If a satalite weighs 90 kg at 10000 miles from the earth, how far away is it when it weighs 10 kg?

Answer 1

since it weighs 1/9 its original weight, and

F = GMm/r^2

and the masses involved have not changed, that means that r^2 has grown by a factor of 9. So, the satellite is 3 earth radii away from earth center, or 2 earth radii high.