There's a rather curious misconception, or intuition, that many people have related to gravity, and this is sometimes seen in movies and TV. This misconception is that if there's a very large object orbiting a planet (eg. Earth) and it's broken up to small pieces, all of the pieces will fall down. (A related concept is that if small pieces get loose from the large object, eg. garbage or such, they will likewise fall down to the planet.)
I find this misconception rather curious. It's the exact reverse of Aristotelian gravity.
You see, in antiquity there was among some philosophers the concept that heavier objects fall faster than lighter objects. In this case it's the exact reverse: The intuition seems to be that lighter objects fall faster (ie. are pulled more strongly by the planet's gravity) than heavier objects. If the orbiting heavy object gets broken to smaller pieces, or it lets small pieces loose, those pieces will now be pulled by the planet's gravity (because they are no longer attached to the heavy object) and fall down.
It's understandable that it's unintuitive that the falling speed, and thus the orbit, of an object does not depend on its mass. It doesn't matter if what's orbiting the Earth is a tennis ball or a mountain-sized rock: The orbital speed and altitude will be the same for both (if their initial conditions are the same.)
Moreover, breaking up the mountain-sized rock to small pieces isn't going to change anything. The pieces will still orbit the planet in the same way.
Now, if the breaking up was caused by a large explosion, this changes things a bit. However, it does not cause all the pieces to fall down (which is the most common intuition, and depiction in fiction.) Some pieces may fall down, others may be ejected from the system, but the majority will remain in orbit, albeit many in different ones from the original.
This is related to another misconception that many people have, and that's the concept that orbits are extremely "fragile", and that even a slight nudge will cause the orbiting object to plunge to its destruction. That's not so. In fact, it's actually pretty hard to make an orbiting object fall down. You need a rather precise force in a rather precise direction for a rather precise amount of time for the new orbit to hit the planet. Most other directions will simply make it take a different orbit.
(If the orbit gets so close to the planet that the object starts skimming its atmosphere, that changes things, because the atmospheric drag will start to slow down the speed of the object, making it fall down eventually. However, the majority of orbits are not that close.)
In the case of the exploding heavy object, many of the orbits will be unstable, meaning that they will eventually fall to the planet or be ejected from the system. However, in many cases "unstable" means that it takes years, thousands of years, if not even millions of years, for that to happen. Not the few minutes that it takes in movies.