What would the force of gravity be if the International Space Station were 500 km above the surface of the Earth?

Question

The force of gravity on an object varies inversely with its distance from the center of the Earth. The radius of the Earth is 6378 km. The International Space Station orbits approximately 350 km above the Earth, and the force of gravity acting on it is approximately 2.7 x 10^12 Newtons. What would the force of gravity be if the International Space Station were 500 km above the surface of the Earth?

Answer 1

350km above the earth is 6378+350=6728km above the centre.

500km above the earth is 6878km above the centre.

If the gravitational force varies inversely with distance from the centre of gravity, the ratio 6728/6878=0.9782 approx. So gravity would be reduced by this factor: 0.9782×2.7×10¹²=2.64×10¹²N approx.

If the force varies inversely as the square of the distance (and I think that’s what applies here) then we need the ratio of their squares: (6728/6878)²=0.9569 approx.

So gravity would be reduced by this factor: 0.9569×2.7×10¹²=2.58×10¹²N approx.