Question

Earths mass is 6 x 10^24kg and its radius is 6.38 x 10^6m
(6380 km ). Use the inverse-square law to show that in space-shuttle territory, 200 km above the earths surface the force of gravity on a shuttle is about 94% of that at the earths surface.

Answer 1

Let the acceleration of gravity at 200 km altitude be g' and the value at sea level be g. Then

g'/g = (6380/6580)^2 = 0.94013

The rounds off to 94%, to the nearest 1%.