Variations of Gravity (g) with altitude

Variations of Gravity (g) with altitude

Suppose a body of mass m is placed at the height h from the surface of earth. Here the distance b/w them is R + h where M is the mass of earth. Suppose g_h is the gravitational acceleration at this position. So gravitational force is

F = GMm / (R+h) ² ------ eqn (1)

as we know that the force is equal to the weight of body. That is

F = W = mg   ------ eqn (2)

From both eqns we get

g_h = GM / (R+h) ² --------- eqn(3)

As the mass of earth is

                              M = gR² / G     

              ••►  GM =  gR²  put this in eqn 3. So

g_h = gR²  / (R+h) ²

This shows that the value of g decreases as h increases. Hence the value of g decreases as altitude increases.