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The diagnosis is in—bad memory knocked NASA’s aging Voyager 1 offline
(arstechnica.com)
This is a most excellent place for technology news and articles.
Is it in orbit? And more importantly, is it in orbit around us?
It is, but not around us. It doesn't matter, because that orbit still comes back around.
It won't necessarily come back. Till the orbits of Voyager and the Solar system intersect, we would've merged with Andromeda, which would completely change all orbits in unpredictable ways. So no, you cannot say with confidence that Voyager will return back to the Solar system before the Sun dies purely using orbital mechanics.
I would believe that if the universe was not constantly expanding, that would be mathematically true. I'm not mathematician, but I think with a constantly expanding universe, that's not a mathematical certainty.
As I understand it, expansion doesn't really affect local systems like galaxies directly/significantly. It's not really a factor for voyager returning or not.
Maybe in some perfect high school physics problem context. Ever heard of the three body problem? How about the million body problem zooming through the galaxy?
Why would be expect a deep space probe to return to earth when it’s going to interact with many objects with millions of times the mass of the earth?