Originally posted by vivify
What is the escape velocity to break free of the galaxy's gravity and exit?
Voyager is believed to have left the solar system (though there's some debate on that). Say it did: wouldn't Voyager need extra velocity to break from the sun's gravity? How can it exit simply by continuing to travel? Or is there something I'm missing?
These kind of probes gain velocity with no fuel expended by slingshot effect around a massive planet where the planet loses a tiny bit of velocity but because of gravitational attraction and the path the probes are aimed to take, will gain a lot of free velocity so all it takes is a close encounter with a Jupiter or Neptune and it will be slung outwards at an angle you chose by the vectors of the probe's approach and exit. So it's not too difficult to achieve solar escape velocity.
As to the galaxy, if I understand it correctly, the entire solar system is in orbit around the center of the galaxy and the velocity is about 300 km per second, roughly. So you go the square root of 2 times whatever orbital velocity you see and you have galactic escape velocity for anything in the solar system, so 1.414 times 300 is about 425 km/sec to get out of the galaxy at our distance from the center. Closer to the center, of course, that velocity goes up and further away, that escape velocity goes down some, except the whole galaxy is akin to everything sitting on a plate and rotating instead of being independent.
That is the result of dark matter being something like 5 times the mass of our kind of matter so the galaxy cannot rotate like it would if the regular matter we are made of was the main constituent of the galaxy.
That will complicate the escape velocity formulas for sure. But at least our local escape velocity will be around 425 Km/second.
So that probe will probably be picked up by Andromeda galaxy in a billion years or so but maybe it will be going so fast it will gain velocity by the same method as a probe going by a planet so maybe it will sail on till the universe folds up shop.