Results 1 to 18 of 18

Thread: Relativistic ringworlds

  1. #1
    Join Date
    Jul 2005
    Posts
    18,309

    Relativistic ringworlds

    I've just finished Stephen Baxter's Xeelee: Redemption, which features more of Baxter's vast mega-structures and time-periods. In this one, he uses a ringworld a light-year in radius, spinning at just a whisker short of light-speed, so that its inhabitants experience 1g of centripetal acceleration, while undergoing massive time dilation (a gamma factor of 5 million). It's a simple application of the a=v/r equation for centripetal acceleration, and it comes out the neat way it does because of the odd coincidence that lightspeed divided by the length of a year is very close to being one gravity of acceleration.
    Trouble is, Baxter neglected the effect of relativity on acceleration. We're familiar with the fact that, as you accelerate towards lightspeed, 1g of acceleration in your moving frame translates into considerably less in the rest frame - there's a factor of gamma-cubed involved for linear motion. A similar thing happens for transverse acceleration, of the kind required to steer your starship in a circle - a marginally more benign gamma-squared conversion.

    So Baxter's ring has a centripetal acceleration of 1g in the rest frame, but its inhabitants would be pulling 25 trillion g in the frame corotating with the ringworld. Oops. We're going to need a bigger ring.

    We need a radius of gyration that produces just one 25-trillionth of a g at lightspeed, in the rest frame. That turns out to be 2.4e13 light-years - inconveniently large, even by Baxter's standards.

    Shame. It was such a nice idea.

    Grant Hutchison

  2. #2
    Join Date
    Oct 2009
    Location
    a long way away
    Posts
    10,815
    Quote Originally Posted by grant hutchison View Post
    We need a radius of gyration that produces just one 25-trillionth of a g at lightspeed, in the rest frame. That turns out to be 2.4e13 light-years - inconveniently large, even by Baxter's standards.
    Or rotate slower? Presumably, not much slower because of the non-linearity of relativistic effects (I suppose even I could do the math, but I don't think I can be bothered...)

  3. #3
    Join Date
    Jul 2005
    Posts
    18,309
    Quote Originally Posted by Strange View Post
    Or rotate slower? Presumably, not much slower because of the non-linearity of relativistic effects (I suppose even I could do the math, but I don't think I can be bothered...)
    Good job I'm here then.
    A 1g ringworld with a radius of a lightyear has a floor speed of about 0.7c, with a gamma of only 1.4. Ten lightyears gets you 0.96c, gamma 3.6. One hundred lightyears gets you 0.995c, gamma 10. It's ... unwieldy. And your building material costs don't just scale with the radius, but with gamma as well, because of relativistic length contraction around the circumference. So the 100ly ring has a (corotating) circumference of more than 6000 lightyears.

    Grant Hutchison

  4. #4
    Join Date
    Jun 2003
    Posts
    8,659
    Worlds orbiting supermassive black holes seem to be a popular choice at the moment. Gargantua and its planetary system in Interstellar is one example; Sean Raymond has described another version, with a million planets in concentric rings, distorted by time dilation and compression.

    Shame that Baxter messed this one up. Does he know yet?

  5. #5
    Join Date
    Jul 2005
    Posts
    18,309
    Quote Originally Posted by eburacum45 View Post
    Shame that Baxter messed this one up. Does he know yet?
    I don't know. But I haven't really looked. (His website has never been particularly chatty, so I doubt if he would post anything about it there.)

    Grant Hutchison

  6. #6
    Join Date
    Dec 2018
    Posts
    105
    Quote Originally Posted by grant hutchison View Post
    but its inhabitants would be pulling 25 trillion g in the frame corotating with the ringworld.
    I don't really know how much acceleration people can tolerate, but I suspect that might be a little bit too much.

  7. #7
    Join Date
    Oct 2009
    Location
    a long way away
    Posts
    10,815
    Quote Originally Posted by grant hutchison View Post
    Good job I'm here then.
    Exactly what I was thinking !

    A 1g ringworld with a radius of a lightyear has a floor speed of about 0.7c, with a gamma of only 1.4.
    Was there a reason he couldn't have done that? For example, did the story rely on the gamma of 5 million?

  8. #8
    Join Date
    Jul 2005
    Posts
    18,309
    Quote Originally Posted by Strange View Post
    Was there a reason he couldn't have done that? For example, did the story rely on the gamma of 5 million?
    Very much so - time travel to the far future was a key plot element.

    Grant Hutchison

  9. #9
    Join Date
    Jul 2018
    Posts
    145
    Quote Originally Posted by grant hutchison View Post
    And your building material costs don't just scale with the radius, but with gamma as well, because of relativistic length contraction around the circumference. So the 100ly ring has a (corotating) circumference of more than 6000 lightyears.

    Wow. Kind of makes you wonder what would happen to such a structure if you then slowed it back down! What would happen to it as it tried to fit 6,000 light years worth of material into a ring thats (now) only 600 light years around?

