The weight W of an object varies inversively as the square of the distance d from the center of the earth. At sea level(3978 mi from the center of the earth), an astronaut weighs 1121 lb. Find her weight when she is 310 mi above the surface of the earth and the spacecraft is not in motion.

Solution:

We assume the weight is W, the distance from the center of the earth is d

So W = k/(d^2), k is a constant.

So

1121 lb = k/(3978^2)

X = k/(3978+310)^2

So

1121* 3978^2 = X * (3978+310)^2

X = 964.77

So her weight  when she is 310 mi above the surface of the earth is  964.77 lb