Terraforming: Enter the ‘Shell World’

by Paul Gilster on December 5, 2011

If we ever achieve manned missions to the stars, one of the assumptions is that we will find planets much like Earth that we might live on and colonize. But what if the assumption is flawed? There are surely many Earth analogues in the Milky Way, but we don’t know how widely they are spaced, and a near-miss isn’t necessarily helpful, as both Mars and Venus attest. People like Robert Zubrin continue to advocate terraforming as a solution for Mars, and it may well happen one day, but supposing we get to another star, would we have the moral right to terraform a world with living creatures on it, even if they didn’t meet our criteria for intelligence?

Robert Kennedy (The Ultimax Group), working with colleagues Kenneth Roy and David Fields, has been pondering these issues and went through a possible solution at the recent Tennessee Valley Interstellar Workshop in Oak Ridge. If we stop worrying about Earth analogues, a range of interesting possibilities open up, as our own Solar System illustrates. We have small planets like Mars, along with what may be a huge number of dwarf planets. We also have moons in a wide range of sizes around the gas giants. Suppose we could transform such worlds by building a spherical shell of matter around them, totally enclosing an atmosphere and living ecosystem?

Beyond the Habitable Zone

The idea seems outrageous, but Centauri Dreams readers are familiar with even more gigantic concepts like Dyson shells, engineering on levels that would require a Solar System-wide infrastructure and a Kardashev Type II-level civilization to build. If we extrapolate advancing technologies that can do gigantic things, we can consider creating an Earth-like environment (in most ways) under a shell that protects the inhabitants from radiation and provides a self-enclosed ecology. The question of a ‘habitable zone’ would disappear because artificial lighting and temperature control would be built in, and the wild card would be gravity, which would depend on which bodies were selected for enclosure. Most would offer gravity only a fraction that of Earth’s.

Kennedy and team wrote a paper for JBIS in 2009 that lays all this out. Working the math on spherical shells, they ponder the fact that if the objective is to contain a 14.7 psi Earth-normal atmosphere, such a shell would experience the same kind of pressure-induced tension found in a balloon. Assume one atmosphere of pressure at the underside of the shell and vacuum above it, and it is possible to choose a shell thickness so that the compressive stress of gravity cancels out the atmosphere-induced tensile stress in the shell. A shell made completely of steel, for example, built to enclose a world 20 kilometers above its surface, would need to be 1.31 meters thick if enclosing the Earth, and 8.05 meters thick if enclosing the Moon.

Moreover, the shell mass used is there simply to create compressive force — opposing the pressure of the atmosphere within the shell — and can be no more than dead weight. The authors figure that enclosing the Earth’s Moon could be done with no more than a 1-meter thick layer of steel if it incorporated 62 meters of regolith on top of it, with open-ended combinations of steel, ice, dirt and rock possible for the job:

It is not actually necessary to use a metal such as iron or steel. Stony materials such as concrete can handle a lot of compression. A strong fabric material that is airtight and in slight tension could be used to support the mass of the shell, which could be mainly rocks and dirt.

The authors contend that a shell with mass equally distributed across the surface of the shell will be stable with respect to the more massive body at the center of the shell:

If the central mass is displaced a given distance inside the shell, gravity will act to restore the shell’s original position with respect to that body. Such is not true for a ring. If there were no way to damp the movement, the shell would oscillate back and forth. A viscous atmosphere will tend to dampen oscillations until the mass center is once again congruent with the center of the shell.

The Riches of Ceres

Now consider the asteroid Ceres. Here the shell, depending on which mass estimate for Ceres we choose, would have to range (if made of steel) from 45.2 to 90.4 meters in thickness — this is the amount of mass that would be necessary to hold an Earth-normal atmosphere. This is one thick covering, providing enough shielding to survive a nearby supernova. Assume you have a terraformed Ceres that is half ocean and you wind up with enough dry land area to approximate the area of Indonesia, on a world where gravity is 1.5 percent that of Earth. Could a human colony survive in conditions of micro-gravity? At this point we simply don’t know the answer.

But think about the scenario for a moment. In an enclosed Ceres, climate is a design variable and lighting can be adjusted to approximate whatever day/night cycle the occupants desire. Imagine the underside of the shell as the urban area, a place where residents live in housing that overlooks the spectacular vista of the interior, which could be maintained as farmland or a nature preserve filled with whatever species the designers choose to introduce. With normal atmospheric pressures and light gravity, human-powered flight would always be an option. The outside of the shell would be devoted to heavy industry for manufacturing and power plants.

