Aristarchus of Samos

Statue of Aristarchus of Samos at the Aristotle University of Thessaloniki

Born| c. 310 BC

Samos

Died| c. 230 BC

Alexandria,[1] Ptolemaic Kingdom

Occupation|

* Scholar
* Mathematician
* Astronomer

Aristarchus of Samos (/ˌærɪˈstɑːrkəs/; 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 that the Sun was just another star.[2]

Born in Samos in approximately 310 BC, Aristarchus likely moved to Alexandria and became a student of Strato of Lampsacus, who later became the head of the Peripatetic school in Greece. According to Ptolemy, Aristarchus observed the summer solstice of 280 BC.[3] Vitruvius writes that Aristarchus built two different sundials: one a flat disc; and one hemispherical.[4] Aristarchus estimated the sizes of the Sun and Moon as compared to Earth, and the distances from the Earth to the Sun and to the Moon. His estimate that the Sun was 7 times larger than Earth (it's actually 109 times, in diameter) brought about the further insight that the Sun's greater size made it the most natural central point of the universe, as opposed to Earth.

Aristarchus was influenced by the concept presented by Philolaus of Croton (Template:Cx - 385 BC) of a fire at the center of the universe (i.e. by contemporary understanding, at the center of the Earth). Aristarchus recast this "central fire" as the Sun, and he arranged the other planets in their correct order of distance around the Sun.[5]

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.[7][8]

## Contents

* 1 Heliocentrism
* 2 Distance to the Sun
* 3 Size of the Moon and Sun
* 4 Legacy
* 5 See also
* 6 References
* 7 Bibliography
* 8 Further reading
* 9 External links

## Heliocentrism

See also: Astronomy: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 ['you' being King Gelon] 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.[9]

Aristarchus proposed that the fixed stars were extremely distant, and because ancient cosmology placed them all on a single celestial sphere, the modern concept of stellar parallax did not apply to his model. He placed the stars at a great distance so that their apparent positions relative to each other would remain constant throughout Earth's motion. Aristarchus reconciled this issue by postulating that the stars were other suns that are very far away,[2] far enough that the parallax was not observable. This implied a universe much larger than had been believed.

It is a common misconception that the heliocentric view was considered sacrilegious by the contemporaries of Aristarchus.[10] 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.[10] In the manuscript of Plutarch's text, Aristarchus says Cleanthes should be charged with impiety.[10] 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.[10] The resulting misconception of an isolated and persecuted Aristarchus is still promulgated.[10][11]

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,[12] 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.[13] Pliny[14] and Seneca[15] 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,[16] 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

Main article: Astronomy:On the Sizes and Distances (Aristarchus)

Aristarchus's third-century BC calculations on the relative sizes of (from left) the Sun, Earth, and Moon, from a tenth-century AD Greek copy

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.[17]

Aristarchus claimed that at half moon (first or last quarter moon), the angle between the Sun and Moon was 87°.[18] 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.[19] (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.[20]

## 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.[21] 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.[22] 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.[21]

Aristarchus (center) and Herodotus (right), from Apollo 15, NASA photograph

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.[21]

## 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. http://www.worldhistory.biz/ancient-history/71176-aristarchus-of-samos.html.
2. ↑ 2.0 2.1 Louis Strous. "Who discovered that the Sun was a star?". http://solar-center.stanford.edu/FAQ/Qsunasstar.html.
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. https://grbs.library.duke.edu/article/view/11941.
4. ↑ Sidoli, Nathan Camillo (22 December 2015). "Aristarchus (1), of Samos, Greek astronomer, mathematician, 3rd century BC" (in en). Aristarchus (1), of Samos, Greek astronomer, mathematician, 3rd century BC. doi:10.1093/acrefore/9780199381135.013.737. ISBN 978-0-19-938113-5. https://oxfordre.com/classics/view/10.1093/acrefore/9780199381135.001.0001/acrefore-9780199381135-e-737. Retrieved December 7, 2021.
5. ↑ Draper, John William (2007). "History of the Conflict Between Religion and Science". in Joshi, S. T.. The Agnostic Reader. Prometheus. pp. 172–173. ISBN 978-1-59102-533-7.
6. ↑ 6.0 6.1 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".[6] 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 did not appear 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.[6]
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. https://books.google.com/books?id=_6qF4vjZvhYC&pg=PA51. "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 κἐντρον25 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 "[the sun] lying in the middle of the orbit" we would have "[the circle] lying in the middle of the heaven".
10. ↑ 10.0 10.1 10.2 10.3 10.4 Russo, Lucio (2013). The Forgotten Revolution: How Science Was Born in 300 BC and Why it Had to Be Reborn. Springer Science & Business Media. p. 82, fn.106. ISBN 978-3642189043. https://books.google.com/books?id=ld8lBAAAQBAJ&pg=PA82. Retrieved 13 June 2017. ; Russo, Lucio; Medaglia, Silvio M. (1996). "Sulla presunta accusa di empietà ad Aristarco di Samo" (in it). Quaderni Urbinati di Cultura Classica (Fabrizio Serra Editore) New Series, Vol. 53 (2): 113–121. doi:10.2307/20547344.
11. ↑ Plutarch. "De facie quae in orbe lunae apparet, Section 6". Perseus Digital Library. Tufts University. https://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:2008.01.0357:section=6&highlight=cleanthes.
12. ↑ Plutarch, Platonicae quaestiones, VIII, i
13. ↑ Neugebauer, Otto E. (1975). A History of Ancient Mathematical Astronomy. Studies in the History of Mathematics and Physical Sciences. 1. Springer-Verlag. pp. 697–698.
14. ↑ Pliny the Elder (AD 77). Natural History, II, 70
15. ↑ Seneca the Younger (AD 65). Naturales quaestiones, VII, xxv, 6–7
16. ↑ Joseph A. Angelo (2014). "Copernicus, Nicholas". Encyclopedia of Space and Astronomy. Infobase Publishing. p. 153. ISBN 978-1-4381-1018-9. https://books.google.com/books?id=VUWno1sOwnUC&pg=PA153.
17. ↑ 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!". Dio: The International Journal of Scientific History 14: 19. http://www.dioi.org/vols/we0.pdf.
18. ↑ Greek Mathematical Works, Loeb Classical Library, Harvard University Press, 1939–1941, translated by Ivor Thomas, volume 2 (1941), pp. 6–7
19. ↑ A video on reconstruction of Aristarchus' method, in Turkish without subtitles. ("Aristarchus of Samos Yöntemi ile Ay ve Güneş'in Büyüklük ve Uzaklıkları" ["Sizes and Distances of the Moon and the Sun by the Method of Aristarchus of Samos"] by Cilga Misli
20. ↑ 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. https://www.google.com/books/edition/Conceptions_of_Cosmos/7tUTDAAAQBAJ?hl=en&gbpv=1&dq=isbn:9780199209163&printsec=frontcover.
21. ↑ 21.0 21.1 21.2 Hirshfeld, Alan W. (April 2004). "The Triangles of Aristarchus". The Mathematics Teacher 97 (4): 228–231. doi:10.5951/MT.97.4.0228. ISSN 0025-5769. https://www.jstor.org/stable/20871578.
22. ↑ Batten, Alan H. (February 1981). "Aristarchos of Samos". Journal of the Royal Astronomical Society of Canada 75: 29–35. Bibcode: 1981JRASC..75...29B. https://adsabs.harvard.edu/full/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. https://archive.org/details/aristarchusofsam00heatuoft.
* Dreyer, John Louis Emil (1953). A History of Astronomy from Thales to Kepler. New York: Dover Publications. https://archive.org/details/historyofplaneta00dreyuoft.

