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Re: [Phys-L] field of an ellipsoidal distribution



On 08/16/2015 12:39 AM, Bob Sciamanda wrote:
Given a perfectly spherical and homogeneous earth, the horizontal
component of the centrifugal force would move earth stuff toward the
equator, reshaping the earth's profile so that the normal force of
rigidity can now, by itself, completely cancel both the gravitational
and centrifugal forces.

To say it a bit more explicitly:

Starting with a planet that is homogeneous and *initially*
spherical and *not* rigid, the horizontal component of the
centrifugal force will move stuff toward the equator, reshaping
the earth's profile. If the process is allowed to proceed to
equilibrium, the result is ellipsoidal. *After* it reaches
equilibrium, it no longer matters whether it is rigid or not
... but beforehand it matters a great deal.

===========

Now let's consider a different case, namely a rigid, strictly
spherical, spinning earth. You can't ask what happens to a
table floating in a lake, because there can't be any lakes.
The surface of a lake is an equipotential, whereas the
surface of a spinning sphere is not.

You could construct a series of terraces and put a small lake
on each terrace, but then the planet is no longer strictly
spherical.