Renaissance Astronomy, Page 25

Renaissance Astronomy, Page 25: [Previous Page] [Next Page] [Class Home Page] Textbook pages 58 - 59

Kepler's Three Laws of Planetary Motion

Unlike Tycho Brahe, Kepler believed in the Copernican system. While Copernicus had correctly placed the Sun at the center of the Solar System, he had erred in assuming the orbits of the planets to be circles. Thus, in the Copernican theory epicycles were still required to explain the details of planetary motion.

It fell to Kepler to provide the final piece of the puzzle: after a long struggle, in which he tried mightily to avoid his eventual conclusion, Kepler was forced finally to the realization that the orbits of the planets were not the circles demanded by Aristotle and assumed implicitly by Copernicus, but were instead the "flattened circles" that geometers call ellipses. This was achieved by Kepler's work on all the Mars observations given him by Tycho Brahe, and Mars just happened to be the most un-circular orbit of all planets then known!

Properties of Ellipses
1. An ellipse has two foci. The sum of the distances to the foci from any point on the ellipse is a constant (A + B = Constant). A circle is a special type of ellipse, where A = B.

2. The amount of "flattening" of the ellipse is termed the eccentricity. A circle may be viewed as a special case of an ellipse with zero eccentricity. Typical eccentricity of the planets is a few percent (nearly circular!).

3. The long axis of the ellipse is called the major axis, while the short axis is called the minor axis (adjacent figure). Half of the major axis is termed a semimajor axis. The length of a semimajor axis is often termed the size of the ellipse. With planets, the semi-major axis refers to the orbital distance.

Kepler's First Law:

I. The orbits of the planets are ellipses, with the Sun at one focus of the ellipse.
The planet follows the ellipse in its orbit. The Planet-Sun distance is constantly changing as the planet goes around its orbit. For illustration the orbit as rather eccentric; remember actual orbits are much less eccentric than this.