Re: Bulges

["Mark Sylvester" <msylvest@spin.it>]

I thought only geography textbooks were confused about tides!

A point or two that I would like to clarify:

Donald E. Simanek writes:

> However the implication in the above is that the bulges are
> somehow *due to* the rotation about the center of mass. This
> isn't true. The two tidal bulges would be there even if there
> were no rotation, that is if you were to 'nail down' the earth
> and moon to the fabric of space, the bulges would still be
> there. The rotation only modifies the bulges somewhat. Many
> textbooks I've seen give students the wrong impression that
> these tidal bulges depend on rotation, and depend on some
> mysterious property of the center of mass. And of course
> students will swallow even a bogus 'explanation' if it 'sounds
> good' without critically examining the details of evidence,
> logic, and fundamental physics. 


The word "rotation" is ambiguous: others have pointed out that the 
rotation of the planet about its axis is necessary for tides to be 
observed at a particular point. Donald is talking about "rotation 
about the centre of mass" which makes me think he means the earth and 
moon going round their common centre of mass, as opposed to being 
"nailed down to the fabric of space" like two spheres in the 
Cavendish apparatus, which he also mentions.

In this latter case there is surely one tidal bulge on each body, and 
not two.

And again:

> I have included this document by Phil Plait after my .sig.
> Notice that he doesn't have to talk about center of mass, or
> centripetal effects to explain the origin of the earth's tidal
> bulges. 

Now what does Phil Plait say?

   >This part is tricky, and is the hardest part of this
   >explanation to understand. A drawing of these forces looks
   >like this:
   >
   >
   >  -->      ---->      ------->
   >  far      center     near
   >  side     of Earth   side
   >
   >where the arrows represent the force (and direction) of the
   >Moon's gravity on these three points of the Earth. Now, we
   >measure the gravity of the Earth relative to the center of
   >the Earth; everywhere on the Earth, the center is "down". In
   >a sense, we see the center of the Earth as "at rest". It is
   >mathematically correct to then subtract the force of the Moon
   >on the center of the Earth from the force felt on the near
   >and far sides. This is called vector addition. If we do that,
   >our diagram will look like this:
   >
   >
   >
   >far        center     near
   >side       of Earth   side
   >
   >(Note that this drawing is not meant to be exact, but just to
   >give a feel for what's happening).

Unfortunately the second diagram did not appear, but it is clear what 
it should be: far side and near side both show forces away from the 
centre of the earth. Plait, however, is "taking the centre of the 
Earth as at rest" and adding "pseudoforces". Naughty. 

Note also that the procedure is NOT mathematically correct if the two 
bodies are "nailed to the fabric of space". In this case it's like 
having two blobs of jelly (in the English sense - I can't think of 
the American word) staked through their centres: they'll bulge 
towards each other, yes, but not away from each other. Or perhaps it 
depends on just how the bodies are nailed. I think the point is that 
you get TWO tidal bulges when the bodies are in free fall, 
accelerating towards each other, regardless of whether there is 
circular motion, but the nailing is a red herring. Centripetal 
effects are not essential, but I don't see how one can avoid the 
centre of mass (Plait doesn't avoid it btw as he is taking the force 
of the moon on the centre of the earth and subtracting the local 
force of the moon), as the whole thing depends on the fact that the 
body has the same acceleration everywhere, determined by the position 
of its centre of mass, but the gravitational pull on it differs from 
place to place, so the body has to deform - in both directions, 
making two bulges.


> The *bulges* do not depend on rotation, but the *tides* do.  If
> the earth and sun were fixed in space there would be bulges but
> not tides. If the earth revolved around the sun but did not
> rotate, there would be two tides a year.
>
> Richard Grandy
> Philosophy & Cognitive Sciences
> Rice University

Richard is talking about rotation of the planet about its axis, and 
he is correct. But I submit that he needs to be clear about what 
"fixed in space" means before we can agree about one bulge or two.

Leigh Palmer writes:

> I also seem to recall
> that the Adriatic has only one tide per day, but my memory here
> may be as defective as it was about Newton's perception of the
> tides. Any clarification would be gratefully accepted.

I've lived on the shores of the Adriatic for 14 years and have never 
observed that there were NOT two tides per day, but I must say I have 
not looked very craefully. The range is small (less than 1 metre) and 
the shores are steep and rocky, so the tides are not very obvious. 
I'll check up!

I have understood some new things answering this. Thanks!

Mark.

*************************************************
Mark Sylvester, UWCAd, Duino, Trieste, Italy.
msylvest@spin.it    tel: +39 40 3739 255
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