A hands-on
demonstration
of retrograde
motion.
This applet below illustrates the apparent motion of an outer planet as seen against a distant background starfield. In the lower panel, the blue dot represents the Earth, and the red dot Mars. The big yellow dot is the Sun. In the top panel we see Mars and the Sun projected against the distant stars.
How to work it: Click on the "Run" button to set things in motion. Be sure to turn tracing on and watch the apparent motion of Mars against the stars as the Earth overtakes it. Try watching for several revolutions, you might see several different curve shapes. You get nicer curves if you slow the motion down a bit.

Applet © Rob Scharein, Hypnagogic Software, Vancouver, BC, CANADA