## The gravity tractor, as shown in the artist’s rendition, is a proposed spacecraft that will fly close to an asteroid whose trajectory thr…?

The gravity tractor, as shown in the artist’s rendition, is a proposed spacecraft that will fly close to an asteroid whose trajectory threatens to impact the Earth. Due to the gravitational attraction between the two objects and a prolonged period of time over which it acts (several years), the asteroid’s trajectory is changed slightly, thus hopefully diverting it from impacting the Earth. If the gravity tractor’s weight on earth is 20,000 lb and it flies with its center of gravity 160 ft from the surface of the asteroid, and the asteroid is homogeneous pure iron with 1290 ft diameter spherical shape, determine the force of mutual attraction. Idealize the gravity tractor to be a particle.

## Answer ( 1 )

mass of tractor

m = 20000lb * 1kg/2.2lb = 9091 kg

mass of asteroid

M = ρV = 7874kg/m³ * (4/3)π(½*1290ft)³(12*0.0254m/ft)³ = 2.506E11 kg

F = GmM / d²

d = (160+1290/2)ft*(12*0.0254m/ft) = 245 m

and so

F = 6.674e−11N·m²/kg² * 9091kg * 2.506E11kg / (245m)²

F = 2.53N * 0.225lb/N = 0.57 lb force