Using a catapult on an asteroid to propel it towards Earth is theoretically viable by applying the principles of momentum and impulse. When a chunk of the asteroid's mass is ejected in the opposite direction of Earth, the asteroid experiences a change in momentum, resulting in a velocity shift towards Earth. This concept relies on the conservation of momentum, which dictates that the asteroid must compensate for the mass it loses. The discussion humorously likens the scenario to an introductory physics course, highlighting the unconventional nature of the idea. Overall, the feasibility of this propulsion method hinges on fundamental physics principles.