Why is Earth's gravity stronger at the poles?

Many sources state that the Earth's gravity is stronger at the poles than the equator for two reasons:

1. The centrifugal "force" cancels out the gravitational force minimally, more so at the equator than at the poles.


2. The poles are closer to the center due to the equatorial bulge, and thus have a stronger gravitational field.

I understood the first point, but not the second one. Shouldn't the gravitational force at the equator be greater as there is more mass pulling the body perpendicular to the tangent (since there is more mass aligned along this axis)?

Answer

The point is that if we approximate Earth with an oblate ellipsoid, then the surface of Earth is an equipotential surface,$^1$ see e.g. this Phys.SE post.

Now, because the polar radius is smaller than the equatorial radius, the density of equipotential surfaces at the poles must be bigger than at the equator.

Or equivalently, the field strength$^2$ $g$ at the poles must be bigger than at the equator.

--

$^1$ Note that the potential here refers to the combined effect of gravitational and centrifugal forces. If we pour a bit of water on an equipotential surface, there would not be a preferred flow direction.

$^2$ Similarly, the field strength, known as little $g$, refers to the combined effect of gravitational and centrifugal forces, even if $g$ is often (casually and somewhat misleading) referred to as the gravitational constant on the surface of Earth.