Effect of Latitude and Rotational Motion on Acceleration Due to Gravity

The latitude at a point on the surface of the Earth is defined as the angle which the line joining that point to the center of the Earth makes with the equatorial plane. It is denoted by $\lambda$.

It follows that at the poles: $\lambda = 90^\circ$, and at the equator: $\lambda = 0^\circ$.

The Earth is not perfectly a sphere but is ellipsoidal in shape. It also possesses rotational motion about an axis through the poles. The value of acceleration due to gravity at a place (at a given latitude) is affected both due to the shape of the Earth and its rotational motion.

Effect of Rotational Motion of the Earth

The Earth has rotational motion of period 24 h about its own axis. As the Earth rotates, a body placed on its surface moves along a circular path and hence experiences centrifugal force. The magnitude of the centrifugal force varies with the latitude of the place.

At the poles, the body moves along a circular path of zero radius, and hence the centrifugal force on the body is also zero. On the other hand, at the equator, the body moves along a circular path of radius equal to that of the Earth.

Since it is the circular path of maximum radius, the centrifugal force $\left( m R \omega^2 \right)$ on the body at the equator is maximum due to earth’s rotational motion. Therefore, the apparent weight of the body varies with latitude due to variation in the magnitude of centrifugal force on the body. the acceleration due to gravity decreases due to rotational motion of the earth and this effect is maximum at equator and zero at poles.