Friday, March 16, 2012

Kepler's First Law

Johannes Kepler was a very famous astronomer. He was one of the first astronomers to understand the physics behind our solar system and how objects orbit one another. If you ever take a course in astronomy, one of the first concepts you will learn about is Kepler's three laws of planetary motion. Today I introduce Kepler's first law of planetary motion.


Kepler's first law: Planets orbit the sun in an ellipse with the sun at one foci .

With the technology and telescopes that we have today, it's easy to show that planets follow a squished circular shaped path around the sun called an ellipse . But how did Kepler know? Back in the early 1600's, astronomer and physicist Tycho Brahe took very precise measurements of the position of Mars in the sky. At the time, astronomers believed that all planets orbited in a circular path with the sun at the center. Assuming this is true, Brahe calculated where he expected Mars to be located in the sky throughout the year. To his surprise, the position of Mars never matched his prediction! He then gave Kepler the task of figuring out why the data and predictions did not match. Kepler discovered that if you model the Earth and Martian orbit using ellipses with the sun at one foci, Brahe's predictions would match up perfectly with his observations! We can quantify how "squished" the circle is using a parameter called eccentricity. An eccentricity of 0 means the planets path is a perfect circle. An eccentricity of 1 means that the planets path is a straight line. Planets orbit with eccentricities between 0 and 1, and most of the planets in our solar system have an eccentricity of <0.1 i.e. almost circular. This law is universal, which means it can be applied to extrasolar planetary systems as well as our own.