Tuesday, May 15, 2012

And Kepler Has His Own Opera - Kepler's 3rd Planetary Law

Kepler's Model of the Solar System
from Mysterium Cosmographicum
(1600) 
On May 15, 1618, famous astronomer Johannes Kepler discovered the 3rd and also last of his planetary laws, and concluded the general revolution of our celestial world that started with Nikolaus Kopernikus about 100 years earlier. And that made him rather popular as he still is today. Did you know that there is a Kepler crater on the Moon, a Kepler crater on Mars, a Kepler asteroid, a Kepler supernova, of course there has to be a space mission named after him, even an opera ('Die Harmonie der Welt' by Paul Hindemith...unfortunately not available at yovisto...at least by now), a Kepler mountain, various universities (including the Johannes Kepler University at Linz in Austria), a Kepler building and even a Kepler graphic processing unit (GPU) on a graphic acceleration card for computers?

I'm quite sure you will remember Kepler's Laws of planetary motion. (If not so, here is a brief recollection...):
    1. The orbit of every planet is an ellipse with the Sun at one of the two foci. 
    2. A line joining a planet and the Sun sweeps out equal areas during equal intervals of time. 
    3. The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.
At the time, Kepler's laws were really radical claims. The prevailing belief was that planetary orbits should be based on perfect circles - at least according to philosophy. Most of the planetary orbits can be rather closely approximated as circles, so it is not immediately evident that the orbits really are ellipses. Detailed calculations for the orbit of the planet Mars first indicated to Kepler its elliptical shape, and he inferred that other heavenly bodies, including those farther away from the Sun, have elliptical orbits too. Kepler's laws and his analysis of the observations on which they were based, the assertion that the Earth orbited the Sun, proof that the planets' speeds varied, and use of elliptical orbits challenged the long-accepted geocentric models of Aristotle and Ptolemy, and finally supported the heliocentric theory of Nicolaus Kopernicus.

At yovisto you might start with a lecture on Kepler's Laws by Prof. Ramamurti Shankar from Yale University. Enjoy!



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