You are explaining to your friends why astronauts feel weightless while orbiting in the space shuttle. They ask you to prove this mathematically. Calculate the acceleration of gravity 250 km above the Earth's surface in terms of g.

(Use Rearth = 6.38x103 km.)

Force of gravity = GMm/r^2 = ma

a being the acceleration due to gravity at some distance r from the center of the Earth. I'll use 6400 km for the radius of the Earth so r = 6734 km or 6734000 meters

a = GM/r^2

plugging in G = 6.67 x 10^-11

M is the mass of the Earth = 6 x 10^24

and r is from above

a = 8.825 m/s^2 = 0.9g

so 90% the acceleration of gravity on the surface.