Algodoo

Orbits are very stable when nothing disturbs them too much. You can see it by making a scene with no gravity or air friction, and throw a ball around another ball with high attraction, after a few tries it will go into an elliptical orbit. In this scene, i've enabled slight gravity, this causes the eccentricity of the orbit to increase until it crashes into the star/planet it's orbiting. If you disable gravity, the circle will orbit in a circular orbit. The eccentricity grows because when it's going down, gravity is helping it, and the faster it goes down, the farther it will go sideways. This will cause it to be slightly more eccentric. When it goes up, gravity is slowing it down, making it's return to the star/planet slower, and the cycle repeats, but with a bigger eccentricity.