Two bodies problem in other reference system

[Vrbic]

Hello,
I would like to try to "model" motion of two gravitationally interacting bodies. But from some "separated" point. I can find the trajectory of mass point to orbits around some other mass point from point of view one of them (using binets formula). But in this reference frame I am sitting in focus (on that point). But I would like to observe moving of these bodies from other reference system, where I am "static" (or sitting at infinity) and the bodies are orbiting each other.
I am thinking it should be possible to transform result where I am in the focus to some other frame, but I don't know how.
Or is it better look at this problem in other way from start? How?

 

[UltrafastPED]

If your "local" model uses elliptical coordinates you should be able to transform those to your rectangular system. You just have to keep track of the relative locations of the origins.