"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!