The Greek Cosmology of Twenty-Seven Nested Crystal Spheres That Aristotle Inherited and Europe Believed for Two Thousand Years

Eudoxus of Cnidus had been trained as a mathematician at Cnidus, had studied briefly at Plato’s Academy in Athens in the late 360s BC, and had founded his own school at Cyzicus on the Sea of Marmara around 350 BC. His most lasting mathematical work was the theory of proportion that became Book V of Euclid’s Elements. His most lasting cosmological work was a geometric model of planetary motion that Aristotle would adopt and that Europe would believe for two thousand years.

The model

The classical Greek astronomical problem of the 4th century BC was the observed irregularity of the visible planets. The five naked-eye planets — Mercury, Venus, Mars, Jupiter, Saturn — did not move smoothly along the ecliptic. They progressed, stopped, reversed (the retrograde motion that is now understood as a perspective effect of Earth’s own orbit), and resumed. The Sun and Moon moved more regularly but each had its own subtle variations. The Pythagorean cosmological tradition that Plato had inherited substantively insisted that celestial motion must be uniform and circular; the observed motions clearly were not.

Eudoxus’s solution was to combine multiple uniform circular motions to produce the observed apparent motion. He proposed that each planet was carried on the equator of a rotating sphere whose poles were attached to the equator of a second rotating sphere, whose poles were attached to a third, and so on through up to four nested spheres per body. Each sphere rotated uniformly about its own axis; the combination of their motions produced the observed irregular path on the celestial sphere.

The total system required:

• 3 spheres each for the Sun and Moon (6 total)
• 4 spheres each for the five planets (20 total)
• 1 sphere for the fixed stars

This gave 27 spheres total. All centred on the stationary Earth; all turning at different rates; all of them substantively mathematical constructs that produced output positions matching the observed positions.

Aristotle’s expansion

Aristotle adopted the Eudoxean framework in his Metaphysics (Book XII) but expanded it substantively. Where Eudoxus had treated the spheres as purely geometric devices for predicting position, Aristotle made them physical: each sphere was a real rotating crystalline shell, and the motion of one sphere had to be physically transmitted through the intervening shells. The bookkeeping became elaborate. Aristotle expanded the model to 55 spheres to account for the physical interaction between adjacent planetary systems.

The Aristotelian version added one further substantively important feature: the prime mover. The outermost sphere of the fixed stars had to be driven by something; Aristotle’s solution was an unmoved cosmic intellect that imparted motion to the outer sphere through a process of intellectual contemplation rather than mechanical contact. The prime mover became one of the key features of medieval Christian-Aristotelian theology — Thomas Aquinas would substantively identify it with the Christian God in the 13th century.

The afterlife

The Eudoxean-Aristotelian sphere model substantively dominated European cosmology from the 4th century BC until approximately 1577. The two specific observational developments that broke it were Tycho Brahe’s 1572 supernova and the Great Comet of 1577 — both observed without parallax and therefore necessarily located beyond the orbit of the Moon, both passing through the supposed crystal spheres without disturbing them. The Aristotelian doctrine that the heavens were immutable and the spheres physical could not survive these observations. Tycho substantively retired the crystal spheres in his subsequent work; Kepler’s three laws (1609–1619) substantively replaced the spherical-motion framework with the elliptical-orbital one.

The Eudoxean spheres had lasted approximately 2,000 years.