# how acceleration due to gravity varies with latitudes

Last updated on April 23rd, 2022 at 02:21 pm

In this post, we will see how acceleration due to gravity varies with latitudes.

## acceleration due to gravity(g) varies with latitudes – how?

Consider a point A on the earth’s surface where the line joining center O to A makes an angle θ with the equatorial plane as shown. The angle θ is said to be the latitude of point A´. (figure 1)

Let us place a small particle of mass m at A. Analysing the forces of on m, from the reference frame of the earth, we find two forces gravitational force (mg) and pseudo force (mω^{2}r).

Here, r is the radius of the circular path followed by m.

r = R cos θ

The resultant force of masses m is given by

F = [m^{2}g^{2} + m^{2}ω^{4}r^{2} + 2(mg)(mω^{2}r) cos(π − θ)]^{1/2}

The effective gravity at point A,

…………………………………………………….. (1)

where g is the acceleration due to gravity at the surface of the earth neglecting the effect of the rotation.

(a) acceleration due to gravity **at poles** (due to the latitudes of poles)

θ = 90º

So, from equation (1)

⇒ g’ = g**Hence, the rotation of the earth has no effect on the gravity at the poles.**

(b) acceleration due to gravity **at equator** (due to the latitude of equator)

θ = 0º

So, from equation (1)

=> g’ = g [ 1 – (ω^{2}R/g)]