The remarkable thing about the early Greek system was how well it stands up in modern times despite the official scoffing of science. An example is Johannes Kepler (1572-1630) who, while preparing a mathematics lecture at Graz, Austria, had drawn on a blackboard an equilateral triangle exactly enclosed in a perfect circle. Exactly enclosed within the triangle, Kepler drew another perfect circle. While looking at the diagram, Kepler suddenly realized that the two circles shared a ratio that duplicated that of the orbits of Jupiter and Saturn. Kepler embarked on an attempt to prove that the five platonic solids could be used to determine the orbits of the planets. He failed in this endeavour but he did instead formulate his famous laws of planetary motion.

Johannes Kepler was the true father of celestial mechanics. His theorizing coupled with the precise observational data of his colleague, Tycho Brahe (1546-1601), led Isaac Newton (1642-1727) to formulate his law of gravitation.

Kepler was a true scientist but it should also be noted that he was also an avid Pythagorean. He once stated, "God is a geometer." Kepler is most famous for his laws of planetary motion. Let's review them as they are some of the most important thoughts ever to come out of the West.

Kepler's first law of planetary motion was formulated in 1605:

1. Planets move in ellipses with the Sun at one focus.

Assume two planetary orbits with a common focus, semi-major axis, and period. One orbit is more eccentric than the other. In fact, one orbit describes a circle, the focus of which is at the centre. So, in a circular orbit, the sun will occupy the centre. The more eccentric orbit describes the standard ellipse which has two foci, one near each end. As an elliptical orbit, the sun will occupy one of those foci.

Ironically, Kepler's second law of planetary motion was formulated earlier than the first in 1602:

2. The radius vector describes equal areas in equal times.

In other words, the areas of a sweep of two planets' orbits achieved in the same amount of time, will define the area of each to be identical. This is all the more remarkable because Kepler also discovered that a planet with an eccentric orbit travels faster as it nears the focus occupied by the sun and slows down as it moves away from it. Yet the area swept by that planet when it is closest to the sun and moving at its fastest and the area swept when it is farthest away from the sun and moving at its slowest will still be identical. It is this law that aerospace technicians utilize when they refer to the "slingshot effect" when one of our satellites swings around a planet and uses its gravity to propel it farther out into the solar system. This occurs because the satellite's orbit is highly eccentric and by swinging close around the planet will speed up and be propelled like a stone being swung around in a slingshot and then hurled outward.

Kepler formulated his third law of planetary motion on 15 May 1618:

3. The squares of the periodic times are to each other as the cubes of the mean distances.

Regardless of which planet we choose or its distance from the sun or the eccentricity of its orbit, if we square the period of its orbit and form a ratio to the cube of its mean distance from the sun, that ratio will be identical for all the planets.

Kepler published his first two laws in his 1609 book Astronomia Nova. He published his third law in 1619 in his book Harmonices Mundi. Kepler's laws apply not only to planets orbiting the sun but to any celestial body orbiting another. They apply as much to the moon orbiting the earth as to the earth orbiting the sun. In this sense, they are universal. As stated, these laws, particularly the third one, are what inspired Newton to formulate his law of gravitation. Newton could see an underlying principle to Kepler's laws and sought to uncover it and his law of gravitation was the result.