# What is the value of acceleration due to gravity at the center of the earth?

Last updated on April 16th, 2021 at 09:40 am

What is the value of acceleration due to gravity at the center of the earth?
The value of the acceleration due to gravity at the center of the earth equals zero.

Mathematical Proof of the same:
At the center of the earth, depth from the earth’s surface is equal to the radius of the earth.

We know the equation or formula for the acceleration due to gravity at a depth from the earth’s surface is as follows:
g2 = g (1 – h/R)  [ Proof or derivation of the equation here]
[ here g is the acceleration due to gravity on the surface of the earth, g2 is the acceleration due to the gravity at a depth h, and R is the radius of the earth]

So we have to put h = R in the equation to find out g2 at the center of the earth.

Therefore the value of g at the center of the earth

is g (1- h/R) = g (1 – R/R)

=g (1-1) = 0

So we can see, the value of the acceleration due to gravity at the center of the earth equals zero.