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Although gravity is one of the weakest forces in the universe, it is very easy to utilise as all you need is mass. The general premise behind the gravity tractor is to "park" a spaceship next to an incoming asteroid and use the attractive gravitational forces to pull the asteroid away from a trajectory that will strike the earth.
The spaceship would need to use thrusters to prevent being pulled into the asteroid but would not need to be capable of actually landing.
Here is a video of Neil DeGrasse Tyson explaining the concept.
Specs
Pros
Pro Not dependent on asteroid characteristics
The gravity tractor method has advantages over nuclear explosions in that it is effective on "rubble pile" style asteroids which are impossible to deflect via explosions.
The gravity tractor method would be effective on asteroids spinning too fast to be physically pulled.