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I was reading about orbital rings, and more specifically I was thinking about how one could be constructed. It obviously would need angular momentum, because each piece of the ring (if separated from the ring) would not be stationary with respect to the Earth's inertial frame. This sort of got me thinking about a smaller scale experiment and had me realizing I have no idea what physics would do in this specific situation.

Here's the example:

A man on the ISS has a fishing pole with a reel of infinite unbreakable fishing line. The reel is also quite extraordinary and can release slack at any rate the man decides.

  • Would the orbital motion of the ISS allow the line to trail behind it?
    • At what rate would he need to be letting out slack?
    • If it was letting out this line this quickly, would it maintain a circular shape?
  • If enough line was let out to equal the circumference of the ISS's orbit, could the ISS meet back up with the fishing line?
    • If we could meet back up with the beginning of the line and connect it into a ring, would it maintain angular momentum?
    • Would it be less stable or more stable than an ordinary satellite?
  • If any of these assumptions are wrong, what would happen?

I'm mostly concerned with the reasons why it wouldn't work. 'Meeting back up with the original location' is the least of which I am concerned about. I'm more concerned about the stability of the ring, provided it did meet back up (or if my thinking on the fact that 'letting out slack' wouldn't function as I've assumed), which led me to articles like non-linear dynamics of ring-world systems.

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  • $\begingroup$ The ISS drifts 4 degrees a day, so I'm pretty sure it wouldn't meet back up with the beginning of the line--not 100% sure though. $\endgroup$
    – called2voyage ♦
    May 7 '19 at 15:16
  • $\begingroup$ @called2voyage Other items in the same orbit (like the line) would drift the same amount. That's not the reason this won't work. $\endgroup$
    – BowlOfRed
    May 7 '19 at 15:58
  • $\begingroup$ @BowlOfRed There are multiple reasons this won't work, but are you sure other items would drift the same amount? I would think the amount of drift depends on a lot of factors. $\endgroup$
    – called2voyage ♦
    May 7 '19 at 15:59
  • $\begingroup$ @BowlOfRed In order to get the line to trail the station, it would have to decelerate relative to the station. This would alter the angular frequency of the line, thus altering the amount of drift. I'm not sure if it would be a meaningful difference though. en.wikipedia.org/wiki/Nodal_precession $\endgroup$
    – called2voyage ♦
    May 7 '19 at 16:04
  • $\begingroup$ I'm mostly concerned with the reasons why it wouldn't work. 'Meeting back up with the original location' is the least of which I am concerned about. I'm more concerned about the stability of the ring (or if my thinking on the fact that 'letting out slack' wouldn't function as I've assumed), which led me to articles like non-linear dynamics of ring-world systems. $\endgroup$
    – Magic Octopus Urn
    May 7 '19 at 16:33
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Would the orbital motion of the ISS allow the line to trail behind it?

Ignoring the "line" part and just thinking about the end of it, you have an object that is drifting backward with respect to the station. This means it's orbiting more slowly and must therefore be in a higher orbit. So you have to get the end of the line into this (slightly) different orbit to begin the process.

You'd then have the problem that the line must be pulling on the object at least some of the time. This is going to increase the angular momentum of the object, which will cause it to drift into a still-higher orbit. When the ISS catches up to it, the orbit will be quite different. So it seems to me to be unstable with no mechanism to bring it back to stability.

My assumption is that if you had a completed ring, it would be unstable similar to the way a ringworld is. But this would be even more complex to analyze since it can shrink and deform. I'm not going to be able to work out what happens after it is perturbed.

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  • $\begingroup$ That's a good way to put it. I'm guessing the only way you could deploy an orbital ring like this is having each part that you "snake out" have some sort of phasing motion, to slow then re-enter the orbit x meters behind the ship that's deploying it. Thinking about an orbital ring as very many small points in the same orbit makes the thought process easier, thanks. $\endgroup$
    – Magic Octopus Urn
    May 7 '19 at 18:48

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