Is a Topopolis' Orbit Truly Unstable?

[DET]

Background: Larry Niven's Ringworld was declared to be unstable because it rotates fast enough to create artificial gravity on the inner surface (never mind the structural material issues) and is therefore not technically in orbit around the central star.

So I've been reading up on the topopolis megastructure, which is essentially a torus that stretches all the way around the central star. It generates artificial gravity by rotating around the minor radius, like a very long O'neill cylinder that connects to itself.

Several sites have commented that the structure would have an unstable orbit, like a ringworld. But the topopolis can orbit at orbital velocity, so why would the orbit be less stable than, for instance, a bunch of O'neill cylinders in the same orbit?

 

[Janus]

It has nothing to do with the rotation velocity, it has to do with it being a solid structure and behaves as a single unit. If one part of the ring gets nudged just a little closer to the the main body, the opposing side gets nudged away. Gravity pulls harder on the closer side than it does the other, Thus the whole structure is pulled in that direction. This increases the imbalance of the pull, shifting the ring even further...
James Maxwell did the original analysis of this scenario which led to the conclusion that Saturn's rings could not be solid structure for this reason.
A bunch of orbiting O'neill cylinders are different in that the cylinders are not rigidly tied to each other and there is no feedback between them. They are independent units. Nudging one cylinder has no effect on the orbit of any of the others, it just shifts into a altered orbit while the others remain in theirs.

 

[DET]

So a bunch of O'neill cylinders connected in a ladder configuration would have the same issue? Even if the connector was just cable? (even though that's unlikely to be the case)

 

[nikkkom]

Yes

 

[Nik_2213]

IIRC, Niven was rather embarrassed by the finding that his Ringworld's orbit was dynamically unstable. He had to add prodigious station-keeping thrusters, weave them into the story arc...

 

[DET]

Ah, but he didn't have physicsforums, did he?

 

[anonymous nobody]

Almost 30 years ago a friend of mine in Huntsville was working on a model of a long cord to be deployed in space by the Shuttle. I was in grad school then taking non-linear dynamics. I told him that since the cord contained many other cords that it would snap from the instabilities that would appear so his linearized model which was computationally nice was wrong.

In comes NASA to validate my idea: https://www-istp.gsfc.nasa.gov/Education/wtether.html

It was called the 'space tether' and it snapped as predicted. The issue is not why was I right, but why the experts were wrong. Back to Niven world all objects are non-linear. In the regime where most of us live we do not notice these non-linearities thus we fallaciously fall for linearized models which in many cases but not all work. We think of space as empty but it is not it is just in most cases a very diffuse and cold gas. This is the environment of something very large, in space, many many non-linearities, gas pressure, radiation pressure, gravity waves, micro-meteors and on and on.

It took nature more than 2 billion years to build up life and we live in a nice, warm and largely linearized cocoon, that when we leave us becomes wild, dangerous and unpredictable.

 

[hutchphd]

Almost 30 years ago a friend of mine in Huntsville was working on a model of a long cord to be deployed in space by the Shuttle. I was in grad school then taking non-linear dynamics. I told him that since the cord contained many other cords that it would snap from the instabilities that would appear so his linearized model which was computationally nice was wrong.

In comes NASA to validate my idea: https://www-istp.gsfc.nasa.gov/Education/wtether.html

It was called the 'space tether' and it snapped as predicted.

I am confused. The NASA reference cited blames the abruption of the tether on entrained air causing an ionization path. What does this have to do with nonlinear dynamics ? Interesting experiment though. I do wonder about the dynamics of the "space elevator"...