In the Android game "Osmos" you can experiment with maneuvering a spaceship in a gravitational potential. Once the app is started, go to level 3 "solar".

The game is like Saturn's ring. You are a snowball in the ring surrounded by other snowballs and you can observe the differential motion between nearby snowballs. You can also change your momentum and observe the effect on your orbit.

If you are on a circular orbit of radius R and you want to change to a circular orbit of radius 2R, what is the most efficient strategy? How would you draw a diagram to illustrate this?

The game is also like a model of an accretion disk. In the sun's accretion disk, objects accumulated by gravity into planets and the same thing happens in Osmos. Large objects tend to accumulate faster than small objects and the end result is a set of planets with widely-separated orbits. This phenomenon is mirrored in Osmos because in the game, large objects tend to accumulate faster than small objects.

Suppose you want toplay the game with the purpose of observing how accretion works. You could move your spaceship to an orbit in the Kuiper belt so that it doesn't interfere with the accretion. After the accretion has finished, what does the result look like?

"Liquid Simulator" is an interactive fluid dynamics simulator.

"Wolframalpha" is a versatile calculational tool.