Question

Starting from Newton's law of gravitation, show the variation of the acceleration due to gravity with the height from the surface of the Earth​

Answer 1

Hello Dear,

◆ Gravitational acceleration at height -

Let,

M = mass of earth

m = mass of object

R = radius of earth

h = height of object

g = gravity at surface

g' = gravity at height

At surface of earth, according to Newton's law of gravitation -

F = GMm/R²

mg = GMm/R²

g = GM/R²

At height of h from surface of earth, according to Newton's law of gravitation -

F' = GMm/(R+h)²

mg' = GMm/(R+h)²

g' = GM/(R+h)²

Dividing g' by g,

g'/g = [GM/(R+h)²] / [GM/R²]

g'/g = R²/(R+h)²

g' = gR²/(R+h)²

This explains how gravitational acceleration varies with height.

Thanks dear...