- A JAVA Interactive Tutorial

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For any two bodies interacting via a force acting along the line
connecting them, **the line
joining the two bodies sweeps equal areas in equal times. **
The gravitational force is one such force.

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 to deduce the law above as well as two other laws)
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, by adjusting the **Eccentricty** slider,
and then pressing **Submit**.

**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" (press **Continue**)
and watch for the motion of the planet (Don't touch the other buttons yet). Does it
have constant speed? If not, where along the orbit is it slower/faster?
Pressing **Show Velocity** will display a green arrow which indicates
the direction, and magnitude of the velocity.

Do you need help in running the applet? | |

Let us now test Kepler's second law. Press the

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 adjust the parameters of the orbit and press

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.