If there is a supermassive black hole at the centre of our galaxy, why is our galaxy so stable?
1 Answer
Because a black hole's gravity is all-powerful only within a limited amount of space. Most of our galaxy is so far away from the hole that things are safe even if they move relatively slowly.
Explanation:
What makes a black hole able to capture everything, including light, is when all its mass can simultaneously exert gravity in one direction at close range.
To understand this, suppose you could go inside the Sun and get within 10 km of the center. Most of the Sun's mass is then equally distributed in all directions around you, and thus can't pull you in one direction. Only the small part of the Sun's mass in a ball concentric with the Sun and lying below you can exert a net force towards the center. The Sun's gravity becones weaker not stronger as you get close to the center, once you get inside most of its mass.
But suppose that the mass, instead of being in a big fluffy ball a million km or so across, were concentrated in one point so you could not get inside any of the mass. Now at a distance of 10 km all that mass is pulling you onwards, not just a tiny bit of "net" mass. You experience far stronger gravity than what you find 10 km from the actual center of the Sun, or hundreds of thousands of km away at the surface of the real Sun. And it keeps strengthening as you go within 8 km, 6 km, 5, 4 , ...
At 3 km away from the concentrated solar mass, with all the mass still below you, gravity becomes so great that you have no chance to escape, not even light can escape anymore, never mind that light could have escaped from the center if there had been a big, fluffy Sun with its mass all spread out. That 3 km is called the Schwarzschild radius corresponding to one solar mass. It's the range within which a mass must be concentrated to get that all-powerful gravity. General relativity tells us that the Schwarzschild radius is directly proportional to the amount of mass.
How does this relate to the center of our galaxy? Here we see a lot of concentrated mass, maybe four million times the mass of the Sun. The Schwarzschild radius is then four million times that of one solar mass, thus 12 million km. That is a lot of space ... or is it? The volume inside the Schwarzschild radius would not even engulf the orbit of Mercury, let alone a whole galaxy over a hundred thousand light years across.
So, only a very tiny part of our galaxy is exposed to the full gravitational power of that central black hole. Most of it has a much weaker, more "ordinary" gravity around it.