Taken to an extreme, we get this:

… the subterranean zones of small celestial bodies would offer vast – virtually unlimited – cubic for support functions and resource extraction. Consider that the interior of Ceres – half a billion cubic kilometers – could contain almost exactly the same working volume as a world-spanning city which packed the entire surface of Earth, oceans included, with billions of 1 km high skyscrapers, each the rival of Burj Dubai. In the light gravity of Ceres, every bit of that volume would be easily reachable and cheaply exploitable, unlike the deep wells and mines of Earth. A shell world might well be the richest planet in its solar system, once the huge cost of englobement was paid off.

Building for Safety (and Aesthetics)

Numerous dangers could beset a shell world, including many that already threaten our planet, such as the impact of large asteroids, but we could avoid some problems — volcanoes and earthquakes spring to mind — if we choose or build worlds without plate tectonics, and issues like solar flares would have little effect given the shielding the shell world’s inhabitants could rely on. A rupture in the shell would be a hazard, but a small shell world like Ceres would have a shallower gravity well than Earth and be less likely to draw in an asteroid. Moreover, any shell world would include the kind of planetary defense systems that a civilization capable of building the shell in the first place would be able to deploy. Shell maintenance, safety and improvement would doubtless be an ongoing project.

The paper works through one possible construction scenario involving the Moon and considers the massive amounts of energy required to move the needed terraforming materials (roughly one quadrillion tons), obviously requiring huge advances in energy production and space transportation. But it’s a fascinating vista, one that sees the creation of hanging cities on the underside of a shell that represents an area equal to four times the area of the United States. The surface of the re-made Moon can be tuned up to be as Earth-like as we choose to make it, the entire project taking hundreds and more likely thousands of years to see to completion.

The presence of hanging cities will diminish the required surface loading by inert material. Lighting would be artificial, with solar energy (assuming the shell world is near a star) powering up the lights, or power plants on the surface of the shell doing the job if the world were built in deep space. The paper argues that shell worlds all the way out to the Kuiper Belt could have an Earth-like insolation, ecology and diurnal cycle. And imagine this:

Existing electro-luminescent displays (ELD) only provide about 1-2 W/m2 of radiant energy in various colors from red to blue-green, but their state of the art (brightness, efficiency, cost) is rapidly advancing… Since ELD materials are presently available in all three primary colors and can be subdivided into addressable segments, we can imagine a pixelated ceiling of video wallpaper simulating the natural sky of Earth (clouds, sunsets, stars, etc.) or generating any arbitrary scene. The postindustrial motto “everything is media” means art can reach its fullest expression in the canvas of a shell world.

If we do become the Type II civilization capable of building such structures, we’ve not only opened up numerous worlds within our own system for colonization, but have also gained the experience needed for constructing stable generation ships for long-duration interstellar flight. And because shell worlds could be located anywhere a suitable moon or planet is found, we should consider the possibility that alien civilizations may already have constructed such worlds around red dwarf stars or even brown dwarfs, which may outnumber all other kinds of stars. The traditional concept of a habitable zone may not be the marker we’ve always assumed it to be, with prospects for SETI extending to worlds that would not before now have gained our attention.

The paper is Roy, Kennedy and Fields, “Shell Worlds: An Approach to Terraforming Moons, Small Planets and Plutoids,” JBIS Vol. 62 (2009), pp. 32-38. If you’re a science fiction writer in search of a setting, you must read this paper. I’ll also let everyone know when the Oak Ridge presentations become available online so you can see Robert Kennedy’s talk and slides.


Sputnik_wrangler December 8, 2011 at 20:16

Thanks to all for a stimulating discussion of our concept. Would that the traditional print media was this vigorous, substantive, and timely!

At this point in the discourse, it does not look like we will achieve consensus with every single one of the commenters. I’ll just sum up our view to say, that in this context, the consideration of the shell’s interior flat g-field with the englobed planet is unimportant. The important effect, upon the shell, is that due to the strongly curved gradient of the relatively massive central body.

It has always been our intention, with each new paper about our concept, for example at the Aosta symposium this summer, that we explore the concept at higher and higher levels of detail as well as considering a broader set of issues. Obviously an exhaustive treatment of the topic is as big as a world itself – nearly infinite grist for the researchers’ mills.

