Re: Moon's synchronism

[David Bowman <dbowman@tiger.gtc.georgetown.ky.us>]

Concerning where Bill Beaty wrote:
> . . .                                               .  The moon is still
> supposed to be swinging with a slight rotary oscillation, but I don't know
> if that is left over from the original swinging, or if it's from
> interaction with the sun, etc.

As I recall, this rocking motion is due to the fact that the moon's
orbital angular velocity around the earth periodically increases and
decreases in synchronism with the distance between the moon and the earth
as it executes its somewhat elliptical orbit.  Since the moon's spin
angular velocity doesn't keep up perfectly with these changes its
orientation relative to the earth is alternately ahead and behind its
average orientation. Once the moon's orientation relative to the earth
becomes somewhat rotated wrt its equilibrium orientation, the earth's
tidal interaction with the moon's quadrupole moment causes a restoring
torque on the moon tending to reorient the moon's prolate bulge back
toward the earth.  The natural resonant frequency of this restoring motion
differs from the driving frequency (from the elliptical nature of the
moon's orbit).  Thus this rocking motion is effectively described as an
off-resonance driven high-Q (nearly) harmonic oscillator.  (Just how high
the Q is depends on the dissipative rheological properties of the moon's
interior and how inelastic the tidal kneading of the moon is as it rocks
in the earth's tidal gravitational field gradient.  I have no idea what
this Q value for the free rocking motion actually is though.)

David Bowman
dbowman@gtc.georgetown.ky.us