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Note: I'm working on a far future sci-fi setting for a novel series which aims to blend elements of both "soft" and "hard" science fiction concepts. I'm aiming for the series to be as grounded and consistent as possible whilst still allowing some elements of speculative physics. Most places in the galaxy are well within a post-scarcity economy, and any group or in some cases individual can afford a fleet of automated construction and mining drones if they so choose. Stellar and planetary scale megastructures are commonplace, up to Dyson scale and in some cases even larger.

The seedy capital of a region of lawless space is a tower almost 5000km tall built on an Venus-mass planet in the outer regions of a star system (not a space elevator). The tower, which we can provisionally call the Spire, was originally intended to be constructed to geosync orbit, but events in the distant past led to the abandonment of the tower and its subsequent takeover by criminal/corporate groups. The tower has a base 100 kilometres wide and makes use of active support and materials such as carbon nanotubes in its construction, and has a population in the hundreds of millions if not low billions. Much of the internal volume of the tower is given over to vacuum train tubes intended to bring cargo up and down the Spire. The planet's crust is robust and geologically dead.

Having recently come across an interesting Isaac Arthur video on super tall space towers (up to geosync, using active support and carbon nanotubes), my question is that would such a tower like the Spire be feasible with access to these technologies?

Many thanks!

Note: In this context, active support or an active structure is referring to the use of a constant stream of matter (such as iron ball bearings) to impart momentum within a structure to provide support, as in the concept of a space fountain. The main advantage is that this allows for very large structures without relying on compressive strength, with the main disadvantage being that constant power is required to maintain the matter stream.

Note 2: The tower serves as a kind of "neutral zone" for these groups, which largely self-govern themselves such as historical pirate enclaves, havens etc. Any form of combat within the vicinity of the tower is strictly forbidden and harshly dealt with.

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    $\begingroup$ Oh, yeah. I remember hearing Isaac Arthur on that subject, I'd forgotten. Thanks for the clarification. Could you add that detail to the question for others., as you know, comments don't last. $\endgroup$
    – Escaped dental patient.
    Aug 7 at 0:37
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    $\begingroup$ Not a point about feasibility, so I won't put it in an answer, but the twinned phrases "criminal capital", "lawless space" and the concept of a megastructure that requires active support seems like a short-lived combination. $\endgroup$
    – jdunlop
    Aug 7 at 0:42
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    $\begingroup$ at 5000km its trying o be a space elevator whether you want it or not, 5000km puts it inside the van Allen belt and low earth orbit. It may not functionally work like one but it is experiencing all the worst forces of one. The ISS is not even a quarter of the way up this thing. $\endgroup$
    – John
    Aug 7 at 13:33
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    $\begingroup$ @Nemactual As an ex-publisher, your entire first paragraph can be shortened to "I have magic." Almost nothing about this question or the question's background has anything to do with hard science. From the perspective of the science-based tag, nothing about what you're asking is scientifically possible at this time or within a future encompassing potential advancements. So the question of feasibility is "no" due to the tag. Finally, for future reference, asking more than one question is literally a reason to close the question. $\endgroup$
    – JBH
    Aug 7 at 14:56
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    $\begingroup$ @Nemactual Cheers. Keep in mind that the science-based (and the hard-science) tags don't share your optimism. They're literally meant to reflect only what we know today - which includes limitations in material science. There is no such thing as a valid answer concerning (e.g.) a Dyson Sphere with the science-based tag other than, "sorry, can't be done." Scientific optimism is what the science-fiction tag is for. $\endgroup$
    – JBH
    Aug 7 at 17:24

4 Answers 4

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Not possible

For every action, there is an opposite and equal reaction.

The surface of your planet could not endure the reaction force of your active support system. All of the force you exert upwards to keep your tower from crumbling under its own weight will also exert a downwards force. When solid objects get into the scale of thousands of km, they stop acting like solids and act more like fluids. Your tower would quickly sink down through the crust, burying itself in the planet instead of sitting neatly on the surface.

