I'm making a game which takes place in an asteroid field that is very dense - I'm talking close enough that one is able to jump between asteroids (provided you have some sort of additional thrust behind your movements). These asteroids range in size from about the size of a house to a few kilometers in diameter. Is this actually possible? If not, what sort of sci-fi excuse can I present to account for this anomaly?
Some additional information: These asteroids have enough gravity to pull objects towards them (asteroids of a few kilometers in diameter have about the same gravitational pull as Earth for gameplay reasons), and they are static (they don't move. This is mainly because you'd need a NASA super-computer to calculate all ~5000 of these guys on screen at one time).
Edit: Thanks for the answers! Seeing the top post gave me an idea for how it will work. It's likely that I'll have it take place quite a while after a planet or moon got shattered; long enough for fragments (asteroids) to begin merging inwards, but not so long that they would form together or anything. Once again, thanks for the help with this! I'm not much of a physicist myself, so the outside perspective was quite helpful. And as for whoever suggested adding the magic tag, that was actually one of the options I was considering up until now ;)