Cosmic Theories of Eudoxus


Eudoxan Spheres

Eudoxus of Cnidus (~400 - 347 BC) took up Plato's challenge and devised the 'Eudoxan Spheres' seen here.

An outer sphere rotates round a vertical axis. An inner sphere rotates at the same speed, but in the opposite direction, round an axis that is fixed to the inside of the outer sphere and offset from the vertical. The net effect is that a body (e.g. planet) fixed to the 'equator' of the inner sphere moves in a figure of 8 (known as a hippopede).

Eudoxus believed this backward and forward motion could be used as a basis for constructing a mathematical model of planetary movement, including retrograde motion. To do this two more outer spheres are needed, one to draw the planet west to east at an appropriate rate and one to create the daily passage of everything across the sky.

An Embarrassment of Spheres

Arrangements of spheres can be used to approximate the Sun and the Moon's movements. Aristotle described a model of the cosmos using 27 nested spheres rotating in various directions and at various speeds. The outermost sphere carried the fixed stars. This model, combined with 'earth/water/air/fire' at the centre, was a view of the cosmos maintained by many people well into the middle ages.

Details of how Eudoxus and Aristotle  arranged all the spheres are not clear from available historic documents. Various schemes have been proposed by historians. For example, in the lower diagram, the outer sphere rotates twice as fast as the inner one (but in the opposite direction). 

Even though the inner sphere is swinging about madly, the path of the planet is a fairly good circle relative to the Earth and has occasional retrograde motion. Given enough spheres it is possible to construct a model of the cosmos with all of the planets included.

However, the Eudoxan Sphere approach did not agree very well with observation.  It did not represent the angular speed of the planets correctly nor did it accurately reproduce the path of the planet during periods of retrograde motion.

Another major problems was that it did not explain the variation in brightness of the minor planets, (planets other than Sun and Moon), which was presumed (correctly) to be due to changes in distance.


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