I guess that's where distance and velocity come in? So if you only move it a small amount, over a great distance it would be enough to make a hit a miss? Say we have 18 months a millions upon millions of miles before impact. We push it successfully a short distance which makes its trajectory a miss for earth. We could then plan out where it will be in the future and in necessary do it again? I don't know much about the subject or the math that goes into something like this. It's just really interesting

Say someone spots a planet killer, how much time would we need to put up a fight? Now that we know its entirely possible to deflect. Obviously the bigger the object the bigger we would need the craft to be for deflection, right?