World Builders™                                                                        Session One  --  Astronomy        
         
       Kepler's Laws    

                                         of Planetary Motion

                                       Second Law

This law tells us something about how fast planets travel.  

Kepler's Second Law

A line joining a planet and the sun sweeps out equal areas in equal intervals of time.


 

 

Here we have a picture of a planet going around its sun in an elliptical orbit.
Sometimes the planet is close to the sun, sometimes it is far away.

When the planet is near the sun, it travels quickly.
When the planet is far from the sun it travels more slowly.

Kepler figured out something very interesting.

Suppose that you observe the planet when it is at X.
You come back two weeks later and it is at Y.

Later you observe the planet again. Now it is at A.

You come back again two weeks later. The planet is at B.

Now suppose that we draw a diagram like the one above.

 
We draw lines from X and Y to the sun.
This makes an enclosed space.
We paint the space -- in this picture, green.
We draw lines from A and B to the sun.
This makes an enclosed space.
We paint the space -- in this picture, blue.

Each of these colored areas represents two weeks of the planet's journey.

   Kepler discovered that the area of the blue space = the area of the green space.
     (If you were going to paint these spaces, each one would need the same amount of paint.)

When the times that the planet uses to move are the same, the areas are the same.


 Let's connect this to something that we know already.

When you throw a ball up into the air, it starts off quickly.

As it rises into the air, it travels more slowly, because the gravity of the earth is pulling against it.

The ball goes more and more slowly.
Then the ball reaches a point where it stops going up.

It starts going down.


Gravity is still pulling on the ball.
As it falls, the ball goes more quickly.

Let's look at this planet in orbit.  Now the sun is the source of gravity.

 

 

When the planet is moving away from the sun, the sun's gravity pulls at it and slows it down.

Finally the planet is moving so slowly that the sun's gravity is stronger than the planet's momentum.

At this point the planet starts moving back towards its sun, just like a falling ball.
Now the sun's gravity makes the planet move faster and faster.
It looks as if the planet might just keep going!

However, the pull of the sun's gravity is too strong.
It swings the planet around.
Now the planet is moving so quickly that it can go on its long journey again.

Let's look at Kepler's Second Law again. Does it make sense now?
A line joining a planet and the sun sweeps out equal areas in equal intervals of time.
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© 1998. 2003. Elizabeth Anne Viau. All rights reserved. This material may be used by individuals for instructional purposes but not sold. Please inform the author if you use it at eviau@earthlink.net.