  10. #10
    Join Date
    Oct 2005
    Posts
    26,925
    Quote Originally Posted by grant hutchison;2494964It's a simple application of the a=v[FONT=&
    /r equation for centripetal acceleration, and it comes out the neat way it does because of the odd coincidence that lightspeed divided by the length of a year is very close to being one gravity of acceleration. Trouble is, Baxter neglected the effect of relativity on acceleration.
    That also puts the kibosh on the idea that we could travel to the stars in a reasonable time if we had unlimited propulsion power and could sustain acceleration of 1 g for a year or so. But in order to get the relativistic length-contraction advantage that brings the time down from centuries, we would run afoul of the effect you describe. So if the human body is only comfortable at 1 g, we gain no advantage from the relativistic regime, so we're talking centuries to get anywhere even in principle (never mind all the other issues)!

  11. #11
    Join Date
    Jul 2005
    Posts
    18,309
    Quote Originally Posted by Dave241 View Post
    Wow. Kind of makes you wonder what would happen to such a structure if you then slowed it back down! What would happen to it as it tried to fit 6,000 light years worth of material into a ring thats (now) only 600 light years around?
    Nothing good.
    The reverse problem - spinning something up from a standing start to a relativistic rim speed - is the basis for something called the Ehrenfest "paradox" in relativity. (It's only a paradox if you assume a completely rigid object, which turns out to be incompatible with relativity.) Anyway, there's nothing to stop you having a rigid object that's already rotating at relativistic speeds - Baxter actually points out that his ringworld would have to be built already rotating, for this reason.

    Grant Hutchison

  12. #12
    Join Date
    Oct 2005
    Posts
    26,925
    Quote Originally Posted by grant hutchison View Post
    Nothing good.
    A reference to the all-time best AI line from a movie? The AI in Interstellar was the only part I really liked.

  13. #13
    Join Date
    Jul 2005
    Posts
    18,309
    Quote Originally Posted by Ken G View Post
    A reference to the all-time best AI line from a movie? The AI in Interstellar was the only part I really liked.
    I don't actually recall the line. I found TARS a somewhat slappable character, I'm afraid.

    I don't know the origin of my own use of the phrase (I've just spent a few minutes trying to think where I might have acquired it) but I'm told I used it a lot at work (where a sort of weary pessimism was pretty much part of the person specification), so I guess it's not surprising it surfaces here, too.

    Grant Hutchison

  14. #14
    Join Date
    Oct 2005
    Posts
    26,925
    The scene I liked was when TARS was asked what would happen if an attempt was made to dock with the malfunctioning space station, and TARS simply said, "nothing good." To me that was such a breath of fresh air over the obligatory "there would be a 99.4% chance of explosive decompression" or some typically Spock-like response.

    I overstated the severity of the gamma^3 correction on interstellar travel, it hurts but with a proper acceleration of about a comfortable g for more than a few years t of proper time, the distance in light years covered in the rest frame is et/2 . So the exponential can certainly get you pretty far in a decade.

  15. #15
    Join Date
    Jul 2005
    Posts
    18,309
    Quote Originally Posted by Ken G View Post
    I overstated the severity of the gamma^3 correction on interstellar travel, it hurts but with a proper acceleration of about a comfortable g for more than a few years t of proper time, the distance in light years covered in the rest frame is et/2 . So the exponential can certainly get you pretty far in a decade.
    Yes, rest-frame distance is a hyperbolic cosine function of on-board elapsed time, so it starts to look like a simple exponential fairly quickly.

    Here's how it goes, at 1g with a mid-course turn-over so as to come to a halt at the destination.
    relativistic journey.jpg
    Fifty years gets you to the edge of the observable Universe.

    Grant Hutchison

  16. #16
    Join Date
    Feb 2005
    Posts
    11,637
    Let's say one of these got built--and big enough so it is, what ((.99.

    What happens to be if I try to run that one mile an hour to break lightspeed--what would I feel at one g?

    Would it be like in anightmare--seeing the heat-death of the universe as I am slowly trying to run away from a plodding monster behind me and I feel as if in molasses?

    There's your cosmic horror right there.

  17. #17
    Join Date
    Jul 2005
    Posts
    18,309
    Quote Originally Posted by publiusr View Post
    Let's say one of these got built--and big enough so it is, what ((.99.

    What happens to be if I try to run that one mile an hour to break lightspeed--what would I feel at one g?

    Would it be like in anightmare--seeing the heat-death of the universe as I am slowly trying to run away from a plodding monster behind me and I feel as if in molasses?

    There's your cosmic horror right there.
    No, nothing like that. You'd run that extra mile an hour (assuming you can run that slowly), and nothing much would change.

    Grant Hutchison

  18. #18
    Join Date
    Apr 2007
    Location
    Nowhere (middle)
    Posts
    37,175
    Quote Originally Posted by publiusr View Post
    Let's say one of these got built--and big enough so it is, what ((.99.

    What happens to be if I try to run that one mile an hour to break lightspeed--what would I feel at one g?

    Would it be like in anightmare--seeing the heat-death of the universe as I am slowly trying to run away from a plodding monster behind me and I feel as if in molasses?

    There's your cosmic horror right there.
    You'd feel like you were running in 1G. Subjectivity!
    "I'm planning to live forever. So far, that's working perfectly." Steven Wright

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •