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A planet recently discovered was explored and proved unworthy of terraforming: It is mostly made of carbonaceous minerals, classifying it as a carbon planet. However, one of the explorers does not see that as a hurdle. He seizes the opportunity to mine the abundant carbon and build space elevators using carbon nanotubes fibers. The space elevators will serve to hold-on a sheet made-out of carbon fibers as well. This sheet is the foundation for the "flat earth". The setup looks like this: enter image description here

The image is not to scale, and the number of "ropes" holding the basket to the surface of the planet is not final. The idea is that the basket spins along with the planet. The content comprising the atmosphere, water, soil and biomass is held-down to the surface using the centrifugal force. The flat Earth has rims which serve as the walls holding the volatiles on the surface. edit: This is a side-view. The basket is a disk with rims holding the atmosphere. The anchorage points to the basket may serve as anchorage as well as mountain tops, therefore simplifying engineering issues. Each anchorage point is connected to several distant points on the planet's surface. This setup should prevent the basket from "folding" and spilling volatiles into outer space.

At its final state, the planet will serve as a "moon" to the dwellers of the flat Earth. It will, however, remain at the Zenith and will only change phases along the day/night cycle.

So, is my setup stable enough? Will the surface remain flat, or will it bend and fold? Assume there are enough "ropes", and planetary "anchors" are sufficiently massive to avoid being lifted away.

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  • $\begingroup$ So, the terminus station of a space elevator setup is moving fast enough that centrifugal force overcomes gravitational attraction enough to hold an atmosphere... The answer to your question about bending and folding very much depends on the size of your station and what materials you have available to build it: after all it’s basically a giant bridge anchored to the void. $\endgroup$ – Joe Bloggs Mar 22 at 13:33
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    $\begingroup$ My instincts tell me that the centrifugal force will try to curve the flat base into an arc, so the outer edge area of the flat world may experience stronger "downward" acceleration than the center area. $\endgroup$ – BMF For Monica Mar 22 at 13:37
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    $\begingroup$ Do you have values for the size of that thing? I got the feeling that you won't get a sufficient spin speed, at least not before spinning the planet appart. (I assume you want to spin the planet up, because if you don't the centrifugal force has no chance to counteract gravity.) Give me the mass and radius of the planet, the desired distance between the disc and the planet, the discs mass and the desired "gravity" on the flat earth and I can crunch some numbers. $\endgroup$ – TheDyingOfLight Mar 22 at 14:05
  • $\begingroup$ If you are interested in other concepts for building flat earths check out this ( youtu.be/JGu-DYTYzzE ) video. $\endgroup$ – TheDyingOfLight Mar 22 at 14:09
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    $\begingroup$ The Center of the Flat world would also feel the planets gravity more then the edges which would make the center or Hub of the FE attempt to move faster that the outer edges or Rim otherwise it would buckle in the center and curve the flat surface. it might just be easier to find a supermassive turtle and 4 giant elephants... $\endgroup$ – Blade Wraith Mar 22 at 14:13
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This is a clever idea

There may be enough science to prove this wouldn't work, but I don't think that should matter. It's a clever idea, and clever ideas make for good stories.

One of the reasons why space elevators are thought to be stable is that the terminus of the elevator is far enough away from the Earth for the centrifugal force caused by the rotation of the Earth to overcome the Earth's force of gravity.

  • An argument could be made that this works for space elevators because we're basically dealing with a single connection point on Earth. The moment we introduce two or more we introduce instabilities due to a thousand variables including the natural stretch of the material due to stress, temperature, local gravity, etc. I counter with the use of substantially beyond industrial grade computer-controlled winches, designed to tighten or slacken individual cables to (a) keep the platform stable and (b) keep it at an average distance from the Earth. Besides, their existence introduces interesting sub-plots to the story. (Like an anti-flat-earth religious movement that sees the platform as an ecumenical threat and decides the winches are the weak spot!)

  • Centrifugal force would cause the center of the disk to bulge away from the planet. Gravity would cause it to bulge toward the planet. That would likely cause a lovely standing waveform oscillation that would make everyone seasick and eventually destroy the platform. However, I could imagine designing the platform perhaps like an optical lens, thicker in the middle, to minimize this behavior. (Or the inhabitants get used to being seasick because, like very tall buildings built to withstand the sway caused by wind, the platform is simply built to withstand the flex. Might be an interesting source of power, like ocean currents....)

  • Your biggest problem (and perhaps the biggest argument against this being scientifically practical), is that your cables keep the platform from winging off into space, but they don't keep it from tipping. Generally, you're relying on centrifugal force to stop that from happening, but what if a meteor (or a new teen driver) hits the platform, space-side, on the edge? How much force this would take would depend on how far away from the planet the platform is (increasing centrifugal force). Living on the underside of the platform (looking at the planet, which makes the day/night cycle really complex as you'd only actually see the sun during — from the planet's perspective — the twilight periods of morning and evening. You'd have reflected light during planetary day and no light during planetary night. That would be so weird....) However, no matter how far out the platform is, there will always be an impact force causing it to tip. You could use rockets to recover, or possibly those winches, but you would need something. (The problem with the winches is that the only way they could recover would be to pull the other side of the platform closer to the planet in an effort to right the tip... pulling the platform closer to the planet isn't necessarily the safest thing to do. If they succeeded in righting the platform before the critical "fall to the planet's surface is inevitable" point, then they'd need to gently reel out the cables.)

  • Finally, your cables would not be capable of stopping the platform from twisting. I think this is the least likely issue, but it's worth bringing up because once it started twisting (rotating around a center perpendicular to the planet below) the cables would act like springs and you'd have the devil of a time getting it to stop. Once again, rockets, but that seems inelegant. The winches might help. It's worth thinking about. A geologist or climatologist would need to confirm my next statement, but I think the Coriolis effect1 of the planet would naturally induce the twist, making it something you'd need to plan for (bear in mind I'm expecting you to cable the platform in 3D).

BTW, you'll want to use a circle, not a square. The corners of a square make the math needed to correct for the things I just discussed a blooming mess.


1John Dvorak points out that I'm misusing the Coriolis Effect in this instance. I haven't had a chance to go read up on it more, so bear in mind that this application is likely in error.

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  • $\begingroup$ Coriolis force only acts on objects that are in motion with respect to the rotating frame of reference. You'd only have centrifugal force to deal with, and you do want that one -- unless you mean secondary effects from the platform's sway and corrections, in which case it would make the math so much more interesting (unless, and you obviously would, throw the problem at a simple neural network and call it a day), but it shouldn't induce oscillations... $\endgroup$ – John Dvorak Mar 22 at 15:23
  • $\begingroup$ I may be misunderstanding here, but wouldn't the edges bulge rather than the center? My initial understanding was that, if you back the whole thing up, putting the center at the right orbital velocity for its altitude where it experiences no centrifugal forces, then, because the edges stick out into higher orbital altitudes where the corresponding orbital velocities are lower, and because the edges share the same greater OV of the center, they'll feel an outward tug as they try to achieve a higher orbital height to compensate the greater orbital energy. $\endgroup$ – BMF For Monica Mar 22 at 15:29
  • $\begingroup$ If the edges moved slower than orbital velocity at their height, then gravity would win and they'd feel a net planet-ward tug. If the edges moved faster than orbital velocity at their height, then gravity would lose to a net centrifugal force space-ward. Again, I believe I might be mistaken, but I'm not entirely sure how just yet. $\endgroup$ – BMF For Monica Mar 22 at 15:30
  • $\begingroup$ @JohnDvorak, by "in motion with respect" means unattached or not intrinsically influenced by, right? $\endgroup$ – JBH Mar 22 at 15:41
  • $\begingroup$ @JBH no. A something being non-moving in the rotating frame of reference of something else means that they rotate around the same axis at the same speed, such as a stable flat earth would. $\endgroup$ – John Dvorak Mar 22 at 15:44
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Proposals.

  1. Your basis is not a carbonaceous planet. It is a large alien spacecraft of some sort that was found adrift. It is badly damaged and has lots of weird stuff inside that no-longer works. Human engineers managed to hack two engines. With those engines they can spin the spacecraft, really fast and now that is all this spacecraft does. No-one wants to be on this spacecraft when it is spun up to the speed necessary to generate gravity-like centrifugal force on the flat world. A robot is in charge of the spinning engine.

  2. Your flat world is tethered to the spacecraft as you propose. It is much larger than the spacecraft. The combination is asymmetric and does not spin well. There is a solution.

  3. A second flat world is tethered opposite to the first. With two flat worlds and the alien spin engine between, it becomes symmetric, like a centrifuge, and a doable deal.

