🚀 go-pugleaf

In article <scottj-211292091243@iamac-1.dml.georgetown.edu>, scottj@magic.dml.georgetown.edu (John L. Scott) writes:
>The high tide facing the moon is, of course, explained by the gravitational
>pull of the moon.  However, there have been at least two explanations for
>the high tide on the opposite side of the earth:
>
>   A.  The moon stretches the earth
>   B.  Centrifugal pseudo-force
>
>So... which is it, A, B, both, or neither?

Both.  By definition, a tide is caused by the moon stretching the Earth (it'd
be pretty hard to tell there was a tide if there were no stretching, no?). 
Now, the Earth is always accelerated toward the moon by the gravitational force
of the moon.  The average acceleration is equal to that felt by the center of
gravity of the Earth.  However, since gravitational force goes as 1/r^2, the
part of the Earth nearer the moon feels a larger acceleration (causing a bulge
toward the moon) and the part further from the moon feels a smaller
acceleration (causing a bulge away from the moon).  If you call the distance
from the center of the moon to the center of the Earth R the radius of the
Earth r, and the mass of the moon M, then the side near the moon feels an
acceleration of:

	   GM
	-------
	(R-r)^2

the center of the Earth feels an acceleration of

	GM
	---
	R^2

and the side furthest from the moon feels an acceleration of

	  GM
	-------
	(R-r)^2

Since the Earth is held together by its own gravity, the whole Earth is
accelerated at the same rate.

This means that the side of the Earth closest to the moon feels an acceleration
from the moon, RELATIVE TO THE REST OF THE EARTH, of

	  GM	  GM	 (2Rr - r^2)GM	  2rGM
	------  - ---  = ------------- ~= ----
	(R-r)^2	  R^2	  (R-r)^2*R^2	   R^3

while the side furthest from the moon feels a relative acceleration of

	  GM	  GM	 (-2Rr - r^2)GM	   -2rGM
	------  - ---  = -------------- ~= -----
	(R+r)^2	  R^2	  (R+r)^2*R^2	    R^3

These relative accelerations are tides, and, to a first order approximation,
you get equal bulges on both sides.
--------------------------------------------------------------------------------
Carl J Lydick | INTERnet: CARL@SOL1.GPS.CALTECH.EDU | NSI/HEPnet: SOL1::CARL

Disclaimer:  Hey, I understand VAXen and VMS.  That's what I get paid for.  My
understanding of astronomy is purely at the amateur level (or below).  So
unless what I'm saying is directly related to VAX/VMS, don't hold me or my
organization responsible for it.  If it IS related to VAX/VMS, you can try to
hold me responsible for it, but my organization had nothing to do with it.