Re: Bulges

[Leigh Palmer <palmer@sfu.ca>]

David Dockstader asks:

> Have I got this right?

In a word, no!

> Lee wants to throw water on the nailed down earth and moon.  I claim, and I
> think Mark would agree, that if you throw water on the earth all the water
> will
> run over to the moon side of the earth, one bulge.  To get water on the other
> side of the earth one needs to spin the earth moon system about the center of
> the mass.  The obiting of the center of mass is not needed to get oblate
> shapes
> it is needed to get water on both sides of the earth!

My Earth is not spinning*. I said to throw water on the earth only. You and
anyone else "agreeing" that all the water will stay on the side nearer the
Moon won't make it so. This is not a democracy where you win because you
have me two to one. Nature is on my side.

This misrepresents what I said, and badly. My intention in dumping an ocean
on the spherical Earth was to produce a system in which would then be
permitted to relax to a position of minimum potential energy in the
rotating frame. Your view of the Earth being nailed down and then having
water dumped on it is not correct. If one dumps only a bathtub full of
water on the Earth (or perhaps even just a Lake Superior) then what you
envision will be the result, and the surface of the water only will be an
equipotenial. All the water will, indeed, pile up on one side. That
situation is inevitable if the core is constrained to remain accurately
spherical. It arises because the equipotential surfaces in this problem are
themselves not spherical; I've already told you that they are prolate, with
two bulges. If you must do your experiment, dump a bathtub full of water on
the side of the Earth opposite the Moon. That, too, will pool up around
that point and it will not migrate around to the Moon side at all.

Trust me, your intuition is faulty. If you dump an ocean's worth of water
on the sphere it will do as I suggest. If there is enough water to wet the
entire surface of the sphere then it will be deepest at two places which
we've been calling the bulges. I think your error arises because, as I've
said before, forces do not help you to grasp this concept well; you should
be thinking of the potential in the rotating frame instead. Solve the
problem as I suggested originally and you will understand the result. Until
you solve it yourself the concept will remain vague, and you will be
tricked into misconceptions such as the one you outline above.

Most of all, please don't claim predictions of the model that it does not
make. It is not my model (I'd be proud if it were) but it is a realistic
one, and it does yield the result claimed.

Leigh [sic]

*A spinning Earth would only introduce a viscous phase lag to the tidal
bulges (the high tides on the spherical Earth would occur after the Moon
passes overhead).