If we assume your tower has a roughly conical shape (the best shape for making a tall tower like this), then it will have a volume of about 39,300,000 $km^3$. Office buildings made of traditional steel and concrete have a density of about 350 $kg/m^3$. Using carbon nanotechnology, you can probably get about 5-10 times as much compressive strength for your mass as a high-end concrete and steel constructed building. So, let's say your tower probably has a density of about 35 $kg/m^3$. This means that its total mass is about $1.3755 \times 10^{18} kg$. The base of your tower is about $7.8540 \times 10^9 m^2$, meaning that the base of your tower will exert a downward force on the planet of about $1.5534 \times 10^9 N/m^2$, based on Venus's gravity. Most natural stone has a crush force of about $1.8 \times 10^7$ to $6.7 \times 10^7 N/m^2$ depending on its composition. When you exceed this force, the ground will behave like a liquid, letting your tower freely sink into it. In other words, your tower is about 23.1 times as tall as the crust of a rocky planet could theoretically endure. Probably closer to 40-100 times too tall when you consider the weight of the things inside your tower. So, if you want to go for scientifically believable, about 50-200 km is about how tall you can make a tower with that base to height ratio. Even if you make room for massive improvements in building materials, the ground you build on is not getting any better than it is today.

This gives you a few options:

  1. Make your tower MUCH smaller. Works, but also boring.
  2. Give your tower a "root structure" that gives it contact with about $3.2 \times 10^{11} m^2$ to $7.8 \times 10^{11} m^2$ of ground for the active support system to push against. Kind of a neat solution, but frankly still does not address the issues brought up in lupe's answer
  3. Give your tower a MASSIVE subterranean empty space so that it actually floats in the solid rock of your planet following the principles of buoyancy... though this will violate some serious material integrity principles which will need to be solved separately.
  4. Hold up your tower using science that does not presently exist. This can be done by either making it out of some unobtanium allowing you to solve for the problems in #3, or use something like anti-gravity to negate the effects of your tower's weight on the planet. This is probably your best solution because it is the least contestable in the case of a bad calculation or overlooked limiting factors while still making your super tower a possibility. Also, you have described your tech level as being a highly advanced K2 civilization. They SHOULD have all sorts of technology that seems borderline magical to us. You can't conceivably advance that far and not invent stuff that flies in the face of our current understanding of science.
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  • $\begingroup$ @Nemactual When you push something with a magnet, the magnet receives an opposite and equal force even if it does not touch. $\endgroup$
    – Nosajimiki
    Aug 7 at 4:52
  • $\begingroup$ I also wonder if the object is large enough (massive enough) to affect the spin of the planet. The top of Mt. Everest is 6382 km from the center of the core. The top of this building would be 11,382 km from the center of the core and easily 500X (if not more) the mass of Mt. Everest. $\endgroup$
    – JBH
    Aug 7 at 15:02
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    $\begingroup$ @JBH a bit, but probably not noticably so. I's skinny enough, and much less dense than solid stone, that it should still only be a tiny fraction of the planet's total mass. $\endgroup$
    – Nosajimiki
    Aug 7 at 15:43
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    $\begingroup$ "Natural stone has a crush force of about, 1.8e6 to 6.7e6 N/m^2 depending on its composition". It's much stronger. Granite is about 140e6 in compression. Existing bulk-produced ceramics get to 3000e6 compressive strength. These numbers are starting to look feasible with pylons and perhaps secondary diagonal active members which can spread the weight further. $\endgroup$
    – Kevin Kostlan
    Aug 7 at 17:55
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    $\begingroup$ @KevinKostlan Opps, that was supposed to be e7 not e6. I've updated my calculations. Yes, specific natural rocks can get up to 14e7, but not across a 100km wide area. At this scale, even bedrock consisting of high amounts of granite will have enough limestone and other softer materials in between that will break apart allowing the ground to displace at much less than 14e7. Synthetic ceramics are a moot point unless the whole planet is a giant construct... which is doable for a K2 civ, but not specified by the OP. $\endgroup$
    – Nosajimiki
    Aug 7 at 18:59
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You're going to have a killer maintenance schedule

And, by that, I mean lack of maintenance is likely to kill everyone on the tower.

