(a) Find dF/dr and explain its meaning. What does the minus sign indicate?

the negative sign indicates that the magnitude of the gravitational force decreases with respect to r.

cutting r in half will increase F by a factor of 8.(b) Suppose it is known that the earth attracts an object with a force that decreases at the rate of 2 N / km when r = 20,000 km. How fast does this force change when r = 10,000 km?