14.9:
Variation in Acceleration due to Gravity near the Earth’s Surface
Consider an object of mass m suspended from a spring scale attached to a rigid support. At the Earth's equator, the scale reading, which is the magnitude of the object's apparent weight, equals the magnitude of its true weight minus the magnitude of the centripetal force.
However, if the object suspended from the scale is placed at some other latitude λ, then the centripetal force acting on the object is directed towards point P on the rotational axis, away from the Earth's center.
Hence, the apparent weight of the object equals the true weight minus the cosine component of the centripetal force directed towards the Earth's center.
In general, by dividing the equation by m, the net acceleration g' of the object away from the poles is less than the acceleration due to gravity by a factor equal to the centripetal acceleration.
The Earth is an oblate sphere having an equatorial radius greater than its polar radius. Thus, its variable density also contributes to the variation in acceleration due to gravity.
14.9:
Variation in Acceleration due to Gravity near the Earth’s Surface
An object's apparent weight is its weight measured by a spring balance at its location. It is different from its true weight, the force with which the Earth pulls it, because of the Earth's rotation. Mathematically, an object's apparent weight equals its true weight minus the centripetal force that keeps it in a circular motion along with the Earth's surface every 24 hours.
The difference between the true and apparent weights is proportional to the square of the Earth's angular speed. Since the Earth's angular speed is relatively small and its square appears in the difference, the net effect of the Earth's rotation is only 0.34% of an object's weight.
However, this effect smoothly decreases as one moves from the equator to the poles. The variation is formulated by invoking simple geometry; since each object rotates along a circle covering the latitude at which it resides, the difference between the true and apparent weights depends on the object's latitude. The maximum effect is at the equator and the minimum at the poles. At the poles, the apparent weight equals the true weight because the Earth's poles are non-rotating.
The Earth's radius also contributes to the difference between true and apparent weight. Earth is not a perfect sphere; its radius is about 30 km greater at the equator compared to the poles, because the interior is partially liquid, which enhances the Earth's bulging at the equator due to its rotation. Hence, the Earth's bulging results in an object's apparent weight being smaller than the true weight by an additional factor. This factor can be shown to be comparable to the factor related to the Earth's rotation.
This text is adapted from Openstax, University Physics Volume 1, Section 13.2: Gravitation Near Earth's Surface.