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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.
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