The Greek Astronomer Who Proposed That the Earth Orbits the Sun Eighteen Centuries Before Copernicus

Aristarchus of Samos (c. 310 – c. 230 BC) was one of the senior astronomers of the early Hellenistic Library of Alexandria. He worked primarily on the geometric astronomy of the Sun-Earth-Moon system in the period c. 280–260 BC — about 50 years after the foundation of the Library and approximately 100 years before Hipparchus would produce the canonical Greek stellar catalogue. His exact biographical details (when he arrived at Alexandria, who his teachers were, whether he ever returned to his native Samos) are not well-attested in surviving classical sources; what survives is one of his treatises and several second-hand reports of a more important treatise that has been lost.

The surviving treatise is On the Sizes and Distances of the Sun and Moon (Greek: Περὶ μεγεθῶν καὶ ἀποστημάτων ἡλίου καὶ σελήνης), a short geometric work of approximately 20 propositions that uses a clever observational argument and rigorous Euclidean geometry to compute the relative sizes and distances of the three bodies. The treatise is the earliest substantially-intact extended exercise in mathematical astronomy from the entire Greek tradition. The lost treatise is the one that proposed heliocentrism.

The size and distance calculation

The geometric argument of On the Sizes and Distances hinges on a single observation. At the exact moment of the half-Moon — when the Sun illuminates exactly half the lunar disk as seen from Earth — the Earth-Moon-Sun angle is exactly 90 degrees. The Sun-Earth-Moon angle at that moment can be measured directly by observing the angle between the Sun and the Moon as seen from Earth. The three angles of the resulting Earth-Moon-Sun right triangle are then known: 90 degrees at the Moon, the observed angle at the Earth, and the remaining angle (180 minus the two) at the Sun.

The ratio of the two sides adjacent to the Earth’s vertex (the Earth-Sun distance and the Earth-Moon distance) is then a simple trigonometric function of the observed Earth-vertex angle. Aristarchus measured the angle as 87 degrees and concluded that the Sun was approximately 19 times further from the Earth than the Moon was.

The actual angle is approximately 89.85 degrees, and the actual Sun-Earth distance is approximately 390 times the Moon-Earth distance. Aristarchus’s geometric method is exactly correct; his observational angle measurement was off by about 3 degrees (a substantial error, given the difficulty of identifying the exact moment of the half-Moon and the limited angular-resolution of Greek-period observing technique) and his conclusion was therefore numerically wrong by a factor of about 20. The methodological point — that the relative distances could be computed from a single observation by a few lines of trigonometry — was substantively correct and was a substantial advance over the previous Greek astronomical tradition.

The same treatise applied a similar geometric argument to the relative sizes of the Sun and Moon. Aristarchus knew (from observation of total solar eclipses) that the apparent angular diameters of the Sun and Moon as seen from Earth were approximately equal; if the Sun was 19 times further away than the Moon, the Sun must therefore be 19 times larger in linear diameter — and therefore approximately 7,000 times larger in volume. The Earth-Moon size ratio was estimated separately (from the lunar shadow during lunar eclipses) at approximately 3:1, giving an Earth-Sun ratio of approximately 1:7. The Sun, on the Aristarchian calculation, was approximately 343 times larger than the Earth in volume.

These were the first numerical estimates of the relative sizes of the three bodies in the entire history of human astronomy. They were wrong in absolute magnitude but correct in their fundamental insight: the Sun is much larger than the Earth, the Moon is much smaller than the Earth, and the conventional pre-Aristarchian belief that the three bodies were of comparable size was substantively incorrect.

The heliocentric proposal

The size calculation led directly to the heliocentric proposal. The argument is preserved only in second-hand reports, primarily in Archimedes’s The Sand Reckoner (c. 230 BC), where Archimedes is making a separate calculation about the number of grains of sand required to fill the universe and references Aristarchus’s larger-universe hypothesis as a relevant alternative cosmological framework. Archimedes writes:

Aristarchus brought out a book consisting of certain hypotheses, in which the premisses lead to the conclusion 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 Aristarchian argument was approximately as follows. If the Sun was much larger than the Earth (per the size calculation above), it was more reasonable to suppose that the smaller body orbited the larger than that the larger orbited the smaller. The standard objection to a moving Earth — that we should observe stellar parallax (the apparent shift in stellar positions as the Earth moves around the Sun) — could be answered by assuming the stars were much further away than the diameter of the Earth’s orbit, far enough that any parallax shift would be below the angular-resolution of Greek observational instruments.