We will not withdraw our work from JBIS, for the simple reason that our paper was already peer-reviewed before publication by a committee, including astrophysicists, whom JBIS appointed. Furthermore, the JBIS paper was a zeroth-order introduction of the shell world concept; in which the stability consideration was noted, but not analyzed in detail. (For example, other important considerations such as illumination, radiation protection, economics, wealth, life, and longevity, were also noted, but not analyzed in detail. Future directions of research were suggested. A shell world is a great big blackboard of ideas.) Also, the shell world is not *premised* on this one gravitional interaction, nor does the shell world’s stability depend *solely* on a gravitational restoring force. There is an independent restoring force, due to differential atmospheric pressure as a function of height as already discussed, which appears at first-order to be sufficient by itself to passively maintain the shell’s symmetric position around the central body. Losing one avenue of control (which we do not stipulate in any case) in no way invalidates the independent method. Unlike some structure which require unobtainium, balonium, or wishalloy to be realized, the Shell World is not predicated on counterfactuals. We do stipulate that the peculiarities of particular enclosed worlds might require active control measures, such the dynamic masses used in modern skyscrapers to limit wind-induced sway. One can imagine for example a hex-close-packed network, buried deep within the insulating regolith, of water reservoirs connected by pipelines to shift mass around as required. Refinements such as this will be examined in future papers, so stay tuned to the literature.

Robert Kennedy aka “Sputnik_Wrangler”

PS. Some commenters mentioned ice as a construction material. So did we. Indeed, the outer edges of the regolith overburden could be suffused *after inflation* with water to form a water-ice-regolith matrix, for increased ballistic strength and radiation protection.

Eniac December 9, 2011 at 1:06

Rob Henry: I like your conciliatory attitude, but one of the authors (I think? Ken Roy?) actually states in this very discussion, quite clearly, that while the Shell Theorem excludes a force on anything inside the shell, “… it doesn’t state that the central body exerts no net force on the shell” !!? (my emphasis)

Good grief!

Duncan Ivry December 9, 2011 at 11:09

Robert Kennedy (a.k.a. Sputnik_Wrangler), thank you for responding.

“The important effect, upon the shell, is that due to the strongly curved gradient of the relatively massive central body.”

This effect does not exist. You are able to read the pertinent derivation of the shell theorem, I think. If you do not *understand* why the central body — being massive or not is totally irrelevant — does not exert a force an the shell, then you have a serious problem. Your strongly curved gradient thing is plain wrong.

“… our paper was already peer-reviewed before publication by a committee, including astrophysicists, whom JBIS appointed.”

On the one hand, if “the stability consideration was noted, but not analyzed in detail”, how would it help, that your paper is peer-reviewed? On the other hand, simply seeing this stability consideration being noted, should be enough for a competent reviewer to have serious questions immediately.

Now, that gravity is out, “[t]here is an independent restoring force, due to differential atmospheric pressure as a function of height as already discussed, which appears at first-order to be sufficient by itself to passively maintain the shell’s symmetric position around the central body.”

This sounds like some kind of ball bearing, but not with a fluid, but with a gas, as far as I can see. How much atmospheric pressure do you need? I hope you understand that, after all difficulties we had, I’m skeptical, when you say “appears to be sufficient”. Appears? And what does “at first-order” mean? (Technically this usually means involving a variable with the first power or a function with the first derivative. Or do you just mean “relating to the simplest level of analysis”?)

You should see, that regarding the “other important considerations such as illumination, radiation protection, economics, wealth, life, and longevity”, the situation is like this: stability is not everthing, but without stability there will be nothing (I hope you get it; English is not my first language, sorry).

Stephen Zavodny December 9, 2011 at 14:12

I am wondering about the thickness of the shield for Ceres. The artical quotes a steel shell “45.2 to 90.4 meters in thickness — this is the amount of mass that would be necessary to hold an Earth-normal atmosphere ” Keep in mind that at the equator at see level there is only 14 psia of pressure The actual shield could be made much thinner if you utilize that pressure to maintain the integratey of the shield. Make the shield out of a lighter material of a higher tensil strength … like carbon fiber or diamond or other such materials etc… Any civilization capable of building a shield around Ceres will have multiple (exotic to our standards) materials to chose from.

Rob Henry December 9, 2011 at 18:57

Eniac, I must now agree. I had not noticed that Ken Roy was a co-author.

Ken, you have probably made your calculations just as competently as any of us could, so I feel I must explain how we seem to know so instantly that their result is wrong.

“for every action there is an equal and opposite reaction”.

How can a single concept contain such strength, beauty and simplicity that it is one of the premises on which all modern physics is based, yet have such subtlety and seem so counterintuitive, that unless you are soaked in the culture of physics (as opposed to being a highly competent dabbler) you might miss some of its more obvious implications.

To those of us came to physics early we all remember the magic of first realising that when you drop a ball to the ground the entire Earth equally came up to meet it (from the vantage point of momentum). Somehow you must gain a view from that window or some discussions on this subject will remain esoteric to you.

