Heliocentric Model:

While this model is generally called "Copernican" after Nicholas Copernicus, the Polish thinker who proposed this idea in a book published just before his death in 1543, several ancient Greeks also put forth the same idea. Copernicus proposed that the Sun is at the center of things and that the Earth and other planets revolve around that center. The work had been circulating privately for some 15 years before it was published, since Copernicus rightly feared attacks from the church. Copernicus retained the idea of circular orbits, complete with epicycles.

The chief arguments for the Copernican system were its greater simplicity relative to the Ptolemaic system (a debatable point at best) and its greater ease of calculation. While few persons outside of astronomy even considered it worth discussing, astronomers, particularly Galileo, became more and more convinced of it. As Copernicus developed the model, it was not significantly more accurate than the Ptolemaic model.

Several observations were important in the shift from the Ptolemaic to the Copernical model. Tycho had observed a "nova," a new star. Since perfection implied lack of change, this was a distinct embarrassment to the Platonic notion of heavenly perfection. Several astronomers also were able to estimate the distances to comets and show that they would have to pass through the crystalline spheres of the Ptolemaic model.

Perhaps the most convincing evidence was that obtained by Galileo, who was the first to systematically observe celestial objects with a telescope. He observed that the Moon had a rough surface, much like Earth, which made the heavenly perfection -- earthly imperfection idea harder to accept. His observation of moons orbiting Jupiter gave an example of a system which might itself be a model of the solar system, aiding in the acceptance of the heliocentric model.

An important refinement of the Copernican model was proposed by Johannes Kepler. Kepler, who had Tycho's data, was engaged in producing an improved set of tables of planetary positions. He tried elliptical orbits as an alternative to circular orbits with epicycles and found that the calculations were much simpler and at least as accurate. This framework led him to make three generalizations which are called Kepler's laws.

First Law: Planets travel in elliptical orbits about the Sun, which is at one of the foci of the ellipse.

Second Law: The area swept out by a line from the Sun to the planet in a given time interval is the same over all parts of the orbit.

Third Law: The square of a planet's period (time for one revolution about the Sun) is proportional to the cube of its average distance from the Sun.

Notice that Kepler was seeing patterns in the data, patterns which only come to view in the context of the heliocentric model. None of these statements make any sense in the geocentric model. Kepler's ability to make quantitative generalizations within the Copernican framework set the stage for Newton's proposal of universal gravitation as a mechanism for planetary motion.

http://www.astro.ucla.edu/~wright/solar_system.html

http://www.geo.lsa.umich.edu/~keken/278/outl2.html

http://sys12.cs.jmu.edu/wwwhomes/cs685/kepler/html/ancient.htm