I had this urge to write a little program to simulate a sattelite orbiting the Earth. Since I don't play Starcraft anymore, I have the time and energy to do it! So I wrote a first version using Matlab:
The easiest part was the mechanics. I spend more time on tiring Matlab details, like how you can do an animation, that you can't have fixed interval outputs with ode45, you have to do interpolation if you want it badly etc.
As for the orbital mechanics part, go check out http://www.braeunig.us/space/. It is a fantastic site.