## Further reading

* Carman, Christián C.; Buzón, Rodolfo P. (26 May 2023) (in en). 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. https://books.google.com/books?id=iE-3EAAAQBAJ.
* Gomez, Alberto (2023). Decoding Aristarchus. Berlin: Peter Lang Verlag. ISBN 9783631892619. https://www.peterlang.com/document/1288830.
* Stahl, William (1970). "Aristarchus of Samos". Dictionary of Scientific Biography. 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, http://www-history.mcs.st-andrews.ac.uk/Biographies/Aristarchus.html .
* Online Galleries, History of Science Collections, University of Oklahoma Libraries High resolution images of works by Aristarchus of Samos in .jpg and .tiff format.

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Ancient Greek astronomy

Astronomers|

* Aglaonice
* Agrippa
* Anaximander
* Andronicus
* Apollonius
* Aratus
* Aristarchus
* Aristyllus
* Attalus
* Autolycus
* Bion
* Callippus
* Cleomedes
* Cleostratus
* Conon
* Eratosthenes
* Euctemon
* Eudoxus
* Geminus
* Heraclides
* Hicetas
* Hipparchus
* Hippocrates of Chios
* Hypsicles
* Menelaus
* Meton
* Oenopides
* Philip of Opus
* Philolaus
* Posidonius
* Ptolemy
* Pytheas
* Seleucus
* Sosigenes of Alexandria
* Sosigenes the Peripatetic
* Strabo
* Thales
* Theodosius
* Theon of Alexandria
* Theon of Smyrna
* Timocharis

Works|

* Almagest (Ptolemy)
* On Sizes and Distances (Hipparchus)
* On the Sizes and Distances (Aristarchus)
* On the Heavens (Aristotle)

Instruments|

* Antikythera mechanism
* Armillary sphere
* Astrolabe
* Dioptra
* Equatorial ring
* Gnomon
* Mural instrument
* Triquetrum

Concepts|

* Callippic cycle
* Celestial spheres
* Circle of latitude
* Counter-Earth
* Deferent and epicycle
* Equant
* Geocentrism
* Heliocentrism
* Hipparchic cycle
* Metonic cycle
* Octaeteris
* Solstice
* Spherical Earth
* Sublunary sphere
* Zodiac

Influences|

* Babylonian astronomy
* Egyptian astronomy

Influenced|

* Medieval European science
* Indian astronomy
* Medieval Islamic astronomy

* v
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* e

Ancient Greek mathematics

Mathematicians
(timeline)|

* Anaxagoras
* Anthemius
* Archytas
* Aristaeus the Elder
* Aristarchus
* Apollonius
* Archimedes
* Autolycus
* Bion
* Bryson
* Callippus
* Carpus
* Chrysippus
* Cleomedes
* Conon
* Ctesibius
* Democritus
* Dicaearchus
* Diocles
* Diophantus
* Dinostratus
* Dionysodorus
* Domninus
* Eratosthenes
* Eudemus
* Euclid
* Eudoxus
* Eutocius
* Geminus
* Heron
* Hipparchus
* Hippasus
* Hippias
* Hippocrates
* Hypatia
* Hypsicles
* Isidore of Miletus
* Leon
* Marinus
* Menaechmus
* Menelaus
* Metrodorus
* Nicomachus
* Nicomedes
* Nicoteles
* Oenopides
* Pappus
* Perseus
* Philolaus
* Philon
* 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)
* Elements (Euclid)
* On the Sizes and Distances (Aristarchus)
* On Sizes and Distances (Hipparchus)
* On the Moving Sphere (Autolycus)
* The Sand Reckoner

Problems|

* Problem of Apollonius
* Squaring the circle
* Doubling the cube
* Angle trisection

Centers|

* Cyrene
* Library of Alexandria
* Platonic Academy

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