how acceleration due to gravity varies with latitudes

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 (mω2r).

figure 1: how acceleration due to gravity varies with latitudes
figure 1: how acceleration due to gravity varies with latitudes

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 = [m2g2 + m2ω4r2 + 2(mg)(mω2r) cos(π − θ)]1/2

The effective gravity at point A,

equation showing how acceleration due to gravity varies with latitudes
equation showing how acceleration due to gravity varies with latitudes

…………………………………………………….. (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 – (ω2R/g)]

how acceleration due to gravity varies with latitudes
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