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 parts, so the ring will be accelerated towards the earth. Also, the ring will start to depart from circularity. The parts nearer the earth will be pulled even closer, and those farther away will move even farther away, then they would if the ring remained circular. The main effect of the weakness of the ring is that, as it approached the earth, there would be strong tensile forces on the ring, which would probably tear it to pieces before it hit the earth. After that happened, the component parts would happily remain in orbit. Maxwell's prize paper on the stability of Saturn's rings has something on the subject of the (lack of) stability of a solid ring.

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