B Hypothetical ring world thought experiment

[DaveC426913]

I know this won't work, I'm having trouble explaining why to someone who thinks it will.

Make a ring around a planet. Give it low walls. Fire countless pellets at hypersonic speeds around the inside of the ring. The pellets are moving at super-orbital speed, pushing the ring outward, making it rigid.

Supposedly, this will also keep it stable over the planet, since essentially, you've got forces pushing outward on the ring in all directions.

I know that this does not work. I know it's because
a] the pellets are not in "orbit", since they are restrained by the ring and therefore cannot move freely in an elliptical orbit, trading altitude for velocity and back again, and
b] the net gravitational force on such an object is zero. So it has no reason to stay stable.

I know this arrangement is slightly different from Larry's Niven's Ringworld, but it's a difference that makes no difference. (A fact that is lost on my adversary).

How can I describe the problem in a way that will disabuse him of the notion that the supposed super-orbital push of the pellets will cancel out?

 

[haruspex]

I'm unfamiliar with the works of L. Niven, but I'm guessing Ringworld is a spinning solid ring. If so, yes, that is clearly equivalent to the set-up you describe. It would have gyroscopic stability against rotations about an axis through the planet, but not in regard to displacements within its plane. If your interlocutor cannot grasp that then you might do better to save your efforts (and stability).

 

[sophiecentaur]

If your interlocutor cannot grasp that then you might do better to save your efforts (and stability).

I tend to agree here.

Supposedly, this will also keep it stable over the planet, since essentially, you've got forces pushing outward on the ring in all directions.

This clearly is only 'supposedly, as you say. The net reaction force from the centripetal forces on the fast particles has nothing to do with any other external forces that could act so you could just as easy have a rigid ring and discuss that. An attracting mass in the centre of the ring will produce instability and it will end up with one part of the periphery resting on the 'ground'. I think that is the lowest Potential Energy situation and there would be no net restoring force to maintain all sections of the ring at equal distances from the centre of the planet.
If you replace the massive ring with one with no mass but place equal masses at diametrically opposite positions, the force on one will be
gm/(R+ΔR)² and the force on the other will be gm/(R-ΔR)²
In a simpler form, the difference is c where
1/(a+b)² - 1/(a-b)²=c
With some jiggery pokery I got that c always has the same sign as b which implies that there resultant force for an imbalance is always in the direction of the imbalance. i.e. it's unstable and so will be a ring. It may be stable if the ring spins at orbital speed (exercise for the student, perhaps?)

 

[Janus]

James Clerk Maxwell, while considering the rings of Saturn, was able to mathematically prove that a solid ring in such a configuration would not be stable. The slightest perturbation would cause it to start drifting so that it would eventually brush up against the body is was rotating around. It doesn't matter how fast the ring is spinning. This was the nail in the coffin for the idea that Saturn's rings were solid.

Niven's Ringworld suffered the same problem,(something pointed out to him after the novel was published) So he addressed in in the sequel by adding fusion ramjets placed around the rim that would fire when needed to keep it stable. (Part of the plot of this novel revolved around idea that after the original civilization that built the ringworld fell, a subsequent civilization started to cannibalize the ramjets in order to build exploration ships.)

 

[DaveC426913]

I don't think these will convince my ... interlocutor. (Good word. I actually went looking for synonyms for opponent.)

Pretty sure he's convinced the hypervelocity pellets act as if they are in orbit.

 

[sophiecentaur]

Can't you just send him to PF?

 

[DaveC426913]

I thought about that. :)

He seems to have come around. I've convinced him that the 'dynamic' part of his hyper-V pellet stream means it can be kept artificially in position by tweaking the stream as needed.

 

[andrewkirk]

I've been lurking in this thread since it started, hoping the discussion would clarify things like what the pellets are for, in which direction they are fired, and whether the ring is a topologically a torus (the OP mentions walls but not a roof), and thereby save me having to ask these dumb questions. But that hasn't happened, so can anybody please explain about the pellets and what they are supposed to do? If the ring is not a torus I'd imagine the pellets would shoot off into space rather than going around the ring. If it is a torus, I imagine they'd alternately ricochet off the roof and floor of the ring as they make a zig-zag way around it.

I feel I must have completely the wrong mental image of this set-up. Does one need to read RingWorld to understand it?

 

[haruspex]

the pellets would shoot off into space rather than going around the ring

It says they're on the inside of the ring. I imagined them as on a frictionless track.

 

[DaveC426913]

The walls and no roof are my addition, to simplify the model.

Ideally, you'd have an inhabited ring, with evacuated tubes running underfoot. The hypervelocity pellets are magnetically guided around the ring, proving an outward pressure. This riffs off a space fountain inasmuch as it uses high-V pellets to provide push - though the ring is an entirely different animal.

Some light reading:
https://en.wikipedia.org/wiki/Orbital_ring
http://www.orionsarm.com/fm_store/OrbitalRings-I.pdf
http://www.orionsarm.com/fm_store/OrbitalRings-II.pdf
http://www.orionsarm.com/fm_store/OrbitalRings-III.pdf

 

[DaveC426913]

If you'd like to peruse the thread, it's here:
https://forum.cosmoquest.org/showthread.php?165316-Could-you-terraform-Jupiter

 

[andrewkirk]

Thanks @DaveC426913 and @haruspex. It makes sense to me now.