The Gravity of a Black Hole at Large Distances
      Many people have the mistaken impression that black holes can "suck up" anything that has the misfortune to get close to them. It is true that inside the event horizon of a black hole, gravity is so strong that nothing can escape its pull; but outside the event horizon, that isn't necessarily so.
      Suppose that the Sun became a black hole, this very instant. What effect would that have on us? Well, in about 8 minutes and 20 seconds, the light that has already left the Sun would pass us, and in its place, we would see -- the stars. Without sunlight lighting up the sky, the stars would appear, the same as they do at night, except they would be the stars currently hidden by the Sun's glare, rather than the ones visible after the Sun goes down.
      Very close to the Sun (which would be totally invisible, since black holes give off neither light nor any other kind of radiation under normal circumstances), a careful examination of stellar positions would show that they are a little further apart than usual, due to the gravitational effect of the black hole on light passing near its event horizon. However, presuming that the mass of the Sun were not changed during its (miraculous) collapse to a black hole, there would be no other observable effect of its becoming a black hole, and in particular, the planets would continue their orbital motions just the same as if the Sun were its normal size.
      Now, the average person might assume that because the gravity of a black hole Sun would be very strong near the black hole, it would also be strong elsewhere; but there is nothing in the mathematical formulae which describe the force of gravity which says how big the Sun is; only its mass determines its gravitational effect on objects at large distances. As long as its mass remains the same, its gravity will remain the same, anywhere outside its surface, whether it is as large as it is, or as small as a pin-point. In particular, as long as the Sun is smaller than the orbit of the Earth, the gravitational effect of its mass on the Earth would be absolutely the same as now, regardless of its size.
      Now, there are places where the Sun's gravity would be higher, after becoming a black hole, than before; but they are all inside its original surface. In a normal object, as you move into its interior, the net gravitational force of the layers above you is zero, so only the material between you and the object's center exerts a net gravitational force on you. Moving into the Sun as it currently exists, the gravitational force on you would be less than if it were a black hole, according to the mass which lies outside you. For instance, 90% of the way into the Sun, 90% of its mass lies outside you, so its gravitational force is only 10% of what it would be if the Sun collapsed to a black hole, and all of its mass were still pulling on you, instead of just the mass between you and its center. (Not that it would make a lot of difference, since most of the force on you at that point, inside the present-day Sun, would be the downward weight exerted by the layers lying above you!)
      To summarize, if the Sun could magically be transformed into a black hole, its gravitational effect would remain the same for all objects outside its surface, but would increase for objects inside its current surface, according to what fraction of the Sun's mass normally lies above or below them. A similar situation occurs for real black holes, except that when stars die and become black holes, they normally shed large portions of their mass, so that even outside their original surfaces, the gravity they exert on other objects would less than their original gravitational forces. (You may find it useful to look up a discussion of 'runaway' stars elsewhere on the Internet, instead of waiting for me to find the time to add such a discussion to this site.)