Gravitational tractor. In some science fiction stories, a “tractor beam” is used to pull an object from one point in space to another. That may not be just science fiction. It has been proposed that a “gravitational tractor” could be used to “tow” an asteroid. In theory, this tractor could be used to deflect asteroids that would otherwise collide with the Earth. A typical asteroid that could significantly damage life on the Earth might have a radius of 100 m and density 2000 kg/m³. The “tractor” would be just a very massive spacecraft; in current designs, it would have a mass of about 2 × 10⁴ kg. 

(a) What is the maximum gravitational force the tractor could exert on the asteroid? 

(b) What would be the acceleration of the asteroid? 

(c) If the tractor stayed near the asteroid for 1 year, what would be the deflection of the asteroid? 

(d) Consider an asteroid initially headed straight for the Earth with a speed of 3 × 10⁴ m/s. If the tractor first comes close to the asteroid when it is 6 × 10¹¹ m from the Earth (near the orbit of Jupiter), will the asteroid hit or miss the Earth? For simplicity, ignore the gravitational force of the Earth on the asteroid. NASA is seriously considering the development of such a gravitational tractor.