Assuming the base is made larger, as @Nosajimiki points out, the next issue is that active structures need everything to keep working. Imagine, if you will, the number of times power has gone out in your building. Now imagine if any time this outage lasted for more than a couple of hours, the building would fall down. Now fill the building with pirates.

If the power goes out longer than the backup power lasts? Everyone dies

If the backup power generators/batteries break? Everyone dies

If the HVAC system breaks? Everyone dies.

If the magnets at the top to redirect the ball bearings break? Everyone dies. Some by ball bearing grapeshot, others by crushing, some because a stream of ball bearings neatly sliced the bit of the tower they live in off

If the cooling system for the magnets breaks? Everyone dies. Some by ball bearing, crushing, etc, some by fire, superheated magnet coolant and minor explosion.

If the airlocks, walls etc break anywhere from kilometre 9 and up? Everyone dies.

The other charming feature of this kind of structure is that failures tend to compound. If a magnet at the top breaks, the ball bearings are likely to puncture a whole bunch of important electronics. Same with the magnets at the bottom. A loss of vacuum in the ball bearing tubes would lead to a mass of red hot ball bearings not quite making it to the top of the structure, before jamming somewhere and causing additional breaches.

You might have a fleet of automated constructor drones, but when some drunken moron in a tricorn hat uses them for target practice, who is going to fix the critical power conduit damage on sector 5 caused by the exploding space-meth lab? Where do they get electronics they can't make? Raw materials?

Keeping an active structure running is a tough task for a functioning government. Make it some sort of space tortuga, and everyone will be dead within two weeks.

Incidentally, this is the kind of thing stopping us from building an active structure/space elevator. We probably have the materials to do it, power could come comfortably from a few dedicated nuclear power stations, we make some great magnets. But if it cuts out, it kills everyone in a neat line from the tower base

Edit: I think I'd agree about the tech level meaning these challenges have been solved, but, most importantly, no one would be building active structures if you're at that tech level, because to get there you'd need materials that are strong enough to straight up build a tower, or some way of screwing with gravity. You're not going to mess around with a structure whose primary failure mode is to spray red hot ball bearings through the living quarters and then collapse.

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    $\begingroup$ @JBH, mostly true... but this does sort of expose a problem with the OPs basic premise. If you have such a civilization, then you should already WAY past asking questions about magnets and ball baring's. Hard Science becomes a bit of a silly goal for a civilization that is well into K2 technologies. $\endgroup$
    – Nosajimiki
    Aug 7 at 15:32
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    $\begingroup$ To which I think my answer should have been "Why would a K2 civilisation mess around with a means of building that is likely to kill everyone in it?" $\endgroup$
    – lupe
    Aug 7 at 15:41
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    $\begingroup$ I can't argue with @Nosajimiki - from a worldbuilding process, all these issues would already be resolved. If the OP's premise of stellar and planetary megastructures being commonplace is accepted as a condition, then by definition the answer is, "yup, it's feasible in your world because you've already defined it to be so." $\endgroup$
    – JBH
    Aug 7 at 17:32
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    $\begingroup$ @Nemactual no problem, it was fun to write - I kind of love active structures, because of how hilariously lethal they are from an engineering perspective. Also, for the purposes of the description, I'm assuming your tower is about as law abiding as, say, florida :P $\endgroup$
    – lupe
    Aug 7 at 18:26
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    $\begingroup$ Also also, humans die from the introduction of antagonistic elements to their active support system. A drunken pirate doing ad-hoc target practice next to the maintenance drone storage centre could be analogous to standing next to a radiation source for a few hours. A malicious maintenance engineer whose loved one was killed by the crime family ruling the tower and who wants to see it all burn could be analogous to Amanita phalloides. $\endgroup$
    – jdunlop
    Aug 8 at 17:51
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@Nosajimiki has a point; your tower is impossible as written.

