In episode 11 of the Inuyashiki anime, Mr. Inuyashiki, a super-powerful 'robot' made from the technology of an advanced alien race, flies to space in order to stop a "giant" (no exact specification on it's size) asteroid from hitting the Earth. However, his chosen method is shooting missiles at it which, given the size of the asteroid, did not prove very effective. Hiro- another 'robot' that is the same as Mr. Inuyashiki- then joins him and self-destructs in an attempt to redirect the path of the asteroid. From the beggining of the anime we know that the technology they posses in their 'bodies' is enough to "destroy the Earth" as the aliens said. Yet it took both Hiro and Mr. Inuyashiki to self destruct in order to redirect the asteroid enough.
In previous episodes these characters exhibited enough thrusting force (from the thrusters in their back) to safely land a large travelling plane filled with people that was plummeting down without control, but it is not mentioned if that is the full extent of their strength. These characters are completely humanoid in appearance but with a completely mechanized interior.
Under the assumption that we have thrusters that are as strong in thrust as physically and scientifically possible, created with hypothetical alien technology, but with the limitation of fitting on an average person's back would it be possible for two of such individuals to alter the course significantly enough for the asteroid to not hit Earth? Or would it be more feasible to accomplish the same mission with strong enough explosions?
For simplicity's sake assume that the asteroid is heading straight to the center of our planet and it's size and mass is just enough to theoretically destroy all life on earth and the time that the characters have at their hands is 48 hours. Speed of the asteroid is unknown.
If impossible for the scenario in question, how much thrusting force (and/or over which period of time) would we have to apply to re-direct an asteroid that's large enough to destroy humanity? Would it make more sense to use explosions even though the force from an explosion would be spread in all directions? Or would an entirely different maneuver be more plausible?