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Re: Bulges





On Mon, 3 Mar 1997, Mark Sylvester wrote:

The ultimate point that I'm after is whether Donald is correct in
saying that one can dispense altogether with acceleration in
discussing the tides, and explain everything in terms of the gradient
in the gravitational force only. It seems to me that both are
required, or else equivalently one must use an accelerated reference
frame.

Sorry to consume bandwidth, but I did not say that the tides are due
*only* to the gravitational gradient. The size of the bulges is slightly
modified by rotational effects associated with the equatorial bulge. To
summarize, I said.

(1) The two tidal bulges are predominantly due to the gravitational
gradient.

(2) Even without rotation, the gravitational gradient will produce two
bulges in the earth. (Your analysis above fails to take into account the
variation in force strength and direction on the jelly-blobs from equator
to pole.) Several correct analyses have been posted here already, though
no one has yet provided the equation for the bulge profile (a messy
calculus problem).

It's an interesting point that the two-bulge result arises from almost any
kind of external force acting from a force center at a distance not too
great with respect to the earth's diameter. That is, the force could be
1/r, 1/r^2, or even r. In each case the exact shape of the distorted earth
would be different. If you want to talk 'causes' here, the cause of the
two bulges is a result of the radial nature of forces with respect to the
external object and the fact that their strength varies with distance.
That is the forces exerted on earth by the moon are radial from the moon
and are distance dependent. One of these conditions is all that's
required. A uniform external field won't, of course cause tidal bulges.
The gradient of the field is all-important.

-- 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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