Aren't both Voyagers still gravitationally bound to our galaxy? They have escaped the sun but not milky way. In this case they will never leave our galaxy.

Good point. A quick google gives 537 km/s as the Milky Way's escape velocity, or 1,201,000 mph. Not going fast enough for that.

Moot point for Andromeda since that's coming here, but it'll never ever get to any other galaxies.

Voyager’s stated velocity is relative to the solar system, which imparts its own velocity relative to the Milky Way to Voyager. Another quick google suggests Sol is swinging around the galaxy at 200 km/s so Voyager’s 17 km/s is really nothing.

Also depends on whether Voyager's velocity is in a useful direction, it could just as easily be counterproductive. But not much difference either way.

But might they not travel through another star system in this galaxy before getting anywhere near another galaxy?

"Voyager 1 will eventually come within 1.6 light-years of the star Gliese 445 — in astronomical terms, this will be a near-miss. But don't hold your breath; the "encounter," for lack of a better term, won't occur for another 40,000 years.

After that, it gets a little difficult to predict Voyager's journey, as chaotic motions within the galaxy make accurate predictions of stellar movements challenging. But given the wide swaths of empty space between the stars, the spacecraft's visit near Gilese 445 is probably the closest that Voyager 1 will approach another star, ever."

https://www.space.com/39161-fate-of-the-voyager-spacecraft.h...

OP said star system. You’re quoting distances to another galaxy.

I’m responding to

>Is it necessarily true that our species will not exist when Voyager 1 and 2 fly through in a galaxy far far far away a long long time in the future?

Thanks for your answer btw, it was exactly what I was looking for as I didn't know the speeds of the Voyagers.