As it happens, I’ve worked on a study of this very issue, and proposed a concept for redirecting objects of moderate size (~1 km diameter iron-nickel bolide). In [POST=12775897]this post[/POST] I addressed the feasibility of shifting the trajectory of an incoming hazardous object. Redirecting an object of such size is at least remotely feasible, provided you can deliver several dozen devices to intercept with the object, which is more of a logistical challenge than a technical one. Redirecting a much larger object, however, becomes a substantial challenge not only because of the additional mass but because the impulse will impinge upon only by a fraction of aspect of the body and would likely be absorbed as deformation within the body (inelastic transfer or liquification) rather than uniformly delivered to the entire aspect. Moving really large masses requires some fundamentally different method of propulsion than just pushing because at those scales a “solid” body doesn’t act very solid.
Stranger