What keeps most galactic stars from falling into the centeral black hole?

We know from Kepler's Second Law, that a line from a planet to the Sun sweeps an equal area in equal time. The planet's velocity increases when it orbits closer to the Sun. The area swept is a triangle 1/2 r v sin (theta) = constant, asserted by Kepler, based on observations by Tycho Brahe. (From a college physics text book by Ohanian.)

Similarly, stars in the Milky Way galaxy orbit the Andromeda black hole. Conservation of angular momentum keeps most stars from falling in. Also, Newtonian gravity rapidly decreases with distance form the central black hole.

What keeps the stars in a star cluster apart? I believe that the relative motions of the stars and their relative angular momenta keep the stars apart.

How is Modified Newtonian Dynamics involved in keeping stars together and from wandering off into space?

I agree. But it is important to realize that the significance of a black hole is not so much tremendous gravitational effects as it is having all that mass compressed into a tiny space. A black hole has no greater gravitational effect then the same amount of mass spread out would have. There can be small black holes that do not have significant gravitational effects unless you get very close. In fact, many black holes at the center of galaxies are a small percentage of the total mass of their galaxy.

KurtLudwig said:

Similarly, stars in the Milky Way galaxy orbit the Andromeda black hole.

Uh, Sagittarius A is going to be sorry to hear about this change.

phinds said:

Uh, Sagittarius A is going to be sorry to hear about this change.

Technically Sagittarius A* if we are talking the Milky Way black hole.
(Sagittarius A is a larger grouping)

Orodruin said:

Technically Sagittarius A* if we are talking the Milky Way black hole.
(Sagittarius A is a larger grouping)

Huh. I didn't realize that. I've always heard it called Sag-A-Star but thought I'd use the formal name (incorrectly it seems). Thanks for the correction.

It's called Sagittarius A Star because it's not a star. Go figure.

Since we're in all-out quibble mode - stars in galaxies don't follow Kepler's Law. That applies to the situation where the central mass is all there is, and an elliptical orbit among stars that make up a distributed mass is not that.

We've quibbled about the Andromeda black hole. There might (or might not) be two. M31 has an odd double-nucleus structure, which may indicate two central black holes today, two central black holes in the past, or something else. I think "something else" is today's leading candidate explanation, but consensus has shifted in the past and might continue to do so. It's behavior changes on human timescales, so we may get some new evidence that clarifies things some time.