Rob Henry December 10, 2011 at 20:09

After a good nights sleep, I have recovered from the shock of finding that one of the coauthors made such a gaffe, and now realise that if their introduction passed peer review, the atmospheric pressure variation with height must make a reasonable case for Shell World on its own. This brings up a new set of questions, and to formulate them properly I need to start with some back of the envelope calculations.

I must start by building my own model. Reasonable figures for the atmosphere are 100,000 Pa, of air at an average molecular weight of 30amu. Here sound would travel half way around the world in around 4000s. The scale height of such an atmosphere (using the Wikipedia figure for surface gravity) is 300km, so pressure variations with height would be close to linear. Now take the shell and dwarf planet and offset them along an axis. One pole of this offset would experience a restoring force of 0.325 Pa/m, and the other would experience the same force in the same direction. Overpressures in the offset poles would force the offset equator to move along with it iff this procedure did not force a collapse, so we have simple harmonic motion and a reasonable figure for the force along the axis of motion, when averaged out over each sq meter is 0.1 Pa. From the above article they estimate their steel shell is 60m thick, which is about 500,000 kg/m^2, which means the time for it to oscillate from one side to the other is about 7000s.

At first I thought that the good news was that that seems fast enough such that, if oscillations are efficiently dampened, this method seems potentially effective, but even there I could not escape from a horrible thought… Have you ever noticed how even a light wind across a surface can create significant lift. Any winds inside Shell World would start the local roof collapsing, and this as of itself would also create winds. To add to my nightmare I find that Ceres is actually one of the fastest spinning planets.

Just in case your model could be salvaged I went on to the next phase of testing. I went on to adjust the model for tidal force, which given the size of Ceres I felt might be significant. Now remember that we must compare it directly with the height pressure difference, so it would be wrong to work in standard units for tides. We know that the weight of shell balances a pressure of 100,000 Pa, so we want to know how much that weight would increase if we drop 1m, and that is why my result comes in Pa/m. Are you ready for it… it come out at 0.4 Pa/m, which is in excess of the o.325 Pa/m gained from pressure differences of the scale height, so the ceiling would collapse immediately. Your model may still work, but you have to start thinking of it in the order of 100 km of its surface (tides fall very rapidly with distance).

Good luck!

Rob Henry December 11, 2011 at 3:02

I must make some clarifications and correct one error above. My second paragraph was an analysis of shell world as a rigid system. My fourth takes it as a perfectly flexible shell. In the third it is somewhere in between.

A serious error in my last paragraph is the way I describe the equivalent weight gain that shadows the change in pressure. I imply that increasing the original height of the shell above ground level sharply reduces the problem, when the required thickening of such a new shell actually compensates so much that the problem only trails off just by the first power of the radius from the centre of mass.

Ron S December 11, 2011 at 12:03

Rob, one more thing to consider in your model. The atmosphere is a fluid. If the shell moves the atmosphere does not simply compress and rarefy, it moves. After all, the volume between Ceres and the shell is does not vary when either one moves.

You are also quite correct to note that the shell cannot be rigid. That and the fluidity of the air are the dynamics to which that the authors might want to apply an FEA.

Duncan Ivry December 11, 2011 at 15:37

Rob Henry: “… if their introduction passed peer review, the atmospheric pressure variation with height must make a reasonable case for Shell World on its own.”

We should realistically not only assume the above possibility — which may, of course, be the correct one –, but also that peer-reviewing may not be what it should be. I don’t want to put down just the reviewers of this work or the reviewers of the JBIS, but I have seen too many peer-reviewed *and* questionable things already.

We should make up our own mind, which is just what you did above. I’m impressed.

Supporting what you considered, I would add, that a rotating central body and a rotating shell (which would be the usual case, I think) would be accompanied by turbulence in the atmosphere in between. As far as I can tell, this is not a minor problem, but this would imply remarkable pressure fluctuations and not so small forces exerted on the surfaces (the problem gets more serious, if the rotations of the central body and the shell are not completely synchronized, which we should assume).

As a personal remark, all this reminds me of the saying, that imagination is cheap if you don’t have to bother with the details. But, as I would add, then it gets really interesting.

Rob Henry December 11, 2011 at 20:02

There is another way of regaining metastability of a shell around this brave new world, but I’m starting to realise that we have to take the Pol Pot approach to make it work.

