# Space Travel Guide ...

 Variation of Gravity As I have already explained that acceleration due to gravity g is a variable quantity and it varies from place to place. We here, will derive the relation that describes variation of g with altitude. 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 g = GM / R2 …………….. (i) Suppose the body is taken to height ‘h' above the surface of earth where the value of acceleration due to gravity is gh. Then gh = GM / (R + h )2 …………(ii) Where (R+h) is the distance between the centers of body and earth. Dividing (ii) by (i), we get gh / g = GM / (R + h )2 X R2 / GM = R2 / (R+ h ) 2 when h < < R, then gh / g = R2 / R2 ( 1 + h2 / R2 ) 2 = 1/ ( 1 + h2 / R2 ) 2 = ( 1 + h2 / R2 ) -2 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 gh / g = 1-2h / R Thus, acceleration due to gravity decreases with increase in height / altitude.