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Re: Moon's Spin

Jim Green asked:
Why does the Moon keep the same face toward the Earth? In as much as the
orbital period is changing, how does the spin keep pace?

The moon has a fixed mass quadrupole moment (due to it solidifying in a
region where the earth's gravitational field gradient is substantially
different from zero) which is both induced by and interacts with the earth's
tide-producing field gradient. It's current orientation relative to earth
corresponds to a minimum in its (tidal) potential energy of orientation
relative to the earth. Since the moon is relatively solid it resists changes
in its shape caused by a temporary changes in the field gradient that it
finds itself in. So if its orientation relative to the earth were to change
via some small rotation then its orientational potential energy would
increase and a tidal restoring torque from the earth would be exerted on it
tending to restore it to its equilibrium orientation. Actually, during the
course of the lunar cycle the moon's orientation rocks a dew degrees back and
forth about its average equilibrium orientation. This is due to the periodic
speeding up and slowing down of the moon's orbital angular velocity of
revolution as it orbits the earth in an ellipse (in accord with Kepler's 1st
and 2nd laws). This modulation on the rate at which the orientation angle of
the minimum orientational potential energy siderally precesses around the
moon as it orbits the earth causes this forced rocking motion relative to the
current equilibrium orientation. Ultimately, the energy fed into the moon via
this forced AC oscillation is damped via dissipation by viscous relaxation of
the moon's inelastic material properties. This keeps the oscillations in a
steady state so they don't continue to grow with the extra added energy. Also,
I don't think the forced sideral oscillation frequency is very close to the
natural resonant rocking frequency, which keeps the oscillation amplitude
relatively small.

Thus as the moon gradually spirals out away from the earth at some 3.7 cm/yr
(slowing its revolution rate according to Kepler's 3rd law) there are self-
correcting restoring tidal torques exerted on the moon from the earth's field
gradient which keep its orientation locked (mostly, except for the rocking
motion mentioned above) relative to the earth.

David Bowman