The Search for Planets Beyond the Solar System

This article is about one big idea: "The rate at which the distance between us and a given star changes-it increases or decreases over time." This relationship is a powerful tool in detecting a planet orbiting the star and also in determining orbital and physical information, such as the mass of a planet, its velocity, its distance from the hosting star, the period of revolution, and so on. In particular, if a planet orbits the star, we should have a periodic change in that rate. This rate comes to us hidden in the light that we receive from the observed star. Fortunately, we know how to catch the light.

If you are a student in one of the mathematical or engineering sciences who has mastered the usual core courses of calculus and basics from physics, such as laws of motion and the nature of light, then you have the maturity to follow this presentation.

There are several methods for detecting extrasolar planets (planets that lie beyond the Sun's solar system). The "radial velocity" method that is the subject of this paper is the most successful in terms of confirmed discoveries. Working Group [2006] notes that 161 extra solar planets were discovered by this method. An excellent book on this subject with historical and astronomical background is Croswell [1997].

We review some basics of Kepler's and Newton's Laws, and the Doppler shift of light. Then we present a "pure" mathematical model from which the concept of the radial velocity becomes clear. Finally,we return to the application of detecting planets and the determination of other characteristics and orbital parameters.