If M is the mass of the earth, m is the mass of the body which is at the surface of the earth and R is the distance between body and centre of the earth (which is the radius of the earth) . According to the Newton’s law of gravitation the gravitational force experienced by that mass m is given as,
F = G M m/R 2 ………………………(1)
As per Newton’s second law of motion, Force = mass × gravity = mg
Substituting value of force in equation 1 we get,
G M m/R 2 = m g
The formula for Acceleration due to gravity at the surface of the Earth is given as,
g = G M /R 2
Where g = Acceleration due to gravity, G = Universal Gravitational Constant, M = mass of the earth and R = radius of the earth