"Nav" wrote in message
...


Donal wrote:

"Peter S/Y Anicula" wrote in message
...

The moon are a lot closer than the sun. Therefore the gravitational
force of the moon varies more over the earth's surface. It is the
variation in the gravitational force and not the force in itself that
creates the tides.

The moons pull on a water-molecule directly under the moon is larger
than
on a molecule on the far side of the earth, actually it is larger than
"the average pull on the whole earth", and here the moon pulls away
from the earth.
On the far side of the earth (seen from the moon) the gravitation from
the moon is less than average and at this point the moon pulls toward
the earth.


On the far side the tide is "high", ... just the same as at the near side.
If the moon's gravity was pulling the water, then you would expect LW to be
opposite the moon.


Quite so. The tidal gravity force is in the direction of the moon. This
is the potential energy in the system. So, there must be another force
present. The moon has kinetic energy in it's orbital velocity. From
Newton's first law:

F=m r omega^2

It is the difference in the two forces (and the resulting energy minima)
that causes two tides. Simple no? Why invoke something new like
"differential gravity"? Could it be to avoid saying inertial force?

Before I thought you were just arguing philosophically how much we should credit
centrifugal force, but now it appears you haven't really looked at the math at
all. The reason why "differential gravity" is invoked is because it represents
the differing pull of the Moon on differing parts of the Earth. Although this
force is all obviously towards the Moon, when you subtract off the centrifugal
force this is what is left. It is this differing pull that causes the two
tides.

This force can be viewed as having two components, one is on the Earth-Moon (or
Earth-Sun) axis, and the other is off axis. The on axis component varies
inversely with R cubed, outwards from the center of the Earth, and is usually
cited as cause of the two bulges. The other component is pulling towards the
Moon, but since its off-axis, from the an observer on Earth sees this as
somewhat downward. When the total gravitation force is subtracted from this,
the result is a downward pull. This is greatest at "low tide points," half way
around from the bulges, but also in a ring around Earth that includes the poles.
The net resulting idealized surface is a "prolate ellipsoid," squeezed around
the middle and out at the ends.

As a simple "reductio ad absurdum" consider that the tides at the poles are
always "Low" because the Moon is always pulling a bit downward on the poles.
If you only consider the centrifugal force, there is no component of that which
pulls the poles inward.

You can handwave the centrifugal force causes the outward bulge, but
mathematically, the idealized shape of the Earth is caused specially by the
differential forces. Trying to explain it all by "inertia" is just making it
simple for young children, it doesn't really explain what's going on.