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Re: Tidal Motion



Regarding Jim Green's questions of 04 JUL 2000:

Is the nature of the Moon's core known? Solid? Molten?

Does the Moon have a mantle?

Is the magnitude of the tidal motion of the Moon's surface known?

For that matter is the magnitude of the tidal motion of the Earth's mantle
known?

Which has the greater effect on the Moon's orbit the Earth's oceans or its
mantel?

and the part of Gary Karshner's response that said:

...
The Moon's equatorial diameter is greater then its polar diameter (like the
Earth), but it has an even greater diameter in the direction of the Earth,
then it does at right angles to it, a permanent tidal bulge. ...

As mentioned by both Paul J. and Gary K. the Moon's entire interior is
quite probably solid and not liquid.

Because of both the circumstances attending the favored formation
scenario for the Moon, and because of the low gravity in and on the
Moon, the density of the lunar interior is not nearly as depth dependent
and compositionally differentiated as it is for the Earth (whose inner
core is much more dense than its crustal rocks). The density of the
Moon's surface rocks tends to be about 90% of the average density for
the whole Moon.

By checking some data I found in a couple old posts of mine from late MAR
1998 I have estimated that the Moon must be sufficiently rigid so that it
can resist the current local values of the tidal forces and stresses
acting on it due to the Earth. This is because the Moon's shape (i.e.
its spin-induced oblate equatorial bulge and it prolate tidal bulge
aligned with the Earth) are much more out-of-round than can be accounted
for by the current terrestrially induced conditions. If the Moon's
shape could relax to be in equilibrium with the currently applied tidal
and centrifugal forces, the Moon's shape would be much more round, and
it mass distribution would have a much weaker mass quadrupole moment than
it currently has. According to my calculations it seems that the Moon
has a shape and mass distribution that corresponds to one that would be
close to the equilibrium values for a *perfectly* flexible fluid Moon
*if* the Moon was about 2.04 times closer to the Earth (where the tidal
force is about 8.5 times greater) than it is now , *and if* its sidereal
spin rate was about 2.29 times faster than its orbital revolution rate
it would have about the Earth-Moon barycenter *at* that closer orbital
radius.

Thus it seems that the Moon must have frozen up and became tidally
locked toward the Earth a long time ago when the Moon was much closer to
the Earth than it is now. If the Moon had a sufficiently large fluid or
plastic interior, it would presumably not be rigid enough to prevent its
shape from relaxing toward the nearly static equilibrium shape favored by
the current tidal forces acting on it.

The Earth has a land tide as well as an ocean tide. It is much smaller
the order of cm instead of meters.

As I recall, I think the Earth's ocean tidal bulge is not more than a few
10's of cm. This makes for about 1 order of magnitude difference between
the land tide and the ocean tide rather than the 2 orders of magnitude
possibly implied above.

But if memory serves, the ocean tides
account for only about half of the energy loss associated with the slowing
of the earth's rotation.

I'm not a geophysicist and have not done the relevant calculations, but
it seems to me that the energy dissipation from the ocean tides probably
ought to be significantly greater than that due to the Earth's bulk tidal
response. The reason for this conclusion is that, as I understand it,
the current energy dissipation rate from the sloshing of the oceanic
tides is significantly greater than the average value would have been
over geological time when (due to plate tectonics) the Earth had a
substantialy different configuration of oceans and continents.
Apparently an unusual number of ocean basins, gulfs, bays etc. are near
resonance conditions and this makes for an anomalously large overall
dissipation of the oceanic tidal energy. In fact, if the current value
for such large frictional dissipation were used for calculations back
into the distant past, the Moon's orbital recession rate would have had a
signifiantly larger than typical value. (This is because more tidal
energy dissipation on Earth tends to translate into a faster lunar
orbital recession rate and a faster spin-down of the Earth's rotation
rate.) This faster recession value would have the embarrassing effect of
putting the Moon inside the Earth's Roche limiting distance for lunar
stability in less than 3 billion years into the past. Since the Moon is
thought to be nearly as old (over 4 billion years old) as the Earth, this
would present a problem. But if more realistic lower energy dissipation
rates obtained throughout most of geological time were used in the
extrapolations into the past, then it is possible to have the Moon at the
right orbital places at the right times (with the Earth spining at the
right speeds) all the way back to the Moon's creation shortly after that
of the Earth.

In order for the differences in oceanic tidal dissipation rates to be a
large enough effect to solve the lunar recession problem it seems
necessary that the tidal dissipation from the oceans be the dominant (or
at least not a minor) tidal energy dissipation mechanism. Otherwise, if
bulk planetary land tide dissipation effects were dominant (and since we
can probably safely assume that any surface rearrangements would have
little effect on the overall bulk planetary dissipation mechanism and
its rate) then tectonically reconfigured ocean basins would not have
much of an effect on changing the overall dissipation rate enough to
solve the lunar recession problem. Since I think I recall a Scientific
American article from the mid 80's that claimed that the lunar recession
problem *was* solved, that suggests to me that the oceanic tidal
dissipation is probably a bigger effect than the bulk planetary
dissipation mechanisms.

David Bowman
David_Bowman@georgetowncollege.edu