Aspace probe is launched from earth, headed for deep space. at a distance of 10,000 miles from the earth's center, the gravitational force on it is 600 lb. what is the size of the force when it is at each of the following distances from the earth's center?

Newton's gravity equation
F=G(Mm)/r^2
At 10,000 miles you can use the 600lbs to find the value of
G(Mm) in the appropriate units:
GMm=(10e3)^2*600=6e10
So divide this by your other distances squared (in miles). That will be the value of force in pounds. (I don't see your other distances on my app)