I'd like to know when an orbit is closed. I know that, to have a closed orbit, there is a ratio that must be a rational number, but I don't know other things..
What is the orbital motion where both foci are located at one point? I know that an ellipse orbit is motion with two distinct foci.
How do I express the Kepler general orbit $r(\phi)$ in rectangular coordinates? I use the identities $x=r\cos\phi$, $y=r\sin\phi$, and $r^2 = x^2 + y^2$, but I block at some point.