What is the escape velocity of our Galaxy relative to? I've been thinking that everything has a relative escape velocity, if it has Mass, seemingly. You can escape orbit around the earth by accelerating enough. You can escape the orbit of the sun by accelerating enough. Heck, this is kind of a stretch, but even electrons can escape an atom relative to how much electric charge the nucleus holds. What would it be like to escape the orbital velocity of our Galaxy-- and what exactly would it be relative to-- a black hole at the center of the Galaxy? 

The quote was:


  Solar system's orbital velocity is estimated at roughly 220 km/s, and galactic escape velocity for our vicinity at about 537 km/s. So in the direction of Solar system's velocity vector, velocity required to escape Milky Way is ~ 317 km/s. And much more, if this Solar system's own orbital momentum cannot be used to full extent and a launch in other directions is required. This is of course assuming you can launch on a trajectory that avoids getting too close to gravitational influence of other solar systems.


How in the world do you calculate the escape velocity of other galaxies let alone our own-- do we know what the solar systems in the Milky Way orbit and how they orbit it?
One way to think of the Escape velocity is to imagine it backwards.

Instead of a rocket being fired into space, think of the same rocket, starting at rest relative to the Earth at a great distance (for this thought experiment pretend the sun, doesn't exist and the rest of the universe is empty), then let it fall to the ground. No matter how far away you start, the speed when the rocket hits the Earth will always be 11km/s or less. 

So if you start with 11km/s or more at the Earth's surface, you have enough energy to coast forever into space. The escape velocity at the surface is 11km/s, the escape velocity would be different, and lower, if you were already in a high orbit.

We can do the same thought experiment with a galaxy. We know, roughly the distribution of mass in the galaxy (most is in a large blob of dark matter  with the visible disc inside it) Now take a rocket ship a very great distance from the galaxy, and allow it to fall.  As it passes the sun, the rocket will be moving at 537km/s relative to the centre of the galaxy. (there is a black hole there, but it is tiny compared to the galaxy, so has very little effect on the gravity of the galaxy)

If you know how the mass of a galaxy is distributed we can get a good idea of how fast something would be travelling at any point, if allowed to fall. And by the same argument as above, that gives the escape velocity at that point.

The escape velocity around the sun is about 1/600 of the speed of light. The journey to leave the Milky way is at least 30000 light years long, This means it is going to take about 20 million years to reach the edge of the galaxy, since you will be getting slower as the galaxy's gravity pulls you back. Space (as has been observed) is big.