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Re: Indirect high tide cause?



--------- Forwarded message ----------
From: cswartz@notes.cc.sunysb.edu
Subject: Re: Indirect high tide cause?


Yes, the tide on the far side should be less by about 6%.
The usual derivations progress immediately to the first
approximation that R<<r and so terms in r cubed R, and
r square R square are crossed out. This leads to an
inverse r cube law, which can also be obtained by
differentiating the inverse square law with respect to r.

However, if you take the next approximation, you
get a term that reduces the effect (on the far side)
or enhances the effect (on the near side). Each
difference is worth about 3%.
If you have a copy of the book that Tom and
I wrote, look at the derivation on pages 112 -114.
It's hard to type equations on this machine, but
on page 113 there is an equation which with a
first approximation reduces to : delta lower
case g ( g is the gravitational field strength
at the surface of the Earth due to the moon)
equals GM times the fraction with a numerator
2rR and denominator r fourth plus 2 r cube R.
That's for the far side. For the near side the
equation is the same except with -2rR in the
numerator and the denominator equal to
r fourth minus 2 r cube R. That extra term
in the denominator provides the extra 3%.
Of course, the effect is hard to observe
because of the effects of land contours and
the solar contribution which provides a
factor of 1/2.3.
To be sure, time and tide wait for no man.