Re: Moon's Spin

[Jim Green <JMGreen@sisna.com>]

I like David Bowman's posts -- he and I have these good discussions.  

David, I see two problems with what you say -- maybe I am missing something:

> 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.  

1) I am always leery of assumptions made about what happened 5^9 years ago.
The damnedest stories are generated based on assumptions whose main value is
that they make the story itself plausible.  Look at all the convoluted
evolution and plate tectonics stories -- all told as if an historian were
there taking notes. But on the other hand maybe quadrupole measurements have
indeed been made during Moon landings or close orbits.  However, it is just
as reasonable to assume that the Moon fell as a solid from an asteroid or
comet or what ever.  There will be assumption to support any of many theories.  

2) Nobody really knows of course just where or when the Moon solidified, but
all the planetary geophysicists you have steered me to in the last few weeks
(on a slightly different subject) seem to agree that the Moon's "initial"
orbit was very much closer to the Earth than it is now. There is no reason
to assume that the Earth's gravitational field (with it's gradients) 5^9
years ago (when IT would have been molten too) were anything like they are
now or that they were the same at the close orbit as at the current Moon orbit. 

Though you tell a very nice story. I will study it further.

TX

    





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
> dbowman@gtc.georgetown.ky.us

Jim Green
JMGreen@sisna.com