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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