Aristarchus of Samos

• 1. Introduction

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  Aristarchus of Samos proposed something radical: the Sun, not Earth, sits at the center of the universe. He made this argument in the 3rd century BC. His original text has not survived. What we know of it comes from Archimedes, who preserved it in a book called The Sand Reckoner. Archimedes addressed that book to King Gelon of Syracuse. He made clear that the universe Aristarchus described was many times larger than what other astronomers of the era believed. How had an astronomer from a small Aegean island arrived at such a picture? And why did the ancient world, almost universally, decline to accept it? A few clues lie in the instruments he built and the teachers he studied under.

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• 2. From Samos to Alexandria

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  Strato of Lampsacus, the philosopher under whom Aristarchus likely studied in Alexandria, later became the head of the Peripatetic school in Greece. The Peripatetics were Aristotle's heirs, committed to systematic investigation of the natural world. Aristarchus was born in Samos around 310 BC and likely moved to Alexandria to pursue his studies. According to Ptolemy, Aristarchus observed the summer solstice in 280 BC, one of the earliest specific dates attached to his work. Vitruvius, the Roman architect, noted that Aristarchus built two distinct types of sundials. One was a flat disc; the other was a hemispherical bowl. These instruments show a man who worked not only with ideas but with physical tools for tracking the sky.

  Philolaus of Croton, who lived roughly between 470 and 385 BC, had proposed that a fire sits at the center of the universe. Aristarchus replaced that fire with the Sun. He also supported the view of Anaxagoras that the Sun was just another star, with the other stars being farther suns of the same kind. He estimated the Sun to be roughly seven times wider than the Earth. That figure falls far short of the actual ratio, which is about 109 to 1 in diameter. He also found that the Sun was larger not only than Earth but than the other planets as well.

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• 3. The Heliocentric Model

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  In The Sand Reckoner, Archimedes explained how most ancient astronomers defined the word 'universe'. They meant the sphere centered on Earth, with a radius equal to the Earth-Sun distance. Aristarchus proposed a cosmos in which the sphere of fixed stars lies at a distance so vast that the Earth-Sun span is negligibly small. The fixed stars and the Sun remain stationary in his model. Earth revolves around the Sun in a circular orbit, with the Sun at the center of that orbit. Earth also rotates on its own axis once each day. This accounts for the sky's apparent daily sweep without requiring the entire stellar sphere to rotate.

  Aristarchus placed the planets in their correct order of distance from the Sun, a sequence that geocentric models could not reproduce as naturally. If Earth travels around the Sun, the nearby stars should appear to shift position against the distant background as Earth moves through its orbit. No ancient observer detected any such shift. Aristarchus answered that the stars were at distances so vast that the shift was too small to measure. The stars were not lights fixed into a nearby shell but remote suns at immense distances. Earth's entire orbital width was too small, relative to those distances, to produce a measurable parallax.

  The only text attributed to Aristarchus that survives is On the Sizes and Distances of the Sun and Moon. It reveals a different side of his practice: the geometry of measurement.

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• 4. Geometry of Sun and Moon

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  At first or last quarter moon, Aristarchus measured the angle between the Sun and Moon as seen from Earth. He found it to be 87 degrees. Using correct geometry from that datum, he concluded that the Sun lay between 18 and 20 times farther from Earth than the Moon. The true angle is close to 89 degrees and 50 minutes, making the Sun roughly 400 times more distant. His error was in the measurement, not the method.

  Aristarchus also used a lunar eclipse to estimate the Moon's size. During the eclipse, he recorded how long Earth's shadow took to fully encompass the Moon, and how long the Moon remained inside that shadow. From these intervals he estimated the angular radius of Earth's shadow. He then compared the shadow's cone, at the Moon's distance, to the Moon's own width. He found the shadow to be twice the Moon's diameter at a full, non-central eclipse. He also estimated that Earth's shadow extended roughly 2.4 times the Moon's distance from Earth. Combining these figures with his distance estimates, he built a triangle and derived the Moon's diameter. His result was that the Moon is roughly one-third the diameter of Earth. Using the Sun's distance as 18 to 20 times the Moon's distance, he then calculated the Sun's width. That gave a Sun roughly 19 times wider than the Moon, making the Sun approximately six times wider than Earth.

  The implicit solar parallax in his calculations came to slightly under three degrees. Astronomers relied on that figure for many centuries, up to and including Tycho Brahe around AD 1600. Archimedes separately recorded that Aristarchus measured the Sun's apparent angular diameter as half a degree. That figure is close to the modern value of about 0.53 degrees. The surviving text gives two degrees instead, a discrepancy scholars attribute to a misread Greek unit of measure.

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• 5. The Impiety Myth

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  Cleanthes, who headed the Stoic school of philosophy, was a devoted sun worshipper who nonetheless opposed the heliocentric model. Plutarch records that Aristarchus joked that Cleanthes should be charged with impiety. Cleanthes venerated the Sun while denying that it was the center of the cosmos. That exchange appears in Plutarch's On the Apparent Face in the Orb of the Moon. Gilles Ménage, in his printed edition of Plutarch's text, transposed an accusative and a nominative in the Greek. The result was a version in which Aristarchus appears to be the one charged with impiety rather than Cleanthes. Ménage's printing appeared shortly after the trials of Galileo and Giordano Bruno, a context that may explain why the inversion passed without correction. Lucio Russo traced this distortion and showed that the image of a persecuted, isolated Aristarchus is a misconception still in circulation.

  Pliny the Elder, in his Naturalis Historia, wondered whether errors in predicting the heavens might trace to Earth's displacement from the center of the cosmos. Pliny and Seneca both noted that the retrograde motion of certain planets is an apparent phenomenon rather than a real one. That observation is consistent with heliocentrism. Plato, Aristotle, and Ptolemy nonetheless maintained the geocentric model, which the Middle Ages accepted as settled truth. Plutarch also records that Aristarchus presented heliocentrism only as a hypothesis, not as a demonstrated fact. Seleucus of Seleucia, a Hellenistic astronomer who lived a century after Aristarchus, was the first to champion the model as a definite conclusion. He offered a demonstration of it, though no full record survives.

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• 6. Into Posterity

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  Copernicus later revived the heliocentric model, proposing that Earth moves and the Sun is fixed. He knew that Aristarchus had advocated a moving Earth, though it is unlikely he was aware that Aristarchus's model was already fully heliocentric. Johannes Kepler built on the Copernican framework with his three laws of planetary motion. Those laws described the actual paths of the planets with greater accuracy than any earlier model. Isaac Newton later provided the physical explanation, deriving the behavior of orbiting bodies from laws of gravitational attraction and dynamics.

  The crater Aristarchus on the Moon, the minor planet 3999 Aristarchus, and the telescope Aristarchos all bear his name. Aryabhata and Bhaskara I, working independently in the Indian astronomical tradition, developed mathematical models for explaining planetary motion, eclipses, and astronomical measurements. Their work arrived at comparable geometric approaches to measuring the distances between Earth, Moon, and Sun.

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