Let us consider a body of mass M lying on the surface of earth of mass M and radius R. Let g be value of acceleration due to gravity on the free surface of earth.
Then,
Suppose the body is taken to height 'h' above the surface of earth where the value of acceleration due to gravity is gh.
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Then
Where (R+h) is the distance between the centers of body and earth.
Dividing (ii) by (i), we get
when h < < R, then
Since, h < < R, then h/r is very small as compared to I. Expanding the right hand side of the above equation by Binomial Theory and neglecting squares and higher powers of h/r, we get
Thus, acceleration due to gravity decreases with increase in height / altitude.
