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I made a question in WolrdBuilding as I was directed to.

There a user said that with a perfect ball all water would pool to the equator because of centripetal force.

What I do not understand is how would the earth being perfect ball have all the water pooled to the equator when it does not do so now?

A perfect ball would have less difference between the radius close to the poles and the radius around the equator than what the current earth has.

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  • $\begingroup$ The members of SE Physics might be able to give a better answer to this question. The reason for the equatorial bulge is because the Earth spins on it own axis. This causes the poles to flatten & the equatorial region to bulge. $\endgroup$ – Fred Dec 29 '19 at 4:51
  • $\begingroup$ take a tennis ball and soak it in water,spin it and observe where the water leaves the ball.hint: at the equator of the ball. $\endgroup$ – trond hansen Dec 29 '19 at 6:10
  • $\begingroup$ Geodesy thought-experiments are on-topic, as long as they stick to geodesy. $\endgroup$ – Spencer Dec 29 '19 at 17:00
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In short, weird things happen when you combine things that don't combine in nature:

  • the Earth as a perfect sphere
  • the Earth spinning on an axis

Einstein's equivalence principle tells us that accelerations are all the same, no matter what's causing them. So you just add the acceleration vectors up.

The (real) Earth has an equatorial bulge because a stable surface can only exist where those vectors sum to zero:

  1. gravity
  2. residual ("centrifugal") acceleration from the Earth's rotation
  3. the ground holding you up

This is called an equipotential surface and because of the centrifugal acceleration, on a spinning Earth this surface is an ellipsoid (well, mostly; there are small adjustments due to mass distribution).

The constraint of having a perfect sphere means that the materials making up the Earth your fictional planet are strong enough to keep it from ballooning out and filling an equipotential surface.

So if you make your fictional planet a perfect sphere, what you're really doing is changing where #3 happens but leaving #1 and #2 the same.

In other words, you're creating a 26 km deep valley encircling the globe.

Water runs downhill.

So eventually, all of the water will flow down into the giant equatorial valley...

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If the Earth were a perfect ball, which it is not, and had a perfectly smooth and even surface with no basins or irregularities, water would tend to move toward the equator, where it would form a bulge. Meanwhile, gravity would be pulling on this bulge and trying to drag it down, thus preventing it getting any higher and stopping the flow of water into it. To increase the height of the bulge and allow more water to flow to the equator, the Earth would have to spin faster. There is no way that I know of to make the Earth spin faster, on the contrary, it is very gradually slowing down. The oceans do tend to bulge at the equator, as does the more solid part of the Earth, forming the well known equatorial bulge. As you didn't mention any moon, apart from the fact that it slows the Earth's rotation I am ignoring the effect of the moon, as that would complicate matters.

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