Titanium Puzzle Ring, Geostationary Ring. ?
Q: I once read a science fiction book where, many years in the future, the
geostationary orbiting satellites and platforms were connected together (I
can't remember the book's title or who wrote it). Eventually a huge
toroidal ring structure was formed that completely surrounded the Earth
(shades of _Ring World_). The day-night cycle for people that lived on the
ring was about 24 hours long. I got to wondering what would happen if a high
speed transit system was built into the ring. Here are some thoughts I had:
Going one direction around the ring the passengers would feel a force
pushing them away from the Earth. Going the other direction, they would
feel a force pushing them towards the Earth, until they passed a certain
speed (where they "stood still" over the Earth) and then the force would
diminish as the transit system went still faster. As the speed got high
enough the force would begin to be away from the Earth. (Something about
this reminds me of the Red Queen in Alice in Wonderland).
I assumed that the transit system had a small mass compared to the rest of
the ring structure. When the transit system moved in one direction the rest
of the ring structure would move in the opposite direction at a slower
speed. (What interesting effects could be observed if they were about equal
in mass?)
Besides checking my conclusions, what other interesting effects could be
noticed by people living in such a structure? If the average cross section
of the ring was about 30 meters in diameter, and it was built out of
currently available materials (like titanium or fiber composites), how
massive would the structure have to be? Make your own estimates about the
density needed for internal bracing, walls, population, supplies, etc. How
much energy would it take to lift the materials from the Earth or from the
Moon?
A:If it is not actively stabilized, I am sure that the inhabitants would
find it very interesting when the ring crashed into the earth. Such a
structure is dynamically unstable, like the proverbial needle balanced
on its point. (This was pointed out to Niven after the publication of
_Ringworld_.)
I have read so many science fiction books that had geostationary satellites
and towers (space elevators) in the last few years that I can't recall which
one had the concept of linking them into a single structure. Perhaps it was
Arthur C. Clarke (_Islands of Paradise_?), Larry Niven, or Greg Bear. I
don't believe the book discussed the consequences of the structure much, it
just introduced the concept. Perhaps someone can remember the name of a
book that discusses a "complete" geostationary ring.
I think you read _3001_ by Arthur C. Clarke. The world had 4 towers a
couple hundred thousand miles high which were connected by a big ring (it
wasn't finished though). They moved really fast around that sucker.
I believe this system would be different from Ring World in a couple of
ways. Ring World was not in orbit, it spun much faster. Because it spun
faster, it had to be made of an incredibly strong material. When perturbed
I presume it remained circular and the Ring World would push on itself,
de-centering the entire ring. Since the ring goes completely around the
star, there is no strong unbalanced gravitational force to pull it back into
position.
In the geostationary structure, the materials would be less rigid. If a
force perturbed the ring, perhaps the ring would distort and become
non-circular (like a tidal distortion). Perhaps this ability to distort
would keep the system more stable (as if you connected the current
geostationary satellites together with long elastic bands).
Does anyone know where I could find an article on the Ring World instability
on the Web?
I had not thought of this, but you are right -- the ring would no longer
be circular as it moved off-center. However, this effect would _increase_
the instability.
Initially, the ring is circular, and centered on the earth. There are
two, balancing forces on the ring: the centripetal force of gravity
and the centrifugal force of inertia. Now the ring is perturbed by
something, and starts to drift. The ring will move towards the earth,
and the parts nearer the earth will feel a greater force towards the
earth then the further