According to simulations… if a binary star system, with one or both of the stars bearing planets, swings too close to the giant black hole in the center of the galaxy, the end result could be planets zipping outbound at 30 million miles per hour.
Runaway Planets Zoom at a Fraction of Light Speed
Here’s the thing, though… the acceleration and tidal stresses would probably be pretty spectacular. I’d bet that in many, if not not, cases, the “planet” would be converted into a cloud of rubble that would then, over time, reform into a world.
The radiation environment at the center of the galaxy would be pretty harsh, too. No real way that anything resembling an ecosystem could survive the close passage by the black hole. And apart from geothermal heating… if the planet is torn from its star, it would quickly become an extremely cold and dark planet, doomed to exit the galaxy in fairly short order. Taking the long way out, though the galactic plane of the ecliptic, such a planet might exit the galaxy in a million years or so. Going straight “up,” it’d get out in a timespan measured in a few dozen millenia. And once out, it would almost certainly never encounter stars again.