Very cool! I was able to get 2 masses to oscillate around each other in a funny way[1]. Seems they keep going like that forever. What is this kind of equilibrium called?
That's the thing with those kind of simulators (or, actually, with reality), your reference has no relation to the center of mass of the system.
Of course, if you "were there" the reference would be the center of mass, like the reference of the solar system is "The Sun" (or a point inside it)
https://en.wikipedia.org/wiki/Barycentric_coordinates_(astro...
If you limit yourself to looking at the position of one body with respect to another, the orbit will be an ellipse. A circular orbit is simply a special-case ellipse with an eccentricity of zero. This is true for any two orbiting masses -- from the perspective of either of them, the other body's orbit will be an ellipse. And yes, it's always with respect to the common center of mass.
Interestingly, mostly because of Jupiter, the solar system's common center of mass can sometimes lie outside the sun.
https://en.wikipedia.org/wiki/Barycentric_coordinates_(astro...
Likewise, two bodies that are not bound will follow hyperbolas in the center of mass frame.
Or parabolas, which also represent unbound solutions. In an orbital system, a parabolic trajectory represents escape velocity (exactly), a solution in which the escaping body's velocity is in progressive decline, and that reaches zero at infinity.
http://en.wikipedia.org/wiki/Binary_star#mediaviewer/File:Or...
OP: This is an amazing tool to learn the sensitivity of dynamical systems to initial conditions. Well done!
It took a little bit to generate this one.