Gravity around small black holes

[Paul Katan]

If a black hole had a mass similar to the Sun (I know black holes tend to be at least three times larger but let's assume an unusual series of events) how far would the are of extremely distorted bent gravity around it be could it cause closely orbiting bodies to be pulled or pushed out of orbit around the black hole?

 

[mfb]

A black hole has stable orbits around it in the same way all other objects have them. Even better: sun is a bit oblate due to its rotation, which has a notable influence on the perihelion precession of Mercury for example. A black hole is much smaller, so this effect gets much smaller as well.

Relativistic effects become strong very close to the black hole - for 1 solar mass, for distances below ~100 km. There are no orbits around the sun at that distance because sun is much larger, obviously. The lowest stable orbit depends on the spin of the black hole. If it is not rotating, the lowest stable orbit has a radius of about 9 kilometers. The lowest circular orbit is at about 4.5 kilometers (light can orbit here), and everything below that either falls into the black hole or escapes directly.
Note that "radius" is not a trivial concept close to a black hole.

 

[Paul Katan]

Thanks