Kepler's Second Law

At which point of its elliptical orbit is a planet located at a given time? In 1609, Johannes Kepler could answer this question with the following simple law:

Kepler's second law of the undisturbed planetary motion:
The line joining the planet to the Sun sweeps out equal areas in equal intervals of time.

This law shall be illustrated by a computer simulation. On the top right of the panel there is a list where you can select one of the nine planets or Halley's Comet. In addtion, it is possible to determine the orbit of an imaginary celestial body by entering its semimajor axis and numerical eccentrity (don't forget to press the "Enter" key!). You can stop and start again the simulation of the planetary motion by using the button "Pause / Resume" or make it slower. If you choose the option "Sectors", the Java applet will show two sectors of equal areas and two clocks from which you can read the time for passing these sectors (expressed by the orbital period T). The sectors can be enlarged or reduced with a slide control or twisted with pressed mouse button. The vector of the planet's or comet's velocity will be drawn as desired. On the bottom right of the panel the program gives informations about the distance from the Sun (in astronomical units; 1 AU = 1.49597870 x 1011 m) and the velocity (in km/s).

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Physics Applets

© Walter Fendt, April 4, 2000
Last modification: February 3, 2010