That would work if everything in the universe stayed in the same place. It doesn't. Voyager crossed and will continue to cross the path of several planets, moons, ect. On the other hand, they could trace the radio signal.
Interesting thought, but hypothetically I suspect an alien race capable of space travel could extrapolate voyagers origins. Not to mention the craft wont really be that distant in galactic terms in the next thousands of years.
From physics we know that voyagers current trajectory will be tangent to the last gravitational body it interacted with, which I think was one of our gas giants like Neptune or Saturn. So in other words, voyagers exact opposite course will be where it escaped the gravitational pull of the planet (like a stone leaving the sling).
Now, since then that planet has moved in orbit around the sun, and the sun and our solar system have moved as well within the galaxy. So the exact opposite of voyagers course will follow a path to some empty point in space.
The thing is that empty point in space will be in cosmic distances, still very close to our solar system. Considering that our nearest star, alpha century, is what, 4-5 light years away?
Anyway that is my deduction, but for gods sakes Jim, I'm a civil engineer not a physicist.
