Kepler's Second Law
- A JAVA Interactive Tutorial

To use this tutorial, you will need a "JAVA-enabled" web browser.

For any two bodies that attract each other with a force inversely proportional to the distance squared ( F ~ 1/R2), the line joining the two bodies sweeps equal areas in equal times.

This is the modern formulation of Kepler's second law. For a historical perspective of the work of Johannes Kepler and Tycho Brahe (whose careful observation of the motion of Mars were used by Kepler) click here.

Suppose these two bodies are the Sun and a planet (see the "applet" in the separate window). First, let us test your intuition. From Kepler's first law, we know that: the orbit of a planet around the Sun is an ellipse . In the panel of the applet window, choose an eccentric orbit, that is one in which one of the semiaxis is much bigger than the other.

Question If Kepler's second law holds, do you think that the speed of the planet will be constant along its orbit around the Sun?

Now run the "applet" and watch for the motion of the planet (Don't touch the buttons yet). Does it have constant speed? (The blue arrow indicates the direction and its length is the magnitude of the velocity) If not, where along the orbit is it slower/faster?

Do you need help in running the applet?
Let us now test Kepler's second law. Press the start button; after a few seconds, press the stop button. In the panel you can read the amount of time taken to complete that fraction of the orbit as well as the area swept by the line joining the Sun and the planet. To verify Kepler's second law, press the start button. The area traced by the line joining the Sun with the planet will become visible. After the amount of time given by the top box has elapsed, the tracing will stop automatically. You can compare the two areas which have been traced in equal times.

For a strongly elliptic orbit, it is hard to visually verify that equal areas are swept in equal times; but the panel gives you the actual areas swept. As you can see, they are the same.

Now choose "LOAD CONFIGURATION" and try the applet out with another type of orbit.
Last modified . Written by David McNamara and Gianfranco Vidali . Department of Physics, Syracuse University. This project was partially supported by a NSF- Curriculum Course Development Grant.