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Re: Moon's synchronism



On Tue, 17 Mar 1998, Igal Galili wrote:

BTW, it's interesting to consider this phenomenon from a driven
oscillator point of view. The tidal force effectively drives the
moon at a frequency of about 1 cycle per month.

per month, or per 24 h?

Per month, or, more (but not completely) precisely, the time it takes the
moon to complete one orbit about the earth relative to the "fixed stars."

But since that
frequency is *way* above the resonant frequency, the moon's
rotational inertia dominates.

"resonant frequency" of what?

Of the moon's rotational velocity perturbations due to the periodic tidal
torque. I just did a "back of the envelope" (actually more like "two
sheet of paper") derivation of the period for small oscillations of a
nearly spherical but slightly prolate ellipsoid in a gravitational field
gradient and got the sensible result that

T = 2 pi/sqrt(f g')

where f is the fractional difference between the maximum and minimum
rotational inertias about axes through the CM and g' is the local field
gradient. For the moon g' is about 1.4 x 10^-11 s^-2. I don't know the
value of f, but if it were as large as 1% (which I sincerely doubt), the
period would still be over 6 months.

John
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