To get around it, you need your active support to come from a far wider base than just the 100 km square area you are talking about; it needs to come from a far larger base, perhaps 500 km square; so the down thrust needed to create your active support presses against a much wider area.

Perhaps you can discover that your spire is just part of a much much larger underground pyramid, completely occupied by the machinery needed to provide the active support, in fact ultimately the tower does not rest on the crust at all, as it appears, but goes down another 1000 km to rest on the hot mantle of the planet. If you want, that heat can also be exploited to power some of the active support; the pyramid is a geothermal machine.

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  • $\begingroup$ TBF if your tower is 5000km high, a difference of 400km in the base size doesn't make that much difference. Assuming the tower is standing at the center, viewed from the top of the tower, the angular distance between the tower base and a corner of the square is about 0.8° and 4° respectively, It's an improvement but still quite small. $\endgroup$
    – Neinstein
    Aug 8 at 11:58
  • $\begingroup$ @Neinstein The point is to spread out the weight. Going from 100 km X 100 km to 500 x 500, we expand the area of the base by 25x. If need be, we can go to 1000 x 1000, and expand the base area by 100x. So the whole thing doesn't sink, tip and fall. $\endgroup$
    – Amadeus
    Aug 8 at 22:19
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A few ideas:

The planet is a huge diamond

Estimates for compressive strength of bulk diamond range from 3 GPa to 100 GPa. These are above the 1 GPa load at ground calculated by Nosajimiki.

Apparently planet sized diamonds are not entirely unrealistic.

Relativistic ion motors for active support

Send a constant stream of water to the tower at low velocity, wide pipe. Use electricity to accelerate water molecules to near light speed before ejecting them downwards. This way the base does not have to bear the weight of the tower.

The energy requirements are pretty huge. For relativistic ion motors, thrust force approaches F = P / c as the ion velocity nears the speed of light. If we take the 10^18 kg mass estimate, this would take 2700 yottawatts to support, whereas the Sun's total power output is just 400 YW. A planet with lower gravity would of course make it easier.

This does cause a lot of radiation to wherever the matter beams happen to hit. It will also slowly use up the world's oceans, though with efficient enough ion motors this could take millennia.

Fast spinning planet has low geosynchronous orbit

If the planet had rotational period of 3 hours or less, the 5000 km high tower would go past the geosynchronous altitude. The mass could then be hanging from cables, like a normal space elevator.

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    $\begingroup$ The problem is not a planet containing a lot of natural diamond, but a planet made of a single diamond. Carbon based planets would be made of a wide range of carbonates including calcite, aragonite, dolomite, etc with very little actual pure carbon the same way that our crust is mostly made of silicates with very little natural pure silicon. Such planets could have a lot more diamond than Earth by comparison, but it would still be a relatively rare gemstone. $\endgroup$
    – Nosajimiki
    Aug 7 at 19:15
  • $\begingroup$ @Nosajimiki Yeah, it may need some hand-wavium to explain the existence of the huge diamond. The linked article seems to have one possible mechanism (white dwarfs), but who knows whether it is accurate. However the existence of such a diamond is well within bounds of known physics, even if we don't currently know of a process that would create it. $\endgroup$
    – jpa
    Aug 8 at 6:34
  • $\begingroup$ @jpa I'd argue that it needs more handwavium than the mere existence of the tower would need. To form a diamond, you need huge pressure. To find a Venus-sized diamond, you have to look at the core of some dwarf star - but then where did the rest of the dwarf star go? $\endgroup$
    – Neinstein
    Aug 8 at 12:06
  • $\begingroup$ @Neinstein used by the K2 civilization $\endgroup$
    – Or4ng3h4t
    Nov 24 at 14:25

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