Relation between g and G. Using F = ma we know that the force on a mass m at a point where the gravitational intensity of a planet is g is mg. But this force is also given by F = GMm/r2 where M is the mass of the planet and r is the distance from its centreSo F = mg = GMm/r2 and therefore g = GM/r2 If we think about the surface of the planet then g = go and r = R and so: Surface gravity (go) = GM/R2

Considering that earth to be a huge spherical body of (mass) M having (radius) R. Suppose a body of m placed on the surface of earth or above the surface of earth where acceleration due to gravity g. Let F be the force of attraction between the body and the earth according to universal law of gravitation.F = G.M.m/R2 .................(I)Force exerted by body due to earth, so .body starts moving towards earth , then according to Newton's 2nd law. F= mg ( where g = a= acceleration due to going) .........(ii)comparing equation (I) and (ii) G.Mm/R2 = mg g = GM/R2