If you want to use some math to model it for you, you can write a fairly simple program using OpenGL and C. But if you knew enough programming to succesfully do that, then you wouldn't have asked. However, you can download a mathematics program such as Livemath (not too good but it will suffice for your purposes) to model elliptical orbits.
To do so just use the polar formula for an ellipse, a/(1+b*sin(theta)) and model it for whichever a and b you desire in order to model the orbit you want. If you want to add even more realism, you can program this orbit in relationship to the velocity of the orbiting body, and this velocity is going to be determined by amount initially given and the acceleration of the body due to gravity (-Gm_1m_2/r^2). Anyway, all you really need is 1/(1+bsin(theta)) and you should be able to get what you want.