We have derived the equation of g (acceleration due to gravity) and we will use that formula or equation to find out its value. The formula we will use is: g = GM/R2
[Derivation of g formula here]
Value of g from its formula
We will use 3 values in the formula. And those values are for the mass of the earth M, the radius of the earth R, and universal gravitational constant G.
Mass of the earth = M=6 × 1024 kg
Radius of the earth = R=6.4 × 103 km = 6.4 × 106 m.
G = universal gravitational constant = 6.67 x 10-11 N m2 kg-2
Putting the values of M, R and G we get: g = GM/R2 =(6.67 x 10-11)x(6 × 1024)/( 6.4 × 106)2 = 9.77m/s2
The value of ‘g’ calculated above is near the equator at sea level. The value of ‘g’ varies with height, depth, and latitude. See here how the value of g changes with height and depth.