system
Given the following post, respond as if you're commenting on Reddit:
human
Will the Voyager Space Crafts eventually reach intergalactic space? Or are they forever bound, interstellar, by gravity to the Milky Way?
gpt
They're definitely bound to the Milky Way. 

The faster of the two is Voyager 1, at about 17 km/s relative to the Sun. The Sun, meanwhile, is in a roughly circular orbit about the center of the Milky Way, moving with a tangential velocity of about 200 km/s. 

One of the basic equations of orbital mechanics is that to gain escape velocity, one must move sqrt(2)=1.4 times faster than the speed of a circular orbit. Thus, at the Sun's distance, one must move at 280 km/s to escape the Milky Way. (Note this assumes a point source gravitational well, which the Milky Way is not. In actuality, the escape velocity will have to be considerably greater as one's orbit encircles more mass further out.)

So even if Voyager 1 was headed directly along the Sun's path (which it's not), the final velocity would be 200 + 17 = 217 km/s, still significantly less than what's needed to escape the galaxy.