Mutual solar-extrasolar orbital foci

[Loren Booda]

Can there exist a satellite which shares orbital foci with our Sun, and with the extrasolar likes of (e. g.) the Oort cloud - but in particular another star, say Proxima Centuri?

[mathman]

Although theoretically possible, it is highly unlikely. Alpha Centauri is so far away that the mutual gravitational attraction with our sun is negligible compared to overall Milky Way effect.

[Loren Booda]

Thanks, mathman, that makes sense.