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Thread: Ringworld

  1. #31
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    This ringworld instability.

    With a Dyson Shell, gravity inside is neutral. This is because for any element of solid arc, the gravitational attraction is exactly opposed by the opposing element of solid arc. The element of mass of the shell subtended by that solid arc scales with the square of distance, but gravity scales inversely with the square of distance, so the forces balance out.

    This means that a Dyson shell isn't stable, but it isn't exactly unstable. It's neutral. If perturbed, it will continue moving, but the movement won't be exacerbated like a ball rolling off the crest of a hill.

    But in the case of a ring, does this apply?

    The Ringworld is stable along the axis. If peturbed port or starboard (why the Ringworlders use those terms I don't know), it correct itself.

    If peturbed radially, it will not correct. It's not in orbit. But does the shell theorem apply? The Ringworld is a million miles wide. If peturbed radially, the solid arc will indeed initally have the same effect, but eventually, as the far side moves further away, the solid arc will hit the edge of the ring. From that point on, increasing distance does not lead to increased mass both radially and circumferentially, but only the latter, so the element of mass starts to scale only with the distance and not the square of distance. This means the gravity diminishes with distance on the far side, while remaining unchanging on the near side. And so the net force on the Ringworld becomed greater and the structure accelerates into the Sun.

  2. #32
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    The radial acceleration starts the moment the Ringworld moves even infinitesimally off-centre. You seem to be visualizing the shell theorem as if it involved solid angles of some given size, but what is actually going on is the integration of the balance of forces between infinitesimals.
    You can imagine this by thinking that, as soon as one side of the Ringworld moves infinitesimally closer to the sun than the other side, there will be infinitesimal masses along the rim of that section which "see" nothing but empty space in the corresponding solid angle on the far side of the sun.

    So it's dynamically unstable, like the colinear Lagrange points - you can bob things up and down at those points, at right angles to the plane of the orbit, but the slightest displacement within the orbital plane leads to runaway acceleration.

    Grant Hutchison

  3. #33
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    And the way to think about it is that when the ring moves closer on one side, the mass subtended by an element of solid arc decreases with decreasing distance squared, but out of plane arc that subtends mass at all increases with decreasing distance. So overall, that cancels one of the distance terms resulting in mass overall only decreasing linearly with decreasing distance. Hence, why with a ring, you view it as a two dimensional problem.

    Though this is only where the width of the ring subtends a small angle anyway so low angle approximation applies.

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    Integrating it, you can just draw the gravitational potential of a massive circular ring, and see what direction test masses will fall.
    Here's a section taken in the plane of the ring and passing through its centre. The ring radius is 1 unit.
    Click image for larger version. 

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    You can see there are two gravity wells at radii of +1 and -1 (actually, of course, we're seeing one slice through a ring-shaped gravity well), with a broad central summit between them. Any object set down in the plane of the ring, either inside it or outside it, will fall down a gravity well towards the ring. The only exception is the dynamically unstable point at the dead centre of the broad summit. Stuff can hang around there for a long time, but eventually it will migrate into steeper parts of the ring's potential well, and hit the ring.
    Now, in the case of a star, the less-massive ring will accelerate more towards the star than the star accelerates towards the ring, but the result is the same.

    Grant Hutchison

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    "Stable" has a well-defined meaning in control system theory, which is that it has a finite response to an impulse. See http://www.roymech.co.uk/Related/Control/Stability.html

    Neither a [unitary] Dyson sphere nor a ring world are stable by the normal control system definition.
    Last edited by swampyankee; 2017-Apr-26 at 10:47 PM.
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    Quote Originally Posted by Noisy Rhysling View Post
    "rashathraing"? Google fails me.
    It's actually spelled Rishathra.

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    First time I read it I was amused to think so many different species were so ... compatible.

    Has anybody else read a parody called "Molly Ringworld"?

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    Quote Originally Posted by Noisy Rhysling View Post
    First time I read it I was amused to think so many different species were so ... compatible.

    Has anybody else read a parody called "Molly Ringworld"?
    Tell us more....
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    Here's a potential map for a massive ring.
    Click image for larger version. 

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    The section is at right angles to the ring plane, the centre of the ring is at the coordinate origin at lower left, and the ring itself as at the lower edge of the graph in the centre of the evident gravity well. So the coordinates are, in terms of ring radius R, from 0 to 1.5R vertically and horizontally.

    You can see that no matter where you drop something, it will end up falling towards the ring. But at large distances out of the ring plane, it will accelerate towards the ring centre first, and only later experience acceleration towards the ring. It would be interesting to see if there are stable orbits threading the ring plane.

    Grant Hutchison
    Last edited by grant hutchison; 2017-Apr-27 at 04:42 PM.

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    Quote Originally Posted by swampyankee View Post
    Tell us more....
    It had a pink cover, that's all I remember about it.

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    Quote Originally Posted by Noisy Rhysling View Post
    It had a pink cover, that's all I remember about it.
    I understand she is pretty in pink.
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    Quote Originally Posted by Jim View Post
    I understand she is pretty in pink.
    Hence the name. I put it back on the rack

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    Quote Originally Posted by Noisy Rhysling View Post
    Hence the name. I put it back on the rack
    Sounds like one of those movies where the budget for the women's costumes is nil.


