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Re: Tides and tidal bulge



Since I've quit the "c" discussion I thought that I would take some of my new
freed up time and make a couple of nit-picky points concerning Dan M.'s recent
post on tides and tidal bulges. Dan M. wrote:

... The sun's gradient
is tiny compared to the Moon. The nearness of the moon causes the effect,....

According to my calculations, the gravitational field gradient of the sun at
the earth is about 40% that of the moon's field gradient at the earth on the
average. I might call this "small", but I would hesitate to call this "tiny".
BTW for Jim G., the gravitational field gradient of Jupiter at the location of
the earth varys somewhat with the relative orbital positions of the earth and
Jupiter, but its average value is about 6 or 7 x 10^-6 that of the sun. This
I *would* call "tiny".

...
Eventually, as the earth spins down losing energy by frictional heating of the
moon, earth and ocean, the tidal bulges on the earth's oceans WILL occurr
directly under the moon and we will be tidally locked to the moon. Similar
tidal interactions (greatly magnified) regularly turn Io inside-out as
it is squeezed like a tube of toothpaste in Jupiter's gravitational field
at a distance of only a little further than our moon, near a planet with 300X
the Earth's mass.
...
Considering that it seems (as I recall) to have taken 100s of millions of
years for the earth's spin rate to have slowed down by a factor of 2, I think
that we will have to wait an extremely long time for this lock-in situation to
occur for the Earth. I would expect this secular angular deceleration to be
reduced in the far future as the outwardly spiraling moon will exert a
progressiveley less intense tidal stress on the earth the farther out it goes.
It should be noted that it is thought, I believe, that Pluto and its moon
Charon is in this mutual lock-in situation. To a resident of Pluto, Charon
never rises or sets; it just keeps the same positon in the sky. To a resident
of Charon, Pluto never rises or sets either. The Pluto-Charon system is like
a big lopsided dumbell twirling in space.

The tidal flexing that Io undergoes which keeps its interior molten and powers
its volcanos does not seem to be very much due to Jupiter's gravitation. It
is true that Jupiter exerts an intense tidal stress on Io, but that stress is
nearly *static* and doesn't do much continuing tidal work on its plastic
interior (and consequently can't heat it much). This is because Io has a
*very* nearly circular orbit around Jupiter (keeping Jupiter's grav. field
grad. nearly constant in Io's vicinity) and Io, being in a tidally-locked
orientation with respect to Jupiter, always presents the same side to Jupiter.
This means that Io experiences a nearly static tidal stress from Jupiter. The
dynamic tidal flexing that Io experiences seems to be mostly due to it passing
by Jupiter's other moons, most notably, Europa (because of proximity) and
Ganymede (because of mass). I suppose that maybe Jupiter can *indirectly*
contribute to the tidal heating of Io, since when Io passes another moon that
moon's gravitational influence may temporarily pull Io a little out of its
circular orbit around Jupiter thus changing the field gradient that Io feels
due to Jupiter.

David Bowman
gtc.georgetown.ky.us