Ring Suspension Between Binary Masses

[BastianQuinn]

I'm having trouble conceptualizing the variables involved with this system, and I was wondering if some expertise might make the problem much simpler than I believe it to be.

Two massive spherical bodies (Osmium, minimum radius 900km, 5.08m/s^2 surface gravity) orbit each other with a solid or semi-solid washer-shaped ring of negligible mass between them, spinning rapidly. The ring is slightly tilted in the direction of the spheres' orbits. I think gravity exerts torque on the spinning ring which is shifted by its gyroscopic nature to an axis perpendicular to both orbit and rotation, but there is where I get lost because I can't picture what that will do. (I know it depends on the direction of the rotation) I've been looking at things like apsidal precession, or trying to figure out the shape of a theoretical asteroid belt before I weld all the bits together, but I just can't picture the motion.

If this model doesn't immediately deteriorate in all cases, what are the constraints of stability? Does the ring have to be entirely outside the binary orbit? If it's all about trial and error, how do I go about experimenting with this or any other model?

Thank you for your interest in this question, I hope it isn't just "another ridiculous three-body problem."

 

[mfb]

The ring is spinning along its ring direction?

I guess this is easier with coordinates. Let's say x is right, z is up, y is into the plane. The orbit is in the x/y plane, currently the spheres have y=0 so they are in the drawing plane.

The axis normal to the ring plane is (-x,z), pointing to the upper left. This is also the rotation axis? You'll get a net force left on the lower side of the ring and a net force right on the upper side, which means torque in y-direction, so rotation is approximately around the z axis, aligned with the orbital plane.
There is also a different way to tilt it: (x,y). Then you get torque in z-direction and rotation around (-x,y) (?)

Things get more complicated with the orbital motion, unless one timescale is much shorter than the other.

 

[BastianQuinn]

Here I've attempted to illustrate the movement as I picture it (not to scale) The ring is intentionally tilted along the axis of the orbit. The speed of the ring's rotation effectively offsets the torque acted on the disk by gravity, for reasons similar to why the globes don't just smack into each other. By the time the acceleration has changed the velocity, the velocity has taken the matter somewhere else... sorta...

The way that I'm picturing it, there ought to be some combination of speeds at which the ring's motion during orbit "dances" around the spheres without touching it. It would cause some great strain on the structure based on distances and scales and other variables. I want to zero in on what those variables are, I just don't know where to start.

Right now my constraints are that the spheres must be made from Osmium, and the pair need to apply no less than 0.25 g toward the center of the ring. The dimensions of the ring are only limited on the minimum side, and I feel like those limitations are well below any minimum a sustainable orbit would require. (atm, the minimum interior radius is just enough for a sphere to pass through) The speed the ring rotates should not exert more than 2g, and even that would be pushing it. The ring isn't for humans, but other weird things would happen.

I'm just not sure how to move forward in constructing this model so I can start filling in blanks.

 

[mfb]

The ring is larger than the spheres? That will make the gravitational forces complicated. It will also make the rotation of the ring quite slow (and therefore its precession fast), you have to take gravity into account for its internal stress, and many other complications.
Looks like you'll need a numerical simulation.

 

[newjerseyrunner]

Sounds like you are describing 3 body Lagrangian system: http://en.wikipedia.org/wiki/Lagrangian_point#Mathematical_details

 

[mfb]

Well, we have an exact solution for the motion of the center of masses already, and the ring shape is not a point mass.

 

[BastianQuinn]

Yes, I'm hoping to somehow suspend the ring withing the Lagrange points L4 and L5.

I've done some more calculations, though much of it is something like fermi estimation. With my initial guess at the dimensions of the ring, the inside has a radius of 139km, outside radius 557km.

From what I'm hearing here, stability depends heavily on the angular velocity. Using the formula F_c=mrω^2 to calculate ω, I run into an issue with the variable m. The formula assumes a particle or point-mass. I can put a solid guess to the mass that a single radial strut supports, but I think that is too wild a simplification. With these estimations though, the velocity of the outermost portion of the ring is something like 3m/s at the fastest. The slowest the spheres would be traveling and possibly collide with the ring is 1800m/s. As you suggested before, mfb, the larger the ring the slower it will go. Although these speeds do not account for the ring spinning against the gravity of the spheres, they do incorporate the possibility of up to 2g. I can't imagine needing more than that with the slowest spheres only having a surface gravity of a little over 0.5g. I think the only hope for the model is that my estimations for the mass are many magnitudes too high. Even then, I would have to more closely model the actual movement of the system to see if stability were possible.

It would be much safer just to make the ring a lot bigger in the middle, drop the spheres inside, and simplify the forces involved, but it would be less fun.

 

[mfb]

There are no L4 and L5 for two equal masses orbiting each other.

