At what attitude h above the north pole is the weight of an

At what attitude h above the north pole is the weight of an object reduced to 43% of its earth-surface value? Assume a spherical earth of radius R and express h in terms of R.

Solution

g_h = 0.43*g₀

G*Me/(Re + h)^2 = 0.43*(G*Me/Re^2)

Re^2 = 0.43*(Re + h)^2

h = ((0.43)^0.5 - 1)*Re