The geocentric model of the universe is a paradigm which places the Earth at the center of the universe. Common in ancient Greece after the discovery of the (more or less) spherical shape of Earth, it was believed by both Aristotle and Ptolemy. Most Greeks assumed that the Sun, Moon, stars, and planets orbit Earth. Similar ideas were held in ancient China.
The geocentric model assumes a spherical Earth; thus it is not the same as the older flat Earth model. Also, according to this model, the orbits were perfectly circular and not elliptical.
The geocentric model held sway into the early modern age; from the late 16th century onward it was gradually replaced by the heliocentric model of Copernicus, Galileo and Kepler due to the simplicity and predictive accuracy of that newer model.
In this model, a set of fifty-five concentric crystalline spheres were considered to hold the Sun, the planets, and the stars. These spheres (called deferents) revolved at varying velocities around the Earth to account for the rising and setting of celestial objects every day.
However, this simple model of the revolutions of spheres could not explain all astronomical phenomena. In particular, certain celestial bodies were observed to wander across the fixed fields of stars over time; mostly they wandered in one direction, but occasionally they seemed to reverse course. These "wandering stars" were given the name "planet", based on the Greek word planetes, meaning "wanderer". To explain this strange retrogradation, Aristotle claimed that planets were attached, not directly to deferents, but to smaller spheres called epicycles. The epicycles were themselves attached to the deferents; the simultaneous revolution of both sets of spheres created an occasional apparent reversal of the planets' motions across the skies of the Earth.
Ptolemy further modified this model to more accurately reflect observations by placing epicycles upon epicycles, creating an extraordinarily complicated--but fairly accurate--depiction of the cosmos. He also displaced the Earth from the center of the universe, claiming that, while Earth was enclosed by the celestial spheres, the spheres actually revolved around a point called an eccentric, which was near the Earth but not quite on it.
This elaborate theoretical system stemmed largely from one important observation. If Earth did move, then one ought to be able to observe the shifting of the fixed stars due to parallax. In reality, the stars are so far away that this motion is undetectable without careful telescopic observations, but the lack of parallax was considered the death of any non-geocentric theory for a thousand years.
1610, Galileo Galilei used his telescope to show that Venus went through phasess, just like the moon. This observation was incompatible with the Ptolemaic system. In the 4th century BC, Heraclides Ponticus had already proposed that both Venus and Mercury orbited the Sun rather than Earth. The observation by Galileo led to interest in the Copernican system and the Tychonian system, which explain how the Sun is commonly in between the Earth and Venus (see phases of venus).