    Heading back to Ringworld, the required material properties are, if I remember, well beyond the strength of covalent bonds between molecules.
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    Quote Originally Posted by swampyankee View Post
    Heading back to Ringworld, the required material properties are, if I remember, well beyond the strength of covalent bonds between molecules.
    Yes, we had a discussion about this before. I figure the tensile strength of scrith needs to be about 6.5x107 GPa. Which is high, given that carbon nanotube comes in at 130 GPa.

    Grant Hutchison

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    Quote Originally Posted by publiusr View Post
    "I'm going to pee on ALL of that."

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    The arch is the world--and the world is the arch.

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    Quote Originally Posted by publiusr View Post
    Kind of spoiled by the dog. I hate it when dogs wander into a good shot.

    Grant Hutchison

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    Quote Originally Posted by grant hutchison View Post
    Kind of spoiled by the dog. I hate it when dogs wander into a good shot.

    Grant Hutchison
    Weird. That's not actually a renderig of Niven's Ringworld. No shadow square day/night bands, and just a leeeetle to close to a planet.

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    And no fisting.

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    Quote Originally Posted by DaveC426913 View Post
    Weird. That's not actually a renderig of Niven's Ringworld. No shadow square day/night bands, and just a leeeetle to close to a planet.
    Better? https://c1.staticflickr.com/1/53/127...b6a1510e_b.jpg

  22. #52
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    Quote Originally Posted by Noisy Rhysling View Post
    All these renderings struggle to convey the scale. The Ringworld is 1,000,000 miles wide for Pak's sake.

    Also that rendering seems to be the ring wall.

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    Quote Originally Posted by Glom View Post

    Also that rendering seems to be the ring wall.
    Eh?

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    Quote Originally Posted by Glom View Post
    All these renderings struggle to convey the scale. The Ringworld is 1,000,000 miles wide for Pak's sake.
    Yes, if it were the Ringworld, those mountains would be tens of thousands of miles across, and tens of thousands of miles high - the dog would be well outside the atmosphere.
    If that's a planet to the right, then I guess it's supposed to be an Iain M. Banks kind of ringworld - the size of a planet instead of a planetary orbit. But I have my doubts about its tidal stability in that case.

    Grant Hutchison

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    Quote Originally Posted by grant hutchison View Post
    Yes, if it were the Ringworld, those mountains would be tens of thousands of miles across, and tens of thousands of miles high - the dog would be well outside the atmosphere.
    If that's a planet to the right, then I guess it's supposed to be an Iain M. Banks kind of ringworld - the size of a planet instead of a planetary orbit. But I have my doubts about its tidal stability in that case.

    Grant Hutchison
    Why would it need to be thousands of miles high? To keep the atmosphere in you'd just need the rim walls high enough to contain a few hundred miles of atmosphere. The dog could be sitting on Fist of God?

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    Quote Originally Posted by Noisy Rhysling View Post
    Why would it need to be thousands of miles high? To keep the atmosphere in you'd just need the rim walls high enough to contain a few hundred miles of atmosphere. The dog could be sitting on Fist of God?
    Because the mountains occupy a significant fraction of the width of the ringworld (so tens of thousands of miles wide), and are drawn as mountains, which means their altitude is within an order of magnitude or so of their width. And the dog's looking down on them from an altitude considerably greater than their summits. The rim walls are 1000 miles high in the novel. Fist of God protrudes above the atmosphere, which is why it hasn't emptied the entirely atmosphere of the Ringworld into space.

    Grant Hutchison

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    Quote Originally Posted by grant hutchison View Post
    Because the mountains occupy a significant fraction of the width of the ringworld (so tens of thousands of miles wide), and are drawn as mountains, which means their altitude is within an order of magnitude or so of their width. And the dog's looking down on them from an altitude considerably greater than their summits. The rim walls are 1000 miles high in the novel. Fist of God protrudes above the atmosphere, which is why it hasn't emptied the entirely atmosphere of the Ringworld into space.

    Grant Hutchison
    Gotcha. I though you were talking about the "actual" Ringworld. Artists seldom bother with little things like reality.

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    Quote Originally Posted by Noisy Rhysling View Post
    Gotcha. I though you were talking about the "actual" Ringworld. Artists seldom bother with little things like reality.
    Yeah - I was agreeing with Glom that artists struggle to understand the scale of the "actual" Ringworld. If publiusr's image was of Niven's Ringworld, then the mountains in the foreground are bigger than the Earth, and the dog is dead.

    Grant Hutchison

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    Quote Originally Posted by grant hutchison View Post
    Yeah - I was agreeing with Glom that artists struggle to understand the scale of the "actual" Ringworld. If publiusr's image was of Niven's Ringworld, then the mountains in the foreground are bigger than the Earth, and the dog is dead.

    Grant Hutchison
    He both alive and dead until Louis takes him for walkies.

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    I used to go hillwalking with a guy who put is dog in every summit shot. New beautiful view, same scabby and overenthusiastic dog in the foreground.
    It got so's the dog just went and sat in front of anyone who got a camera out.
    "Uh, Jed, could you control your dog for a moment?"
    "He's just being helpful!"
    "He's being a nuisance, Jed."
    "Let him be in your photograph! Where's the harm!"
    "He's sitting on a bird nest I'm trying to photograph really quickly."
    "Oh. OK."


    I'm just glad he wasn't around when I had a chance at this once-in-a-lifetime (for me, at least) shot:
    Click image for larger version. 

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    Grant Hutchison
    Last edited by grant hutchison; 2017-Apr-30 at 07:45 PM.

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