## Shape of the moon's orbit

To use the two applets embedded in this page you need the Imagine plugin.

The radius of the earth's orbit is 100 units, and you can change the radius of
the moon's orbit with a slider.

You also can change the number of revolutions the moon makes around the earth
while the earth make sone revolution around the sun.

To study this problem in more detail, the next applet immediately draws the
full orbit, and again you can change the moon orbit radius and the number of
revoutions of the moon.

Try to answer the following questions:

- When does the orbit have loops and when not?
- When is the orbit convex.

A convex curve can be described as follows:

When you follow it with a car the steering wheel always is on one side, or
in other words, you do a left turn all the time, or you do a right turn all
the time.

Try to find mathematical conditions for loop free moon orbits and for convex
moon orbits.

If you like this example, give me feedback.

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Author: Erich Neuwirth