Question

How does acceleration due to gravity change with the shape of earth?

Answer 1

The variation of g over the surface of the globe is important because it provides information on variations in the shape and internal structure of the Earth.

If we rearrange F = $\frac{GmM}{R^2}$ substituting for M via ρ = $\frac{Mass}{Volume}$ = $\frac{M}{\frac{4}{3}\pi R^3}$ = $\frac{3M}{4\pi R^3}$ , we obtain:

g = $\frac{4\pi \rho RG}{3}$

If the Earth were a perfect sphere of uniform density, g would be constant over its entire surface. But if the Earth deviates from spherical (i.e. if R varies) or if there is a local density anomaly, g will vary.