The Universe of the two spheres One of the first and simplest astronomical theories is the Universe of the two spheres. Since the IV century BC Most Greek thinkers and astronomers believed that the Earth was a small immobile sphere in the geometric center of another sphere in rotation from West to East, much larger, that dragged the stars with it. Beyond this huge sphere there was nothing, no space, no matter. The most important insufficiency of the model of the two spheres resides in the special and apparently complicated movement of the planets. This made the assumption that the planets were located in the outer sphere unlikely, so Greek astronomers began to fill the space between the Earth and the sphere of the stars with other spheres for each of the planets. The relative proximity of the planetary spheres to the Earth was decided according to the velocity of the corresponding planet. Thus, the slowest planet, Saturn, was placed close to the fixed stars; the Moon, the fastest of the planets close to Earth.

**Aristotelian Cosmology **

Aristotle relied on the previous model when formulating his cosmology. The Universe, for Aristotle, was made up of a set of concentric crystalline shells in which the planets were embedded. There were exactly 55 crystalline spherical shells that in a complicated movement, driven by the fixed stars, gave rise to the apparent movements of the planets. These spheres had different axes, they moved uniformly, but with different speeds and directions. Thus, for example, Mars was assigned four spheres. In the innermost the planet was embedded, another gave rise to its daily movement. Another to the annual movement and the last to the retrogradations. This model did not explain why planets glow brighter when retrograde.

**The basic epicyclo-deferent system**

Ptolemy, an astronomer from Alexandria who lived in the 2nd century AD. From C., he elaborated an astronomical model that lasted until Copernicus. Ptolemy admitted from the outset that the Earth was the immobile center of the Universe, that the sky is spherical and rotates, that all the stars move at uniform speed and in circular motions. But with these assumptions, a single circumference per planet was not enough to explain its apparent motions. To explain the movements of the planets quantitatively, it was necessary to complicate the system with epicycles on epicycles and other geometric devices.

**Eccentrics Thus, **

Ptolemy had to introduce eccentricity into his system to avoid some discrepancies between what his model of epicycles and deferents predicted and the results of observing real movements. With the eccentrics, the earth is no longer exactly the geometric center of the planetary orbits and becomes an imaginary point in the surroundings of the Earth. It was still necessary to further complicate the system: the equating point is different for each of the planets.For some planet the equating point runs through a deferent, the center of which is the Earth and it is still the case that the equating point has to travel a distance. deferent, the center of which, by itself

**Equant point **

That was not enough to account for the observed planetary motions. Another geometric device was needed: the equant. This artifice of Ptolemy’s geometric model is particularly interesting, because the aesthetic objections that Copernicus made to him were one of the essential reasons that led him to reject the Ptolemaic model. The equant is the point about which the angular velocity of rotation of the planet’s deferent is constant.

**Generation of an elliptical and a square orbit by means of epicycles **

With all the mentioned geometric devices, the problem of trying to explain the movement of the planets had become a simple matter of the arrangement of the different elements that came into play: a combinatorial game. The question astronomers asked themselves was: what particular combination of deferents, eccentrics, epicycles, and equants can explain planetary motions with the greatest simplicity and precision? With the geometric artifices of Ptolemy, for example, an elliptical trajectory can be explained, for example. And even more difficult! A suitable system of combined circular motions can give rise to a square planetary orbit !! And in general, any geometric shape can be generated from Ptolemy’s model. This model came to worry Alfonso X El Sabio so much that he even said that if God had asked him when making the Universe, he would have recommended a simpler model.