Stability? This system is unstable. You need "infinite" precision or some active control mechanism to keep the ring in place.

What is the purpose of this system?

 

[BastianQuinn]

Believe it or not, an answer like that is what I need. Something to tell me I need not consider this option further because there is no way to make it work. I'll need to come up with a different configuration.

The system is a sub-light generation ship which can divide like a cell. This configuration is just the first to come to mind. The station moves very slowly. The spheres are effectively fission fuel storage and a possible source of gravity. Once they've split, each ring will need to build a new ring and sphere pair. The setting assumes precision fission is possible, and the efficiency of obtaining energy from matter has had time to improve ridiculously, but that anything approaching light speed travel is not possible and that astrogation is too unreliable.

The answer to most "why not make things simpler" questions will be "simplicity is inversely proportionate to awesomeness." The only things I'm avoiding are things which might quickly break immersion because my understanding of physics is limited.

 

[rootone]

Please explain the significance of Osmium for the kind of device you describe.

 

[BastianQuinn]

Please explain the significance of Osmium for the kind of device you describe.

It is the densest-packing radioactively stable atom. I considered gold or lead, since they are important elements in industry, but I chose osmium for its density and I thought a scarcity of gold and lead would put interesting socio-economical stresses on the resulting community. They have ready access to portable fission, but not to fusion, which only happens off-site when harvesting matter from passing celestial bodies. They also generate energy (the form of energy is probably electricity, but it's not specified) locally from the waste-mass of such transmutations. I don't know what happens inside a sphere of osmium of that size (900km radius, chosen somewhat arbitrarily because the mass of the moon at that density has a surface gravity of 0.5g). I know there are compression forces, but I don't know of a reason why it would make a difference.

EDIT: It's also worth mentioning that the internal movements of the humanoid occupants is micromanaged, and they might be able to represent up to half of the ring's mass. Moving that mass inward, outward and around the ring is probably the ring's most potent method of self-correction. Then again, I don't really know how effective those possibilities are, or how easy it is to call shenanigans on everything I've just said.

 

[mfb]

Osmium fission sounds highly impractical.
Also, your spheres need much more osmium than available in the solar system.

And I don't see the point. Gravity is so much easier with rotating rings. No need to carry around massive impractical spheres.
Splitting a sphere of significant size into two parts needs a huge amount of energy, separating the two spheres needs a lot of energy as well. And until you do both together with the initial separation step, you get into trouble with angular momentum conservation.

I don't know what happens inside a sphere of osmium of that size

Nothing special. The density in the center goes up a bit, but probably not much.

 

[BastianQuinn]

Osmium fission sounds highly impractical.
Also, your spheres need much more osmium than available in the solar system.

Impractical I can live with. I can finger-wave furiously enough to make impractical okay.
The ship does not gather osmium. Remote sub-ships fuse other materials into osmium. Practical or not, all this would take is time, assuming the two technologies exist.
I'm not designing something for people to actually leave the solar system in. Even in the narrative, what leaves the Earth's orbit is something spool-shaped and significantly smaller. This is that ship after 4000 years with the assumption that anything we can do now, they can do much more efficiently, and anything we cannot do now is not possible. There are narrative reasons why there has been more optimization than innovation.

And I don't see the point. Gravity is so much easier with rotating rings. No need to carry around massive impractical spheres.

The sphere(s) are only "for" gravity if that's convenient or necessary given their presence. The sphere(s) will have gravity, and the ring will be as close to the sphere(s) as possible. A design that uses that gravity will spend less energy than one that fights it. The mass is necessary because they're traveling at sub-light speeds and astrogation is assumed unreliable. They're over-cautious and assume they may be lost in the void indefinitely.

Splitting a sphere of significant size into two parts needs a huge amount of energy, separating the two spheres needs a lot of energy as well. And until you do both together with the initial separation step, you get into trouble with angular momentum conservation.

If there are ever two spheres, it is not because they tore apart from each other. I'm having a hard enough time finger-waving at the idea of shipping osmium off such a globe in any ammount. If the globes must be formed separately and never orbit, a ring will just be dropped off in a star-system to trash-compact matter until it has a sphere, or the ring and sphere might be built at the same time. I haven't arrived on enough details to judge what that situation should be.

Nothing special. The density in the center goes up a bit, but probably not much.

Well that's quite a relief. =D

At the end of the day, the assumptions I'm moving forward from are that the population lives in the spokes of a ring-shaped station which uses Osmium, harvested through fusion, to fuel fission-based technology. There is some incredibly vague reference to quantum entanglement being used for long-distance communication. From there I'm trying to figure out how this osmium is stored in the greatest quantity possible.

