On a related note, starting from a circular orbit, it takes

1/(2sqrt(2) - 3) ~ 5.83

times more energy to throw an object to the center of a gravity well than it does to throw it out of orbit.

It doesn’t matter how close your initial orbit it, or whether you’re orbiting around the Sun or Sagittarius A*. The ratio is always the same, though gravitational assistance from other bodies often affects the calculations in practice.

I expect we’d send a satellite outside the Milky Way long before we get one anywhere near the center of the galaxy. Not that either mission seems particularly feasible with current technology.