. Kragh, Helge (2007). Conceptions of cosmos: from myths to the accelerating universe: a history of cosmology. Oxford University Press. p. 26. ISBN 978-0-19-920916-3.
23. ^ Hirshfeld, Alan W. (2004). "The Triangles of Aristarchus". The Mathematics Teacher. 97 (4): 228–231. doi:10.5951/MT.97.4.0228. ISSN 0025-5769. JSTOR 20871578.
24. Batten, Alan H. (1981). "Aristarchos of Samos". Journal of the Royal Astronomical Society of Canada. 75: 29–35. Bibcode:1981JRASC..75...29B.

Bibliography

• Heath, Sir Thomas (1913). Aristarchus of Samos, the ancient Copernicus; a history of Greek astronomy to Aristarchus, together with Aristarchus's Treatise on the sizes and distances of the sun and moon : a new Greek text with translation and notes. London: Oxford University Press.
• Dreyer, John Louis Emil (1953) . A History of Astronomy from Thales to Kepler. New York: Dover Publications.

Further reading

• Carman, Christián C.; Buzón, Rodolfo P. (26 May 2023). Aristarchus of Samos: On the Sizes and Distances of the Sun and Moon: Greek Text, Translation, Analysis, and Relevant Scholia. Taylor & Francis. ISBN 978-1-000-86986-6.
• Gomez, Alberto (2023). Decoding Aristarchus. Berlin: Peter Lang Verlag. ISBN 9783631892619.
• Stahl, William (1970). "Aristarchus of Samos". Dictionary of Scientific Biography. Vol. 1. New York: Charles Scribner's Sons. pp. 246–250. ISBN 0-684-10114-9.

External links

• Biography: JRASC, 75 (1981) 29
• First estimate of the Moon's distance and First estimate of the Sun's distance from educational website From Stargazers to Starships
• Aristarchus of Samos, The Ancient Copernicus (https://archive.org/details/aristarchusofsam00heatuoft
• O'Connor, John J.; Robertson, Edmund F., "Aristarchus of Samos", MacTutor History of Mathematics Archive, University of St Andrews
• Online Galleries, History of Science Collections, University of Oklahoma Libraries Archived 2012-05-15 at the Wayback Machine High resolution images of works by Aristarchus of Samos in .jpg and .tiff format.

v t e Ancient Greek mathematics
Mathematicians (timeline)	Anaxagoras Anthemius Archytas Aristaeus the Elder Aristarchus Aristotle Apollonius Archimedes Autolycus Bion Bryson Callippus Carpus Chrysippus Cleomedes Conon Ctesibius Democritus Dicaearchus Diocles Diophantus Dinostratus Dionysodorus Domninus Eratosthenes Eudemus Euclid Eudoxus Eutocius Geminus Heliodorus Heron Hipparchus Hippasus Hippias Hippocrates Hypatia Hypsicles Isidore of Miletus Leon Marinus Menaechmus Menelaus Metrodorus Nicomachus Nicomedes Nicoteles Oenopides Pappus Perseus Philolaus Philon Philonides Plato Porphyry Posidonius Proclus Ptolemy Pythagoras Serenus Simplicius Sosigenes Sporus Thales Theaetetus Theano Theodorus Theodosius Theon of Alexandria Theon of Smyrna Thymaridas Xenocrates Zeno of Elea Zeno of Sidon Zenodorus
Treatises	Almagest Archimedes Palimpsest Arithmetica Conics (Apollonius) Catoptrics Data (Euclid) Elements (Euclid) Measurement of a Circle On Conoids and Spheroids On the Sizes and Distances (Aristarchus) On Sizes and Distances (Hipparchus) On the Moving Sphere (Autolycus) Optics (Euclid) On Spirals On the Sphere and Cylinder Ostomachion Planisphaerium Spherics (Theodosius) Spherics (Menelaus) The Quadrature of the Parabola The Sand Reckoner
Problems	Constructible numbers Angle trisection Doubling the cube Squaring the circle Problem of Apollonius
Concepts and definitions	Angle Central Inscribed Axiomatic system Axiom Chord Circles of Apollonius Apollonian circles Apollonian gasket Circumscribed circle Commensurability Diophantine equation Doctrine of proportionality Euclidean geometry Golden ratio Greek numerals Incircle and excircles of a triangle Method of exhaustion Parallel postulate Platonic solid Lune of Hippocrates Quadratrix of Hippias Regular polygon Straightedge and compass construction Triangle center
Results	In Elements Angle bisector theorem Exterior angle theorem Euclidean algorithm Euclid's theorem Geometric mean theorem Greek geometric algebra Hinge theorem Inscribed angle theorem Intercept theorem Intersecting chords theorem Intersecting secants theorem Law of cosines Pons asinorum Pythagorean theorem Tangent-secant theorem Thales's theorem Theorem of the gnomon Apollonius Apollonius's theorem Other Aristarchus's inequality Crossbar theorem Heron's formula Irrational numbers Law of sines Menelaus's theorem Pappus's area theorem Problem II.8 of Arithmetica Ptolemy's inequality Ptolemy's table of chords Ptolemy's theorem Spiral of Theodorus
Centers	Cyrene Mouseion of Alexandria Platonic Academy
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