The reductive design seems to be the ring(s) practically built onto a single sphere, or, in a space elevator-themed design, anchored to the sphere. Calculations from there would be things like how much space should there be between the sphere and the ring and how to manage attitude with minimal fuel usage. I'm not yet ready for this, but I haven't yet come up with an alternative design. Dual space-elevator spheres might be ridiculous enough to be cool. Probably too cool to work. Gotta find that sweet spot.

I do appreciate how easily some of these ideas are being handled. I wouldn't want to discourage incredulity, since that is what I'm trying to iron out of the design concept. ;)

 

[mfb]

I don't see the point of the spheres. Just spin the ring to create artificial gravity.
Taking trillion (or more) times the spacecraft mass as useless weight is beyond impractical.

At the end of the day, the assumptions I'm moving forward from are that the population lives in the spokes of a ring-shaped station which uses Osmium, harvested through fusion, to fuel fission-based technology.

That does not sound possible.

Also, where is the point having the ring over the sphere(s)? Why not just live on the surface of the sphere(s) (why 2?)? Or, better, dig a few meters into the sphere to get shielding from cosmic rays.

 

[BastianQuinn]

I don't see the point of the spheres. Just spin the ring to create artificial gravity.
Taking trillion (or more) times the spacecraft mass as useless weight is beyond impractical.
That does not sound possible.

Also, where is the point having the ring over the sphere(s)? Why not just live on the surface of the sphere(s) (why 2?)? Or, better, dig a few meters into the sphere to get shielding from cosmic rays.

All exactly the kinds of questions and criticisms I'm looking for.

Can you elaborate on what makes the fission and fusion processes suspect, or should I start a new thread in atomic physics.

 

[mfb]

The science fiction forum could be interesting as well.

Can you elaborate on what makes the fission and fusion processes suspect

I don't see how osmium would be of any use for nuclear reactions.

In Earth's crust, uranium is 300 times more frequent than osmium, by the way. Thorium is 1000 times more frequent. Both can be used for fission.

 

[BastianQuinn]

The science fiction forum could be interesting as well.

I don't see how osmium would be of any use for nuclear reactions.

I need someone vastly more knowledgeable to tell me how ludicrous something is, and I did not see that happening on the science fiction forum. This thread was also not moved, so I felt supported in that choice. If I was wrong, I can stop posting. I'm getting results here, and I'm learning quite a bit very quickly. I'm asking how much of what I'm saying is currently provably impossible, and I'm getting straight answers. I'm not a physicist. I'm sorry if that is annoying. The leading edge of science does not get clear representation, and I'd like to minimize my contribution to further misrepresentation.

Osmium is not going to react on its own, it's not unstable, I know that much. My understanding of what we do now is that we bombard an unstable atom with tiny bits of mass and energy and encourage it to fall apart on its own, like throwing a rock at an unstable hill and hoping it will crumble. Get enough unstable material and enough bits of mass and energy bouncing around and you have a bomb. as far as I know, our technology is not precise enough to do much else with this concept. Experiments being conducted at the LHC are the extreme edge of that discipline. We can now collide single particles and measure the results. Extending the metaphor, right now, the best and brightest know how to smack one solid rock with another solid rock and break it into pieces that might be useful. In time we might be able to do so reliably, and as experiments continue the tools will become more efficient and more precise. Are there hard limits that we know of now which would prevent this progression from reaching a point where a stable atom would be reliably split into specific, desired atoms?

I'm aware that the kicker is massive energy sources, and I'm aware that fission by itself is not a final solution. Harnessing the rest of the energy still in a particle of mass is a big question mark as far as I've read, but I don't need a solution, I'd just like to know if it's been shown to be impossible yet.

If I've reached the end of your patience for my questions or the way I present them, I'm sorry.

 

[mfb]

Osmium is not going to react on its own, it's not unstable, I know that much. My understanding of what we do now is that we bombard an unstable atom with tiny bits of mass and energy and encourage it to fall apart on its own

Only a few isotopes do that. Mainly uranium and plutonium isotopes. Osmium does not.

Get enough unstable material and enough bits of mass and energy bouncing around and you have a bomb. as far as I know, our technology is not precise enough to do much else with this concept.

Nuclear reactors?
Production of radioisotopes for medicine?

Are there hard limits that we know of now which would prevent this progression from reaching a point where a stable atom would be reliably split into specific, desired atoms?

Yes, quantum mechanics. You cannot predict or even control the result of a nuclear fission exactly. Even for those isotopes where fission (without a massive particle accelerator) is possible.

Harnessing the rest of the energy still in a particle of mass is a big question mark as far as I've read, but I don't need a solution, I'd just like to know if it's been shown to be impossible yet.

It is possible if you have a supply of antimatter. You cannot find it in nature (in relevant quantities), so you have to produce it first, which needs at least the energy you can extract afterwards. In practice it will need much more, but this energy can come from a star for example. Antimatter+matter would serve as very compact energy storage then.