It's very far from practical technology, but in principle you can use pieces of the asteroid as reaction mass to 'cheat' the rocket equation. You could also mo

It's very far from practical technology, but in principle you can use pieces of the asteroid as reaction mass to 'cheat' the rocket equation. You could also modify the asteroid's albedo or use solar sails to modify the trajectory of the asteroid. Very far from practical. Such a plot would probably take centuries at least to carry out with reasonably conceived technology.