  4. The blue flat world and the green flat world have sports teams that play each other. People get very passionate.

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  • $\begingroup$ I think that is a 'dumbbell' of an ides :) :) :) $\endgroup$ – Justin Thyme Mar 24 at 16:27
  • $\begingroup$ Symmetry is irrelevant. Think "barycenter". $\endgroup$ – WhatRoughBeast Mar 25 at 13:12
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This is basically an engineering problem.

But a very extensive engineering problem. With a lot of equations and variables. An entire TEAM of engineers engineering problem.

To work, the station has to be geostationary. That pretty much determines how far above the planet it would have to be. The rotation speed of the planet determines the speed of the station, and thus the centrifugal/centripetal gravitational forces, and thus how effective they would be in creating some form of artificial gravity. For instance, geostationary satellites around the earth are not known for their artificial gravity, given the rotational speed of the earth.

The stiffness of the platform is completely engineering. I posit that it would be made with a concave (convex?) shape, so it would 'stress' back into a flat shape.

I am not sure if there is any need for cables to 'hold' the platform, if the planet was large enough edit and if the platform had its own propulsion system. Gravity is the 'cable' that holds satellites to the earth. To spin the platform fast enough to require cables, (i.e., that it needs to spin faster than the calculated speed to hold it in orbit to balance the centripetal/centrifugal forces and the gravitational force), the platform would have to be spinning at a substantial speed, much beyond the escape velocity. If it were edit active geosynchronous, the planet would have to be spinning at the same speed. A cable to hold it would then become a materials science problem. It could be that the required thickness of the cable becomes greater than the diameter of the platform, if the goal is to spin the platform with enough speed to create anywhere near earth-normal gravity.

TL:DR

But the really big problem would be, that the planet would be spinning at such a high rate that anything on the planet would be spun off the surface. After all, we have already established that the spin of the planet imparts a velocity that is greater than the escape velocity of the planet itself. That is the only reason the tethers to hold it would be required in the first place.

And the space elevators would have to provide the power to bring things DOWN to the planet, not to lift them off the planet.

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  • $\begingroup$ Gravity alone would act equally on the platform ("basket"), and all what's on it, including the atmosphere. This would not allow the volatiles to remain on the surface, and will not prevent the platform from bending and spilling its content into space. The idea is to allow the "basket" to orbit the planet at a speed higher than orbital velocity. This is impossible without the cables down to the planet. The cables hold the basket in orbit and allow centrifugal force to hold things down on the "basket" floor. $\endgroup$ – Christmas Snow Mar 23 at 14:47
  • $\begingroup$ Now I am completely confused. If the basket is orbiting faster than orbital velocity, then everything on the platform is trying to get AWAY from the planet, Centripetal/centrifugal force is OPPOSING the planet's gravity. Everything has enough speed, including everything on the planet, to be 'propelled' into space, and the cables and elevator are needed to bring them BACK to the planet. Like spinning a bucket of water around you with a rope. Put something on the rope by your hand that is holding it, , and it will move out along the rope to the bucket.AWAY from you. $\endgroup$ – Justin Thyme Mar 23 at 17:29
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    $\begingroup$ The people on the platform are NOT experiencing a net pull towards the planet from the planetary gravity, but a net 'push' away from the planet by their own velocity, which is greater than the planet's gravity. That's what escape velocity is. If they were traveling exactly AT escape velocity, then their 'push' outwards from centripetal/centrifugal force would exactly cancel gravity, and they would 'float', or be weightless. And they would not need a tether to hold them to the planet. $\endgroup$ – Justin Thyme Mar 23 at 17:34
  • $\begingroup$ @JustinThyme The planet's surface doesn't need to rotate at a rate faster than its own escape velocity for an object which is tethered to the surface at a certain distance to feel centrifugal force. That is what a counter-weight on a space elevator is for. On Earth, tether anything to a distance beyond geostationary at the equator, and it will feel such a force. Go far enough out and, given that your tether holds, you'll get to a point where centrifugal force approaches a gee force, and then two gees. No excessive rotation of the planet is really required. $\endgroup$ – BMF For Monica Mar 24 at 10:21
  • $\begingroup$ @BMF Please note the statement ' with enough speed to create anywhere near earth-normal gravity.'. $\endgroup$ – Justin Thyme Mar 24 at 14:01

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