Jeff Morris wrote:

Sorry, nav, I still can't really buy your argument. It is obvious that you
can't ignore the centrifugal force component if that's the mathematical approach
you're taking. Clearly, if you ignore a major component, the final answer will
be wrong.


YES!

However, when all the forces are summed up and canceled out, there is one major
force "left standing," and that's the "differential gravity" from the moon (and
also sun, of course). "Differential Gravity" is often defined as the pull from
the moon, after the centrifugal force has been removed.

This is where I take issue with such sloppy thinking. Gravity acts ONLY
toward the center of the system. It cannot be relabelled in any way to
make an "outward" force. As a physicist, do you think subtracting an
inertial force from gravity and call it "new gravity" is an acceptable
idea? I say the two are quite different forces and need to be identified
and kept separate. If the force due to the radial acceleration played no
part in the final equation why would it be needed in the derivation at
all? What happens if omega=0 and the body is in free fall? Are there
still two tides?

Anyway, there's no point to my constantly repeating myself so we'll just
have to agree to disagree. In case anyone else is interested, here's a
quote from a teaching site that explains it all quite simply.

http://ijolite.geology.uiuc.edu/04Sp...tes/Lect29.pdf

" TIDES
Periodic rise and fall of water level along coastlines related to the
phases of the Moon.
One cause: The moon’s gravity.
BUT...If this were the only cause, we would have only one high tide
per day (i.e., we would have
high tide when we are position closest to the moon). However, there
are often two high tides and
two low tides per day- why?
The other issue: Centrifugal/centripetal forces.
1. The moon orbits around the earth, and this makes the earth
“wobble”. More precisely, the earth
and moon both orbit around their center of mass.
Analogy: Imagine a large adult and small child holding hands and
spinning around. The
child spins in a wide circle, but the adult also moves in a circle,
albeit a smaller one
because the adult is so much heavier.
2. Because the earth is orbiting (moving a circle slightly) there is a
“centrifugal force”. Or, more
accurately, there is a centripetal force required to move the earth in
that orbit.
Cause for Tides: imbalance of two forces:
1. G = Gravitational attraction between Earth and the Moon (and Sun).
2. C = Centripetal force = Force needed to make the Earth revolve
around the center of mass
(center of gravity) of the Earth-Moon system.
Here’s the imbalance part:
1. Gravity from Moon stronger on side facing moon, weaker on the side
away from it
2. Centripetal force is the same everywhere on earth
3. G and C are exactly balanced at center of the earth
4. They are not balanced in other places that are closer to moon or
farther away from it
• Example: On the side away from the moon, the centripetal force
needed to keep the
ocean water in its orbit is greater than the gravitational force from
the moon
• Net result is like a force away from the moon (a centrifugal “force”)
5. So wherever C and G do not balance, there is force that is large
enough to make water
flow
6. Water flows and forms tidal bulges "


Cheers