Kepler and Gravitation

Summary

Johannes Kepler (1571 - 1630) was greatly impressed by the beauty of the heavens. Using the framework devised by Nicholas Copernicus and meticulous observations he devised three laws from which the motion of the planets could be calculated. Although Kepler had no understanding of why the planets moved in the way they did, his laws are largely correct. They are of great significance for the study of gravitation because the fundamental principles of planetary motion can easily be understood from them. Moreover, these laws formed the background to Newton's thinking about planet interaction and the relationship between masses which led to his Universal Law of Gravitation.

Kepler's First Law states that the path of the planet is an ellipse with the sun at one focus. Although at the time it was commonly understood that the planets moved in circles around the sun, Kepler's data showed this belief to be erroneous. Only by understanding that orbits are elliptical can we begin to explain many of the observed phenomena of planetary motion.

Kepler's Second Law relates the speed of the motion of the planet to its distance from the sun (because the orbits are elliptical, the distance to the sun varies). In fact, it states that if a line is drawn from the sun to the planet (a radius), then the area swept out by that line in a certain time will be a constant. This means that when the planet is farthest from the sun it moves much more slowly than when it is closest to the sun. This law is basically a statement of the principle of conservation of angular momentum for planets.

Kepler's Third Law is somewhat different from the other two: it is more mathematical than the first and second laws, allowing a calculation to be made of the period of the orbit if the radius is known, or the radius to be calculated if the period is known. More precisely, it states that the square of the period of the orbit is proportional to the cube of the radius. This applies not only to planets orbiting the sun, but also to satellites orbiting the earth, and is therefore important in space technology.

In the following SparkNote Topics we shall see how Kepler's Laws formed a framework for Newton's thinking about gravity and how Kepler's laws can be derived from Newton's Universal Law of Gravitation.