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Re: Moon's synchronism



On Tue, 17 Mar 1998, Jim Green wrote:

It may of course be my senility, but I don't understand what you are talking
about -- maybe some of this is due to your not answering my question. (:-)

Jim Green


John, what is your evidence for this??? What tidal force? Are you talking
about water, crust, or magma -- Moon or Earth? I would be grateful for
citations.

Jim,

Sorry. When you asked for my evidence, I mistakenly assumed you
understood what I was talking about. I'm not sure where you need
me to start so let me back up pretty much to the beginning and try
to explain:

The Moon is a prolate ellipsoid with its long (low moment of
inertia) axis pointing generally toward Earth and stabilized in
this orientation via the torque produced by its interaction with
Earth's gravitational field gradient--what I have called the
"tidal torque." This much is well-known. The same effect has
been put to practical use in stabilizing satellites such as the
"Long Duration Exposure Facility" so that one end always points
toward Earth and the other toward outer space.

Now, the Moon's rotational inertia tends to maintain its
*rotational* angular velocity. But, because the Moon is in an
elliptical orbit, its *orbital* angular velocity is *not*
constant. As a result, its "long axis" oscillates about the
instantaneous direction of the gravitational field gradient and
we, correspondingly, see a slightly different face of the moon at
different times during the month. (I'm afraid I'm just going to
have to ask you to draw some pictures for yourself if my words
still don't do the job for which they were intended.)

*If* the Moon's rotational inertia were relatively small or the
tidal torque were relatively large, then the Moon would be kept
tightly in the grip of the tidal torque. The result of this
domination by the torque would be very little deviation of the
long axis from the direction of the gravitational field gradient
and correspondingly little deviation in the face that the moon
present to us during its orbit. (This behavior is analogous to
that of an object with small inertial mass on the end of a stiff
spring with the free end forced back and forth at a moderate
frequency. It is the kind of behavior that one gets from driving
*any* mechanical oscillator well below its natural frequency.)
This is *not* what we see.

What we *do* see is a moon with relatively *constant* rotational
angular velocity--the result of its relatively large rotational
inertia and the relatively small tidal torque. That is, the
moon's behavior is dominated by its rotational inertia. (This
behavior is analogous to that of an object with large inertial
mass on the end of a weak spring with the free end forced back and
forth at a moderate frequency. It is the kind of behavior that
one gets from driving *any* mechanical oscillator well above its
natural frequency.)

The calculations I shared merely corroborate what the evidence
demands--that the natural frequency of the moon oscillating in the
field gradient of Earth is significantly lower than the drive
frequency due to the "monthly" variations in the tidal torque.

I hope this helps. I'd really like to retire from this thread
now. I hadn't expected to open such a can of worms, but I do
apologize for any sloppiness on my part that may have acted as the
can opener.

John
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A. John Mallinckrodt http://www.intranet.csupomona.edu/~ajm
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