The proposal therefore involved three simultaneous claims: the Sun is large and central; the Earth (and presumably the other planets) orbits the Sun; the stars are sufficiently distant that their parallax is unobservable.

All three claims are correct by modern astronomy. The heliocentric model is the modern understanding; the Sun-centred orbital arrangement is exactly the modern Keplerian-Newtonian framework; the stellar parallax was eventually observed in 1838 by Friedrich Bessel using a 19th-century refracting telescope of approximately the same resolution that the heliocentric model required.

Why it was rejected

The Aristarchian heliocentric model was rejected by the entire mainstream Hellenistic astronomical tradition. The leading subsequent astronomer of the Greek tradition — Hipparchus (c. 190–120 BC) — explicitly rejected the heliocentric proposal in his own work and built his subsequent astronomical framework on the geocentric assumption. The Ptolemaic system that consolidated Hipparchian astronomy in the 2nd century AD institutionalised the geocentric model as the canonical Greek-Roman astronomical framework, which was preserved through the medieval Islamic and European astronomical traditions until the Copernican rediscovery of 1543.

The reasons for the rejection were a combination of empirical-observational and philosophical-theological. The empirical reasons:

The expected stellar parallax was unobservable — which the Aristarchian model required to be explained by an extraordinarily large stellar distance, an assumption that struck most contemporary observers as unreasonable on the prior probability.

The expected stellar magnitude variation across the year — if the Earth moved 300 million kilometres around the Sun, the closer stars should appear brighter when Earth was on their side of the orbit — was also unobservable, requiring the same large-stellar-distance assumption.

The expected Coriolis effects on Earth-surface phenomena — a moving Earth should produce observable effects on falling bodies, atmospheric circulation, and ocean currents that were not detected by Greek observational technique.

The expected wind from the Earth’s motion — a body moving at the orbital velocity of the Earth around the Sun (approximately 30 km/s on the modern measurement) should produce a atmospheric headwind in the direction of motion, which was obviously not present.

The geocentric framework substantively explained all of these absent-observations by simply not requiring the Earth to be moving. The Aristarchian framework had to explain the absence of every one of these observations by an additional ad hoc assumption.

The philosophical reasons were stronger. The Stoic philosopher Cleanthes of Assos (c. 330–230 BC), the head of the Athenian Stoic school of the period, called for Aristarchus to be charged with impiety for “moving the hearth of the universe” — the Earth being, in the standard Greek cosmological tradition, the fixed centre of the universe and the home of the gods. The impiety threat was not formally pursued, but the broader Greek philosophical-religious culture was uncomfortable with the heliocentric proposal’s displacement of the Earth from cosmological centrality. The geocentric framework substantively preserved the Earth-centred Greek religious-philosophical tradition; the heliocentric framework substantively did not.

The rediscovery

The Aristarchian proposal was substantively forgotten in the Western tradition after the Hipparchian rejection. The medieval Islamic astronomical tradition (al-Battani, al-Tusi, Ibn al-Shatir) preserved the geometric apparatus of Ptolemaic geocentric astronomy and made significant computational refinements to it but did not seriously revisit the Aristarchian alternative. The medieval European tradition (Roger Bacon, Jean Buridan, Nicolas Oresme) similarly took the geocentric model as the canonical framework.

The Copernican rediscovery of 1543 explicitly references Aristarchus in the De Revolutionibus. Copernicus had read the relevant Archimedes passage in the surviving Greek manuscripts of the period and was aware that his heliocentric proposal was a rediscovery of an earlier Greek theory rather than an original invention. The Renaissance restoration of the Greek mathematical-astronomical tradition was a cultural-intellectual achievement and the Aristarchian heliocentric proposal was one of the recovered Greek positions. The 1,800-year gap between the Aristarchian proposal and the Copernican rediscovery is one of the longest delayed-confirmation gaps in the history of any major scientific claim.

The Hipparchian observational objections were answered over the subsequent 300 years. The telescopic confirmation of stellar parallax (Bessel, 1838) substantively eliminated the most-direct Hipparchian objection. The Newtonian gravitational synthesis of the late 17th century substantively explained why the Earth-surface phenomena that the Hipparchian framework had used as objections (no wind from Earth’s motion, no Coriolis on falling bodies, no stellar parallax) had been unobservable in pre-modern instrumental conditions. The 1543 Copernican publication had restarted the heliocentric inquiry that the 270 BC Aristarchian publication had originated.