What force accounts for Earth's equatorial bulge in an inertial frame of reference?

Question

I am confused as to how Earth's centrifugal effects from its daily spin can be explained from an inertial frame of reference relative to the distant stars. The usual explanation is that the centrifugal force increases with radius, therefore the force is greater near the equator than near the poles, so the equator bulges outwards and the poles flatten inwards. However, the centrifugal force is a pseudo force which is only visible to rotating reference frames such as Earth's inertial frame. In the absence of the pseudo centrifugal force, what other force accounts for the equatorial bulging phenomenon in an inertial frame relative to the distant stars?

Answer 1

On a non-rotating planet, a unit mass anywhere on the sphere at a given radius from the center will have the same inward force. Without rotation, we can assume the surface is non-moving and non-accelerating. Therefore the inward force must be countered by a supporting force/pressure from below.

On a rotating planet, the masses at the equator are accelerating inward. Therefore the net force on the mass must be inward. We know the force of gravity must be (approximately the same), so the pressure applied by the mass on the surface underneath must be lower.

The fluid volume of the planet deforms in response the lower pressure applied by the equatorial mass compared with the polar mass at the same radius.

If the Earth's outward pressure is greater at the poles and lower at the equator, then shouldn't the poles bulge and the equator flatten? Or am I oversimplifying the deformation mechanism?

I (tried to) say the inward pressure from a unit of mass was greater at the poles. If we imagine starting with a sphere, this is going to squeeze the planet in a nonuniform way so that mass flows from the poles to the equator.

At the end of the flow a particular unit of mass at the poles still pushes down more than a unit of mass at the equator. But because there's a bit more mass at the equator, it balances out.

Answer 2

Centrifugal force accounts for equitorial bulge of earth. It depends upon speed, thus maximum at equator and minimum at poles.

Someone may say that it is pseudo force, than according to general relativity, gravity is also such a force. A pseudo force is due to motion of frame, but centrifugal is sometimes inertia of an object.

If composite body of earth feels outward force and make bulge, then how people or things attracted to earth.