Find out the value of g from its formula

Last updated on April 14th, 2021 at 05:18 pm

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.