(Solved): The gravity tractor is a proposed spacecraft that will fly close to an asteroid whose trajectory th ...

The gravity tractor is a proposed spacecraft that will fly close to an asteroid whose trajectory threatens to impact the Earth. Due to the aravitational attraction between the two objects and a prolonged period of time over which it acts (several years), the asteroid's irajectory is changed slightly, thus hopefully diverting it from impacting the Earth. If the gravity tractor's weight on Earth is 20,000 ib and it flies with its center of gravity \( 170 \mathrm{ft} \) from the surface of the asteroid, and the asteroid is homogeneous pure iron with \( 1290 \mathrm{ft} \) diameter spherical shape, determine the force of mutual attraction. Idealize the gravity tractor to be a particle. (Round the final answer to five decimal places.) The force of mutual attraction is