The poles
Explanation
The acceleration due to gravity ($g$) on the surface of the Earth is governed by the formula:
$g = \frac{GM}{R^2}$
Where:
- $G$ is the universal gravitational constant.
- $M$ is the mass of the Earth.
- $R$ is the radius of the Earth.
This relationship indicates that $g$ is inversely proportional to the square of the distance from the Earth's center ($g \propto \frac{1}{R^2}$).
Detailed Analysis
- Effect of Earth's Shape: The Earth is not a perfect sphere but an oblate spheroid. It bulges at the equator and is flattened at the poles. Consequently, the equatorial radius ($R_e$) is approximately 21 km greater than the polar radius ($R_p$).
- At the Equator vs. Poles: Since $R_e > R_p$ and $g \propto \frac{1}{R^2}$, the value of $g$ is minimum at the equator (where the radius is largest) and maximum at the poles (where the radius is smallest).
- At the Centre of the Earth: As one moves deeper into the Earth, the effective mass contributing to gravity decreases. At the exact center, the value of $g$ becomes zero.
- At a Height: The value of $g$ decreases as altitude increases above the Earth's surface. Therefore, at a height of 100 km, $g$ would be less than at the surface.
Key Takeaway
Due to the Earth's geoid shape, the polar radius is smaller than the equatorial radius. Since gravity is inversely proportional to the square of the radius, the value of $g$ is highest at the poles.