Newton’s law of gravitation: According to Newton’s law of gravitation, the gravitational attraction between two massive objects such as planets or asteroids is proportional to d−2 , where d is the...

Newton’s law of gravitation: According to Newton’s law of gravitation, the gravitational attraction between two massive objects such as planets or asteroids is proportional to d−2 , where d is the distance between the centers of the objects. Specifically, the gravitational force F between such objects is given by F = cd−2 , where d is the distance between their centers. The value of the constant c depends on the masses of the two objects and on the universal gravitational constant.

a. Suppose the force of gravity is causing two large asteroids to move toward each other. What is the effect on the gravitational force if the distance between their centers is halved? What is the effect on the gravitational force if the distance between their centers is reduced to one-quarter of its original value?

 b. Suppose that for a certain pair of asteroids whose centers are 300 kilometers apart, the gravitational force is 2,000,000 newtons. (One newton is about one-quarter of a pound.) What is the value of c? Find the gravitational force if the distance between the centers of these asteroids is 800 kilometers.

c. Using the value of c you found in part b, make a graph of gravitational force versus distance between the centers of the asteroids for distances from 0 to 1000 kilometers. What happens to the gravitational force when the asteroids are close together? What happens to the gravitational force when the asteroids are far apart?