If you own a 50 ton spaceship, please do not intentionally hit any asteroids or other objects with it. What you get is smaller objects heading in different directions at different velocities, none of which are all that predictable, and in total more danger to objects in space than before and still significant danger to ground objects. What you want is to turn it harmless. This is done by gently attaching to it and then giving it a controlled push.
I've been curious about what one could do over time just using the pressure of light from the ground, or enough light to gassify material to add delta V, however high power devices for this would also be effective weapons.
Thanks
Bruce