The ancient Greeks studied the heavens and they decided that the celestial bodies could not move on any kind of curve unless it was a circle. To them, the circle was the perfect curve and therefore the only one that was worthy for the path of a celestial body. This theory was originally conceived by Plato, but it was later accepted by all of the Greeks, so they were stuck in a universe where the motion of the planets could only be either in a uniform circular motion or a combination of uniform circular motions. There was a big problem with this model for understanding the motion of the universe, because at certain times, the planets seemed to reverse their direction of motion around the Earth, which we now call retrograde motion. The planets periodically seemed to get brighter and then sometimes they became less bright, which was interpreted to mean that they were getting closer or going further away from the Earth. If the planets only had perfectly circular motion, then the solar seasons would be more equal. At times the Sun seemed to be speeding up and slowing down during various points in the planet’s orbits.
The retrograde motions of the planets, puzzled the Greeks because they needed these planets to turn uniformly and that is not what they were observing. This aspect of planetary motion was referred to as saving the phenomena, and it dominated cosmology all the way up till the time of Newton. The retrograde motion, varying brightness and varying velocities made the Greeks come up with some interesting models to describe the motion of the heavens. The Greeks knew that they had to develop geometrical paths which approximated the motions that they observed and that these could only be fashioned by using circles and motions that were compounded out of circles.
Claudius Ptolemy a Greco-Egyptian, Alexandrian-Roman writer who was also known as a mathematician, astronomer, geographer, astrologer, and poet created a model of the solar system that was a great refinement over the other previous models developed by the Greek astronomers. Ptolemy’s model could accurately explain the motions of heavenly bodies, and thus it became the model for understanding the structure of the solar system. The Ptolemaic model was intricate, but it was able to account for the observed motions of the planets, by having each planet move on a small sphere or circle, that was called an epicycle. This than moved on a larger sphere or circle, called a deferent.
Nicolaus Copernicus a Polish astronomer and mathematician changed everything when he proposed that the Sun was stationary in the center of the universe and the Earth revolved around it. Copernicus came on to this line of reasoning because he was disturbed by the failure of Ptolemy’s geocentric model of the universe as it accounted for the retrograde motion, but it gave no reasoning why this could happen. Copernicus created a concept of a universe in which the distances of the planets from the Sun bore a direct relationship to the size of their orbits. This was not a perfect model either, but it became a start for changing the way the world was viewed.
Most of our knowledge of celestial motions is derived from a Danish astronomer named Tycho Brahe. Tycho spent more than 20 years of his life making accurate measurements of the position of the planets in the sky. When he died, Johannes Kepler inherited all of his data and he used this to write the three laws of planetary motion. Kepler was determined to find the exact orbit of Mars. His preliminary analysis showed that the orbit of Mars was very close to being a circle, but he found that the Sun was not at the center of this circle. He noticed that Mars varied its speed as it went around in its orbit, and it moved fastest when it was closest to the Sun (at perihelion) and slowest when it was furthest from the Sun (aphelion). Kepler believed that the motion of planets must be in a simple steady uniform motion, or at least it must be made up of simple steady motions, and he just needed to find the right geometrical shape.
Along comes Isaac Newton, and he is perplexed leaning on the fence, not knowing if Plato and Aristotle were right or this new gut Kepler, who said that the planets are not in circular orbits, but instead they are in elliptical orbits. In order to figure out who was correct, Newton had to invent a new form of mathematics called calculus and as it turns out Kepler won.