Question

As one moves to a place 3,200 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.

Answer 1

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

calculate the R(=6400)