I see no problem with this kind of cannon, it works at we would expect to see it in a movie. I would not worry too much about the frame of reference, lets just assume it normally stops the object in a "reasonable" frame of reference. The cannon will not be a way to accelerate objects, just because the cannon is moving very fast over the surface of a planet. But its the same issue with speed drives and their "slowdown", this slowdown also seems to choose a reasonable frame of reference.
Just one additional thought, maybe there should be some limit on the size or momentum of the object you stop with it (relative to the energy demands and size of the cannon). I don't think we want a cannon that stops extinction level event asteroids with hand pistols.
Just one additional thought, maybe there should be some limit on the size or momentum of the object you stop with it (relative to the energy demands and size of the cannon). I don't think we want a cannon that stops extinction level event asteroids with hand pistols.