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Old October 10th 04, 01:52 PM
Grimble Gromble
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"AA Institute" wrote in message
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"Grimble Gromble" wrote in message
news:pWV9d.425
Are you familiar with this equation (quoted by Henry Spencer on
sci.space.tech a while back):-
An Earth circling satellite orbit will precess along the equator over
time according to the equation:-
-3/2 * J2 * (R^2 / p^2) * n * cos (i)
[Where J2 is a constant related to Earth's flattening, R is the
Earth's eq. Radius, p = a*(1-e^2) (in which a is the orbit's
semi-major axis and e is its eccentricity), n is the mean motion and i
is the orbit's inclination.]

Being familiar with an equation is not the same as understanding it. That
the earth's flattening is involved suggests that this precession is
caused
by tidal influences experienced by the satellite as it orbits above and
below the earth's equatorial plane. That there is no term relating to the
lunar and stellar masses, suggests that this is a very simplified
analysis
in which all other influences have been ignored. Is there any reason you
introduce this (idealised particulate) satellite into a discussion on
earth
rings? Perhaps you are comparing the effect on an orbiting satellite of
the
earth's equatorial bulge to that of an independently orbiting ring? You
do
realise that there are significant electromagnetic forces operating
between
the 'equatorial' bulge and the 'spherical' earth?


Since each discrete particle in a ring system, such as the one I
envision here, is effectively a *satellite* in its own right, and the
individual particles are orbiting the Earth at appreciably different
distances (the ring has some *width*), the above equation - along with
another similar equation - can be used to show that under certain
favourable orientations of a ring system the particles are unlikely to
scatter significantly.

Probably doesn't make too much sense here... I am working on a short
paper to better illustrate this, which I hope to make available when I
get some spare time.


Sadly, this won't work for a solid ring because the 'individual' particles
are being acted on by the significant electromagnetic forces I referred to
earlier. You might want to consider what will happen to your 'solid' ring
when one of the 'individual' particles on the inner edge has travelled one
more revolution in its orbit than one of the 'individual' particles on the
outer surface. Since the particles won't actually have moved relative to
each other, there must exist stresses with the structure. These tidal
stresses actually exist in any solid body moving through a non-uniform
gravitational field. For small bodies, these stresses are quite small, but
there is a limit at which the gravitational forces acting within the body to
hold it together are overcome by the tidal forces pulling it apart.
Electromagnetic forces are very much stronger than gravitational forces so
we could build a very large space station with little concern, but a planet
circling ring?

Hopefully you can see that not only would you have to constantly monitor and
adjust the position of a ring to maintain its distance from a planet, as
discussed previously, you'd also have to cope with massive tidal stresses
attempting to distort the ring - and I'm not even considering the tidal
effects of the moon here.

Is there any particular reason that you'd want to build a planetary ring
other than inspiration from science fiction stories?

I trust this hand-waving response will not irritate those who deem numerical
simulation to be the be-all and end-all of discussions (though I expect this
comment will).
Grim