For most human’s at sea level, breathing activity is dictated solely by the need to excrete CO2, so just triage off all Shell Worlds emphysemics and we can dial down the oxygen levels to 10,000 Pa without causing any problems. We could reduce the nitrogen levels even further, and in fact needlessly cycling it through the atmosphere rather than keeping it in a biologically useful form just wastes energy. Let’s put N2 at 5,000 Pa. Now we need to fill up the atmosphere with a heavy non-toxic gas of low narcotic effect. there is only one gas that is known to come close to meeting this requirement: sulphur hexafluoride. Even here the narcotic effect is noticeable at 50,000 Pa, so lets flush it in to 30,000Pa. Unfortunately there is nothing we can do about water vapour pressure. Since this world would have no cold trap to vigorously cycle it through and minimal diurnal temperature variations, it would be fixed at 3,500 Pa. This gives an average molecular weight of just over 100. The new scale height is 90km so the pressure gradient is now much higher than the tidal one and Shell World is alive again.

On the down side, we may have to find our architects among the sorts that can amuse themselves by contemplating study of the long-term health effects of this unnatural breathing gas, and there must be a few.

Anyway, with that problem solved we must move on to the next. The above just means that roof collapse is not forced, and this gives a certain metastability. A flexible roof (one not made of unobtainium) will still “want” to collapse everywhere and gravity will pull it down everywhere it can. Once one section droops a little, the slope will mean that the weight of the roof no longer exactly matches the atmospheric pressure and, it being much easier to push air out of the way sideways than vertically squeezing it, it will drop rapidly. Against this trend, ripples from other sections that experience an increased overburden will act to restore these sections. If Shell world works its roof would have to constantly vibrate.

Rob Henry December 11, 2011 at 21:53

Ron S, I did not include air compression in this model and my only (indirect) concession to its potential was to note that the oscillation time of a rigid sphere (using a model that did not include them) was not much more than the speed of sound. If absolutely no air moved from its hemisphere, then near the offset poles, a drop of 1m would result in 5 Pa/m of extra pressure. Similarly I pointedly did not include pressure reductions due to moving air. Even though these temporary pressures are an order of magnitude higher than the permanent one due to altitude pressure variations, they are much harder to calculate, and I am a person not a supercomputer!

I’m please you mentioned it though as it originally felt that that model had validity, but now I see that if I had included them then we would have a half period time of 2000s which is so much faster than sound that a “no net air motion per unit area” model is what I should have used in the ridged shell model. For examining the flexible shell problems I looked at latter though this compression would still play very little part.

Rob Henry December 11, 2011 at 22:28

Duncan Ivry, the rotation problem looks very very serious. To me the most likely solution is to have the shell rotate in lock step with the planet. Even if that worked for a while, I note that if the axis of rotation of each became slightly unaligned, the resulting torque from different average wind speeds at different latitudes will probably exasperate the unalignment. Perhaps there is some stable solution where each axis bobs or rotates around each other??

Eniac December 11, 2011 at 23:19

Rob, I think the deformation problem can be adequately addressed by keeping the roof somewhat lighter than the air pressure, and thus under tension like a balloon. Like a balloon, it should then be fairly stable against local fluctuations and collapse. Of course, too much tension and it will pop. I do not know how wide a range we have to work with, here, but my guess is that there is enough of a range between no tension and too much to achieve a stable configuration.

It is also an option to tie the roof down to the ground at suitable intervals, this will also provide an exquisite amount of control if motorized winches are used.

It is my understanding that a pure oxygen atmosphere at normal partial pressure is suitable for humans (Wasn’t this used in the Apollo program?). That would reduce the air pressure by a factor of five or so, with a similar decrease in mass of the shell.

Duncan Ivry December 12, 2011 at 14:16

In order to synchronize the rotation of the central body and that of the shell without stable connections we would need the shell to be in a — surprize — synchronized orbit (at a well defined distance) around the central body. But both the central body and the shell will show a slow gyration of their axes (precession), caused by the gravitational pull of other bodies. The two movements will probably be different from each other. So, if nobody has a rather new idea, synchronizing will be very difficult, if not impossible. I’m afraid, there is no stable solution.

Except … someone mentioned it already: we could make caverns inside the central body, with the ceilings being kind of a shell, not needing an extra shell above … but, wait, no, that’s too simple.

Rob Henry December 12, 2011 at 16:14

Yes Eniac I believe that you have solved the problem of sagging. To stay with the spirit of Shell World that tension generating excess pressure should be an absolute minimum. That would mean that the internal temperature would have to be tightly controlled, but then it would also need reasonably tight control in the “absolutely no tension” model.

If you combine that with my brave new world atmosphere the required worldwide overpressure would be low and could occasionally go to zero – if it did not do so for long enough to allow the slack to be bunched up sufficiently. That weird atmosphere I gave earlier turned out to be so good at mitigating the problem that it would have taken the shell to bend at least 30 degrees (and, of cause, have each half fold in its pleats be 40km across) before it could forge its way to the ground without being pushed straight back. There would be absolutely no such protection if pressure ever sank to zero with a normal atmosphere if Ceres were our central body and the shell was just 20km above ground.

