Eudoxus was a pupil of Plato's a very long time ago and is credited with coming up with the first geocentric theory of the universe that actually attempted to solve some of the problems with astronomy at the time. One of the main problems was that when the Greeks observed the planets and their motion, the planets would seem to become brighter in appearance at times without any explanation. Also, the planets seemed to travel backwards on their orbits. We know today that this is due to the fact that the earth is rotating around the sun with the other planets and is explained later in Copernicus' heliocentric model.
This backwards motion of the planets didn't make any sense and Eudoxus created a system of circles and axis to explain for such paranoia. Eudoxus' system (shown below) contained 27 spheres, one for the stars, three for the sun and moon, and four for each of the five known planets. These spheres all rotated on separate axis which created the desired effects that correlated with the data taken on planetary motion.
For each of the planets, on axis was aligned with the celestial poles creating rising and setting effects. The second axis was tilted 23.5 degrees and rotated slowly in the opposite direction of the first. The was the axis that created the west-to-east drift of the planets. The third and fourth spheres rotated in such a way to account for the periodic backwards motion of the planets. This model did explain the biggest problems with planetary motion and although there were still some small problems it was widely accepted as the start of a solution.
Here I'll briefly mention Callipus because he did in fact further Eudoxus' model. All he did was add 7 more spheres bring the total to a count of 34 spheres from the previous 27. This made the model even more accurate to what numbers were calculated.
