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Re: Bulges




On Sun, 2 Mar 1997, Leigh Palmer wrote:

Once one becomes used to the rotating frame it is easy to "feel" why this
should be, by the way. A physicist who is aculturated to thinking this way
would never say flatly that rotation does not give rise to the tidal
bulges because he invokes the concept of centrifugal force.

I didn't hear anyone here say that.

Those who
choose to look at the world as though centrifugal forces do not exist may
well say that rotation does not cause the bulges.

Why would they say that? No physicist would deny the cenfrifugal and
Coriolis and other terms in the expression for F = ma (and in the
expression for potential) in a rotating coordinate system. Their 'reality'
isn't an issue here. They must be included if you do the problem in an
accelerating coordinate system.

I claim that if the
bulges can be derived exactly by a model which invokes centrifugal force,
then it is logically defensible to say that rotation causes the tidal
bulges in part.

In part. Agreed. How large a part, relatively?

Just what fraction of the tidal bulge is due to rotation
can readily be calculated from this model by redoing the calculation and
leaving out the centrifugal term. The bulges remain, but they are smaller
if only the gravitational terms are invoked.

If you have the calculation in hand, can you give us the relative sizes?

I *feel* that: The centrifugal terms should give rise to an equatorial
bulge *all round the earth*, but slightly larger on the *far* side of the
earth from the moon because the CM of the earth-moon system is displaced a
bit from the center of the earth toward the moon. The contribution due to
the potential gradiant of the moon's gravity should be two bulges, the one
on the side of the earth nearer the moon should be slightly larger than
the one on the far side. Do your calculations show this? I'd be interested
to know the percent *assymetry* of the equatorial bulge on the near and
far side from the moon, due to centrifugal effects, and how large this is
compared to the assymetry in the two bulges produced by the potential
gradient effect.

I am, of course, considering an earth as a slightly elastic body with no
oceans sloshing around and hitting the continents to complicate the issue.
Or, if you like, an initially spherical earth with a thin ocean layer
covering it entirely.

So, if you are asked to explain why there are *two* bulges, not merely
one, which is the predominant cause? This is the question that textbooks
usually mess up when they attempt an answer. They talk of 'pulling
toward', 'accelerating toward' and misleading things of that sort.

In introductory level textbooks, the closest I came to an account in which
the author seemed to understand tidal deformations was Lerner, Lawrence S.
_Physics for Scientists and Engineers_, Jones and Bartlett, 1996. It's in
a homework problem! Problem 14.41 on p. 388. Lerner sets it up for the
student, gives a brief account of the things which must be considered,
gives the answer, but lets the students do the calculus. I haven't used
this book, having only recently gotten a copy, but on first reading I am
mightily impressed with the sophistication of its end-of-chapter problems.
I shall treasure my copy, for the best books never make it to a second
edition.

-- Donald

......................................................................
Dr. Donald E. Simanek Office: 717-893-2079
Prof. of Physics Internet: dsimanek@eagle.lhup.edu
Lock Haven University, Lock Haven, PA. 17745 CIS: 73147,2166
Home page: http://www.lhup.edu/~dsimanek FAX: 717-893-2047
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