The new worry is that a small and unexpected temperature pulse might burst the structure, since a major point in this exercise is that it carries much lower requirements for strength than many other constructed worlds

Rob Henry December 12, 2011 at 18:28

Eniac, you also bring up several atmospheric questions. Apollo used pure oxygen atmospheres at 1/3 standard atmospheric pressure. They could afford to do so because in microgravity flames can not form, so the ability of a diluting gas to reduce the temperature of flames is useless. Of cause longterm corrosion potential is just proportional to the oxygen partial pressure, and not all humans live at sea level, so that makes me wonder what the perfect breathing gas is for us in a world of constant 3500Pa water vapour pressure and 1/40 of Earth’s gravity. I suspect it would be around 25000 Pa oxygen and 40000 Pa nitrogen.

Your right that it makes absolutely no sense to give Shell World a full atmospheres pressure, and I would think a good compromise is 15000 Pa oxygen and 10,000 Pa nitrogen. You also may note that if oxygen becomes the limiting factor of breathing, and as we reduce the pressure then, despite the water vapour being saturated to the 300K, people will start to suffer large insensible losses of water, and will have to drink far more than we do.

Rob Henry December 12, 2011 at 19:02

In my 16:14 dec 12 comment, I spoke of potential disaster if the pressure ever sank to zero. I actually meant overpressure or tension.

Rob Henry December 12, 2011 at 20:22

Duncan, I’m not sure why you mention synchronous orbits, as the atmosphere contained inside does not make this situation comparable to the geosynchronous satellite one. I think that a much bigger problem comes from the need to exactly match the roof weight with atmospheric pressure, and in this case even a small nonalignment of planet and shell can be fatal if the spin is fast.

That brings me to a problem that I have dismissed as a side issue. Did the authors of this paper know how fast Ceres actually spins? Its 9 hour day makes the dwarf planet so oblate that if they had designed their shell using the polar diameter, they would find that at the equator their shell was not 20 km above the surface, but twelve and a half kilometres below it! The gravity here is 20% less at the poles! Very bad for our purposes.

Perhaps I’m looking at this too much as a problem and not enough as an opportunity. If we capture a new moon for this system in a retrograde motion (by attaching a small rocket then employing the complex interactions of multiple perturbations by other asteroids), then we could transfer angular momentum between it and the shell by (magnetic) connections. Such a system may generate more power than it uses if we are exceptionally cunning, and stabilise a non-rotating solution to Shell World.

Rob Henry December 13, 2011 at 14:42

There are a few factors that I should note.

One of the few good things about Ceres is that it so small that it is hard to find enough slack for the roof to fold enough to collapse with any atmosphere that averages over 40amu.

Slow spinning planets and moos of diameter > circa 1500km (the exact figure depends on their density) , and infused with normal atmospheres should work much better. Their poles can easily be given a higher temperature conductivity than their equators to reduce the problem of the external diurnal temperature variation. The shell would take exactly the same potential energy to place at 20km height because the needed weight is always the same for a given air pressure irrespective of gravity, but the required quantity of steel smelted for each unit surface area drops off, so the cost may not be greater.

Enclosing our Moon with an atmosphere that has a sea level composition at its top will give fully 2 Pa/m air density gradient, and it would suffer a weight gain of only 0.115 Pa/m. That would push back all but the highest angles of bent (steel) from hitting the ground. Mercury is even better, with its atmospheric gradient so strong that it equals pressure differences expected from compression in a model where the atmosphere is not allowed to shift from its local area. Thus this gradient is sufficient here that we would expect it to be able to overcome any instability caused by rapid air movements below the shell without even bothering to do the calculations to prove it!

David Fields December 15, 2011 at 12:52

Rob, Duncan, Stephen et al.,
I’m one of the authors of the JBIS paper. Thank you for your comments about Shell World stability, which are most helpful as we refine our presentation of the concept. My favorite ‘new’ perspective is Rob’s estimation of the effect of tidal forces on the shell. We recognized these as significant asymmetric restoring forces but assumed that the strength of the shell would be adequate to restore the shell position (with, of course, a smaller central body restorative displacement) rather than local shell implosion/collapse.
A major concern with this particular shell design is asteroid impact, which could include a shell penetration at one ‘pole’, an impulse transfer to the central body, and a possible antipodal shell implosion. Actually shell design is ‘everything’ and the aforementioned implosion possibility can be mitigated or even reversed by choosing a more distant shell, a less dense shell, or more dense atmosphere. Such an impact could destroy a shell world, but a natural world is no protection from an asteroid strike either — ask the dinosaurs.

