Question
Fri September 13, 2013 By: Rajneesh Kumar

As one moves to a place 3200 Km above the earth's surface, the acceleration due to gravity reduces to 4/9 of its value at the earth's surface. Calculate the radius of the earth from this data?

Expert Reply
Fri September 13, 2013
height above earth's surface, h = 3200 km
let radius of earth = R
thus according to the following expression for acceleration due to gravity.
g = GM/R2 at the surface of earth    -1
at height h, distance between this point and the center of earth, H = 3200 + R
4g/9 = GM/H2                               -2
thus dividing equation 1 and 2
 
4/9 = (R/H)2
or 4/9 = (R/(3200 + R))2
 
this can be solved easily to calculate R
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