Last stable orbit around a Black HoleLarge masses have a tremendous gravity field - however, that doesn't mean they can actually pull other objects in. In fact, classical two-body orbits around a point mass are reversible - if you let an object drop towards the mass, it will return to the precise same point eventually. Only for orbits around extended objects, it can happen that the test body orbit intersects with a solid surface and is violently ended.
The reason is angular momentum. As a large mass pulls a test body in, the test body accelerates and gets closer - both of which increase the cenrifugal force, which eventually gets so large that the test body is pushed back out against gravity. Only if the initial trajectory of the test body happened to almost intersect with the surface of the central mass anyway, a crash occurs.
At the scale of a solar system, a Black Hole with a radius of 10 km is essentially point-like. Thus, it's actually very hard for anything to be sucked in. In fact, since a Black Hole is an object wita stellar mass, at a distance of a few million kilometers it can be orbited like a star, it's gravitational field is no different there.
Interesting things only happen if you get much closer than that, into the strong gravity field region - some 20 - 30 km from such a stellar mass Black Hole. What happens then is that the effect of the gravity field grows non-linearly - faster than the centrifugal force in fact. Thus, eventually other objects can be pulled in.
There is in fact a last stable orbit - if the test body gets any closer, it will spiral inward. Before that last stable orbit, the test body will come back, but not to the same position as in classical mechanics - this is called the periapsis drag - it will swing around in a petal-like pattern. Note that the last stable orbit is not the event horizon - if the test body has propulsion, it can theoretically still escape till it reaches the event horizon.
Below are orbital simulations with the worldbuilder orbital solver for a test body close to a Black Hole (event horizon shown as black disc):
A classical Newtonian orbit (black) which does not intersect the 'surface' (i.e. the event horizon) always comes back to the origin. An orbit taking General Relativity into account (red) always comes back to the same distance, but the eccentricity vector is dragged around wildly by the strong gravity field it crosses. Changing the orbit ever so slightly pushes the test body over the centrifugal barrier - it reaches the last stable surface, orbits around and then starts to spiral inward from there.
So, in a certain region around the event horizon, Black Holes, unlike classical masses, do pull test bodies in. However, the region is just a few times the radius of the event horizon, and at the scale of a solar system still point-like. The actual mechanism by which Black Holes acquire mass are interactions of material that is orbiting in the accretion disc decelerate material so that it can drift further inward.
Thus, while you don't need to worry about an unstable orbit in the vicinity of a Black Hole, radiation levels and tidal gravity forces will still rip you apart long before you get to the region where gravity is so strong that GR matters.
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