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:
Try to find mathematical conditions for loop free moon orbits and for convex moon orbits.
If you like this example, give me feedback.