Just how do the astrophysic types do the research on asteroids. Why is this important? Well, if an asteroid of over a certain size strikes the Earth, we won't have to worry about paying our taxes.
In this article there is a discussion about the Four-Body Hill Problem. This is not about a drug deal gone bad, rather it is some interesting mathematical discussion of what happens when four objects that have graviational influence on each other come close together. If you are looking for an example of why to use matrixes in the real world this is one of them.
You might be thinking that this is in space, why would I use it on earth. Well, this could make a space oriented game more interesting if you use the REAL equations rather some lame library. Also, like games, Monte Carlo comes up when the researchers are simulating the influence and long term outcomes.
Take a look, some nice picutres if nothing else.