I found the asteroids idea pretty cool, so based on the proposed rules I made a simple bot that bases its decisions on Monte Carlo walks, without any regard to opponent movement, see http://youtu.be/xRujVT9FhKc
for a demo
Even this simple bot has no problem avoiding asteroids. In the end I think this game is all about ship-to-ship combat, which should be very interesting as there are many possible strategies.
My main concern is that a passive defensive player that moves as slowly as possible and keeps pointing at its nearest opponent might be very successful. The latest code addition where the firing ship's speed is added to the bullet speed is a good change because it gives fast moving ships a better reach than a passive ship.
Another defensive strategy would be to run away from opponents ships all the time. That's why the asteroids are a nice aspect of the game, as they can at least hinder the path of fleeing space ships. Maybe the max speed of the asteroids could be made a little higher to make navigation a bit more difficult. Another idea would be to let the smallest asteroids be immune to bullets so the number of asteroids never decreases.
All in all I like this proposal a lot!