Land a mass-driver on the asteroid. Escape velocity is small, perhaps a few meters per second. Scoop up bits of rock, throw them away. Throwing them in a consis

Land a mass-driver on the asteroid. Escape velocity is small, perhaps a few meters per second. Scoop up bits of rock, throw them away. Throwing them in a consistent direction changes the orbit of the asteroid very slightly. With enough lead time, throwing enough mass away may reduce the size of the asteroid sufficiently or cause it to miss the earth.