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At a height of h from the surface of the earth, the gravitational force on an object of mass m is
F = GMm/(R+h)^2
Here (R + h) is the distance between the object and the centre of earth.
Say at that height h, the gravitational acceleration is g1.
So we can write, mg1 = GMm / (R+h)^2
=> g1 = GM/(R+h)^2 _________________ (5)
Now we know on the surface of earth, it is g = GM / R^2
Taking ratio of these 2,
g1/g = R^2 /(R+h)^2
= 1/(1 + h/R)^2 = (1 + h/R)^(-2) = (1 – 2h/R)
=> g1/g = (1 – 2h/R)
=> g1 = g (1 – 2h/R) ___________________ (6)
So as altitude h increases, the value of acceleration due to gravity falls.
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