One of the best ways to see the laws of nature in action is to learn enough about some programming language to be able to do simple algebra, geometry and calculus with it. Then a whole new world opens to your exploration.

You can build your own "solar system", launch comets into orbit, and track their progress governed by the laws of gravity and mechanics. The example shown below has two fixed massive objects (perhaps Saturn with one large moon), and the dashed line shows the track of a third object, launched near the arrow showing its initial momentum. This orbit almost repeats but gradually drifts out of shape leading to a collision with the larger planet. Changing the initial momentum gives a variety of orbit shapes including ellipses and figure-eights. Most orbits in this system are unstable, although some are not. Why then is our own solar system so stable?

The reason for the difference between the model system and the real one is both simple and informative. It turns out that placing the two big sources of gravity in fixed positions instead of allowing them to orbit each other creates "resonant perturbations" which destabilize almost all orbits. For example elliptical orbits about the bigger planet grow in eccentricity with time due to the attraction of the smaller planet. If the two major bodies were in orbit, this effect would average to zero except for special orbits of the comet which happened to have a resonant period with respect to the major orbit. These few special orbits would lead to a collision and loss of the third body by accretion.

One sees in this simple simulation a glimpse of some of the physics that may govern the dark bands in Saturn's rings.

Figure 1. The dashes are equally spaced in time, showing the slowing at the left side turning points. The left planet has one fifth of the mass of the right one, whose ring is just for decoration.