Our original statement of shell stability under linear displacement appeared in Roy, K.I., R. Kennedy and D. E. Fields. 2009. “Shell Worlds: An Approach to Terraforming Moons, Small Planets and Plutoids”. Journal of the British Interplanetary Society 62 (1) Jan., 2009, as follows: “If the central mass is displaced a given distance inside the shell, gravity will act to restore the shell’s original position with respect to that body.”

The concentric configuration is established and maintained by a gravity-induced pressure gradient within the atmosphere between the central body and the shell. In addition to this restoring force, there are second-order effects from any imposed displacement that generate high and low pressure regions, winds, ripples, standing waves, etc.

Since the analytic (neutral stability) shell derivation works only for an evacuated shell, we also employed a finite element calculation which appeared useful for a displaced (or deformed) shell in the presence of an atmosphere. Rob pointed out that such calculations may be weak due to round-off errors but I rather think that the major weakness in our calculations thus far originates more from our choice of too coarse a mesh size.

Factors and mechanisms in the linear displacement stability calculation are well-characterized, compared to those for other scenarios. For example, challenges related to shell and central body spin must be met. One would expect to de-spin the central body (e.g., Ceres) at an early (pre-shell) stage. Past JBIS articles have considered such schemes. There are plausible situations that could induce spin in either the completed shell or the central body, so consideration must be made of under what conditions wind coupling will be sufficient to keep relative spin motion under control. Or… slow spin may provide advantages. Such are facets of the grand engineering challenge.

Best regards,
David Fields

Rob Henry December 15, 2011 at 22:21

David Fields, your comment brings up many more issues, some of which I will go into below.

Firstly if you start talking of despinning Ceres to meet your requirements you might as well talk of star lifting to adjust solar insolation levels. The likelihood is that a civilisation so powerful that it would contemplate the despin of a planet for trivial reasons would probably be able to justify the much higher capital costs that would give Sol-wide benefits. My drift is not fanciful, but to try to point out that that despinning puts Shell World so far into the future as to make your plans redundant. By comparison the large energy cost of lifting of a shell to the great height of 20km on Ceres will be one five hundredth the cost per atmosphere pressure sustained, and note we would have an obvious “place to stand” to accomplish the latter task.

Secondly, as far as I can see, the only advantage gleaned from Shell World vis a vie analogous concepts for human expansion, is the hope that the incredibly low shell tension needed leads to low long-term maintenance costs once it is in place. It makes no sense to rely on the resistance of the shell to bending to fix any stability problems.

A related problem is that, because we can not stop all flexing and wave formation, fatigue will cause (rare?) periodic ruptures in the (steel), so, to continue with our low maintenance strategy, we must have an additional layer of gooey material that either hardens on exposure to the air within, or upon rapid stretching of this layer produced by a breach of the hull. I imagine that this blister would then be fixed at leisure, but I also wonder if this material could also be used to stick the hull to the ground after a large meteorite impact long enough to prevent total collapse before repair can be effected. I think, though, that might be asking to much.
Actually, I would love to know more about the details of your asteroid impact model. I sincerely hope that you have not just factored in the momentum change imparted to Ceres. I reality, we would not be able to measure any change at the antipodes until sound had propagated through Ceres, thence the ground would rebound far faster than is possible by just momentum change, the more elastic the interior the greater this “excess speed” being. Far worse, I would place money on the three powerful waves propagated as sound through the atmosphere, and as P (also sound) and S waves through the shell would each be far more powerful that waves propagated through a highly inelastic body over 900km in diameter! You must also include their effects, (and possible some other more complex waves) to give reasonable approximations of the pattern of damage.

Finally, if you really do solve all other problems, you might be interested to note that the hydrology of this world concerns me just as much as any that I have raised so far. Notice that in an O’Neil habitat much incoming sunlight is in the photosynthetic wasteland, and when the mirrors are switched off to produce night, much heat is transferred out these windows. This produces powerful temperature differences that would give us much dew. In a really large O’Neil world it will also induce those vertical air movements that produce temperature differences with altitude in Earths troposphere. Thus, iff Shell Worlds roof height is at least the order of its atmospheric scale height, we would be able to think of inducing rain by nucleation. None of this is possible on your well insulated world of optimal lighting = complete vapour saturation everywhere .
That is not itself the problem though as we can genetically engineer plants that could make superb advantage of it. The real problem is that it is uniquely vulnerable to the introduction of even one fungi or bacterium that could make even better advantage of such situations. I believe that that would include most of them that we can culture on Earth. Once again I feel that the intrusive nature of the regime that could control this would be oppressive – can‘t you just see your poor populous sweat (literally)!

