Why is the value of ‘g’ minimum at the equator?

The acceleration due to gravity (gg) is not constant everywhere on Earth; it varies due to several factors such as Earth's shape, rotation, and altitude. The value of gg is minimum at the equator for the following reasons:
1. Earth's Shape: Oblate Spheroid
• The Earth is not a perfect sphere; it is slightly flattened at the poles and bulges at the equator, making it an oblate spheroid.
• The radius of the Earth is larger at the equator than at the poles.
• From the formula for gravitational acceleration:
g=GMR2g = \frac{GM}{R^2}
where:
o GG is the gravitational constant,
o MM is the mass of the Earth,
o RR is the radius of the Earth.
At the equator, the larger radius RR results in a smaller value of gg since g∝1R2g \propto \frac{1}{R^2}.
2. Centrifugal Force Due to Earth's Rotation
• The Earth rotates about its axis, and this rotation generates a centrifugal force that acts outward, reducing the effective gravity experienced by objects.
• The centrifugal force is maximum at the equator and zero at the poles, because:
Fcentrifugal=mω2rF_{\text{centrifugal}} = m\omega^2r
where:
o mm is the mass of the object,
o ω\omega is the angular velocity of Earth's rotation,
o rr is the radius of the circular path (maximum at the equator).
• The effective gravity is reduced at the equator as:
geffective=ggravitational−gcentrifugalg_{\text{effective}} = g_{\text{gravitational}} - g_{\text{centrifugal}}
Thus, the outward centrifugal force further reduces the value of gg at the equator.
3. Combined Effect
The combined effect of Earth's larger radius at the equator and the reduction due to centrifugal force results in the minimum value of gg at the equator.
Numerical Values
• gg at the poles: approximately 9.83 m/s29.83 \, \text{m/s}^2.
• gg at the equator: approximately 9.78 m/s29.78 \, \text{m/s}^2.
The difference, though small, is significant in understanding Earth's gravitational variations.
Conclusion
The value of gg is minimum at the equator because:
1. The equatorial radius of the Earth is larger than the polar radius, reducing the gravitational pull.
2. The centrifugal force due to Earth's rotation is maximum at the equator, further decreasing the effective gravity.