[Aperson4321]

Shoot out the trusters? there is no friction to stop the kinetic momentum in space.

Anyway you can rig the asteroid with explosives in the center of it, and just blow it to make a still dangerous giant meteor rain.

The rather hard sci-fi book series by Jack Campbell/(non alias name is: John G. Hemry) by the name lost fleet is full of scenarious where planet dwellers are rather fucked against space forces.

Spoiler: Giant block of metal is all you need to do planetary bombardments from space, just send it off and Newton will do the rest. Good luck stopping the many many tons of a single metal object "dropped" from space.

[maxerickson]

I'm assuming that the first notice of the asteroid changing trajectory will be well before the trajectory is Washington DC. So presumably there is something changing the trajectory. Vaporize that thing. Now the trajectory is not Washington DC and the threat is empty.

[jessaustin]

How about this scenario? There is an asteroid in the solar system we've already directed on such a trajectory. Using the thrust capability that we installed to accomplish that, we're happy to redirect the asteroid, if our demands are met.