Well just to confuse things a bit mo
Even if we only focus on the tide generating potential, there is a
cupple of things that we haven't discussed yet, and one of them has to
do with rotation: "The Coriolis freqency". The other thing one could
include is the "parallax".
I mention this just to make clear that the two models discussed above
both are incomplete.

Peter S/Y Anicula

"Jeff Morris" skrev i en meddelelse
...
"Scout" wrote in message
...
Jeff,
Remember that I first posted that very same sentiment, and even
provided a
graphic. I still believe that to be true, but have modified my
internal
model, giving allowance for the centrifugal force. I'm not a
physicist, but
the way I'm seeing it, there is a middle ground in this
discussion. I'm
curious to know if you're discounting centrifugal force as a
contributor to
the far bulge.
Scout

I've always said that Centrifugal Force can be used as part of the
explanation, as
long as you end up with the same answer. There are several
different ways of looking
at this, all valid. (I hope I can get through this without mangling
the terms too
badly ...)

The problem with Centrifugal Force is that it is a "fictional
force." It is only
needed if you work in a non-inertial, or accelerating reference
frame. If you are in
a car going around a curve, your reference frame is accelerating
towards the center of
the curve, and thus you feel a Centrifugal Force in the opposite
direction. To an
outside observer, the CF doesn't exist, the only force is the car
pulling the
passenger around the turn. The outside observer can analyze the
situation completely
without invoking CF. (The passenger feels CF push him outward, the
observer sees the
car pull the passenger inward.)

In the Earth-Moon system there is gravity pulling both the Earth and
Moon around
curves. Because the gravity acts on all objects, we don't notice
ourselves being
pulled around. The magnitude of the Centrifugal force is to small to
notice, but in
that reference frame it exists. To the outside observer, we're
just in freefall,
being pulled inward by gravity.

The problem with CF arises when you look carefully at the math. One
pitfall Nav fell
into was trying to calculate CF as a function that varies with the
distance to the
barycenter. However, all points on the Earth do not rotate around
the barycenter,
only the center does. Other points describe the same circle around
nearby points, so
that all points on Earth feel the same Centrifugal Force. (This is
a tough concept to
explain in words; its easier to do it graphically. Consider a plate
wobbling around a
point but with no rotation - each point on the plate describes the
same circle.)

BTW, Nav provided two commonly used formulas, one for gravity and
the other for CF.
Although they look quite different, you should appreciate that they
are the same,
since the angular velocity is determined by the gravitational force.
The CF will be
the same (with the opposite sign) as the gravitational pull at the
Earth's center.

Since the CF is a constant force, it can't describe the two bulges
in opposite
directions. It is gravity itself that varies with distance. The
differential force
can be derived either by subtracting the average gravitational force
which causes the
freefall at the center of the Earth, or it can be derived by adding
the centrifugal
force. Since the two are the same, except for the sign, the math is
identical.

So take your pick, either explanation works, and I'm sure there are
others. However,
I hope you can appreciate that explanations like "gravity creates
the inner bulge,
centrifugal force creates the outer bulge" makes physicists wince!