Duncan Ivry December 16, 2011 at 0:20

David Fields, thank you for your explanations.

An idea comes to my mind, when you mention de-spinning of the central body. May be, I’m completely wrong (it’s late at night here), but: de-spinning relative to the sun, or Jupiter, or what else? There is no absolute spinning or de-spinning, if I remember correctly. If the body in question is de-spinned releative to the sun, then it’s not de-spinned releative to Jupiter, and vice versa. So, with at least two massive bodies in the same system there will always be precession — except at some Lagrange points perhaps.

Rob Henry December 16, 2011 at 4:25

Tonight I break a rule of mine: never post a comment involving physics in which I have derived the equations myself when you are drunk, but David Fields enthusiasm is so contagious I want to help! Here goes.

The atmosphere of every body should have a nominal pressure at infinity, and in most bodies with atmospheres that pressure is probably so small as to be less important than even quantum fluctuations of the surrounding “vacuum”, but with Ceres it is significant. At infinity there should be no latitudinal pressure differences anywhere. I calculate this pressure to be P0 * e^(R0/H) where P0 is pressure on the ground R0 is the radius of the central body and H is the scale height. With Ceres this should be 22000 Pa if it has an Earth type atmosphere on its surface. At 1000km from its centre I guess that it should be about 35,000 Pa, so the potential energy cost will not be two dozen times the potential energy cost of a closer sphere as one might expect, but less (it wont be a third this cost just because it is a third the pressure either – calculations here are way more complex than that).

Anyhow, at great height the different speeds of air that comes from different parts of the ground below and mix to contribute to the overall pressure start to cancel each other a bit and equilibrate. Perhaps we can then dream that a very large shell diameters the problem disappears. Then again, perhaps I will wake up tomorrow and wonder how I could have been so stupid yesterday?

Rob Henry December 17, 2011 at 4:18

The answer to my last comment is almost certainly this. The greater object of the above exercise was to reduce the need for a discrepancy in the comparative thickness of equatorial versus polar shell ratios, and at high shell/planet radii ratios, even a small spin can send the thickness around the equator that is needed for equilibrium towards infinity. Not to worry, I can still salvage this from last night: Ceres is such a small world that the conventional formula for calculating atmospheric density with altitude fails at great heights and we should use,
P = P0 * e^-(R0 * h /( H * (R0+h))) where common symbols are as per previous post, h is height and P is pressure at that height.

Anyhow, getting back to the fundamental problem of allowing the roof weight to balance air pressure on Ceres without forcing collapse… So far I have tried increasing the radius, without much success, and introducing a super heavy gas irrespective of possible health implications, but we have yet a third option. We can drop the temperature.

At 275K in still air (wind velocities should be very low here since this world is so well insulated) well dressed humans should be a little uncomfortable outdoors, but perhaps fine in the centre of well insulated dense cities. This new temperature would mean that we would only need to ease the average molecular weight over 34 to retain roof buoyancy. This could be accomplished with elevated levels of the normal human breathing gasses carbon dioxide and argon (though at very high levels CO2 is toxic).

The real benefit of this new regime is that plants could now be grown under plastic to provide a green house effect at, say 300K. This would leach vast quantities of water vapor into that atmosphere, but now we have the potential to nucleate it back as rain, dew, or night frost on the roof of the shell. The hydrology of that looks so much better.

Rob Henry June 21, 2012 at 20:38

I have just had a major revision of the most major point I had against the practicality of shell world, and I thought it sufficiently notable to record this in these archives long after all correspondence has ended.

Building a space elevator around Ceres is at least 1000 times easier than for Earth, and so, much less theoretically challenging. This might make it the cheapest way to get material for building O’Neil colonies, until Ceres loses circa 90% of its angular KE, and circa 1% its mass.

Despinning may still be impractical, but I can no longer exclude the possibility of reducing its spin to the point where building such a shell is possible. We may still have a large equatorial bulge though.

Sean Deany December 20, 2012 at 1:09

Interesting site. I understand that Ceres has about 3% Earth gravity. Jumping 33 m would be achievable by any reasonable fit person. To overcome the long term effects of this low gravity environment the construction of a 225 m radius centrifuge vertically standing a bit like a Ferris wheel could assist the colonists. With the development of carbon nano tubes and super strong structures it may be possible to cover limited areas of the dwarf planet – which I have termed macro terra-formation.

I have recently created a blog site which illustrates scenarios for a Ceres colony.

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