How fast would you have to spin Ceres to rip itself apart?

[Yora]

I am currently watching The Expanse, and it appears that they are simulating gravity on Ceres by building tunnels inside the rock and then spinning up the whole asteroid/dwarf-planet/planet so fast that people are pressed to the ceilings, which then become the floors.

Now this principle works perfectly well in a metal cylinder (NASA demonstrated it back in the 60s or 70s) and the gravity of Ceres is not even 2.7% the gravity of Earth, which is basically negligible if you wanted to make people stand on the ceilings and walk around like they do on Earth.

I looked up the dimensions of Ceres and a calculator for simulated rotational gravity, and to get 103% Earth gravity in a ring with 470 km radius, you would have to make 0.044 rotations per minute, or one rotation every 22 minutes. Assuming it would even be possible to spin Ceres up to this speed, would it still stay in one piece? Or would the centrifugal pull just cause the whole thing to rip itself apart.
Since Cered does not have much gravity, all the material was never pressed together very hard to make itself fuse into a single solid mass. I think the number we'd be looking at is the tensile strength of Ceres. Would it be enough to keep together at 1g?

[factotum]

The problem is, you can't really compare the Ceres from the Expanse with the real-world Ceres--as someone mentioned in your Expanse review thread, the books were written before we got all the recent information about Ceres from the Dawn probe, so the Expanse version is a lot more rock and a lot less water ice than the real thing.

Having said that, we know that ice is just about capable of supporting its own weight under 1g conditions because icicles exist. How that works when you scale it up to a 470km ball is beyond my ken, though.

[hamishspence]

I looked up the dimensions of Ceres and a calculator for simulated rotational gravity, and to get 103% Earth gravity in a ring with 470 km radius, you would have to make 0.044 rotations per minute, or one rotation every 22 minutes. Assuming it would even be possible to spin Ceres up to this speed, would it still stay in one piece? Or would the centrifugal pull just cause the whole thing to rip itself apart.
Since Cered does not have much gravity, all the material was never pressed together very hard to make itself fuse into a single solid mass. I think the number we'd be looking at is the tensile strength of Ceres. Would it be enough to keep together at 1g?

In the Long Earth series by Terry Pratchett, a point was made that if you spun the earth so fast that it rotated once per hour, it would rip apart:


https://thelongearth.fandom.com/wiki...ary_Spin_Motor

http://spacearchaeology.org/?p=105


Given that the Earth is vastly bigger and denser than Ceres, and so has much more gravity holding it together, it's possible that Ceres does not need to spin nearly that fast, to rip apart.

[Lvl 2 Expert]

The problem with spinning up any object for simulated gravity is that to get to simulated gravity, you must first undo all real gravity. If you wanted to spin up Earth so that everybody is pulled outwards by one G you have to basically spin it up until you have 2 G's of outward force, to compensate for the 1 G of inward force. Now that outward force will be working on every object on Earth at the same time, including the Earth itself. Under normal circumstances Earth is held together by gravity, under these new circumstances it is pulled apart as hard as it used to be pushed together. Some planets might survive a while on structural integrity, but it's not really a stable arrangement. Ceres might hold out a bit longer than Earth would. it has never been pressed together quite as well, but it also doesn't have the same giant molten mantle (there might still be subsurface oceans, but probably not to the same degree as there is molten rock in the Earth). Now if you're willing to reinforce the planet, clamp a big metal shell around it or something, it will hold together just fine. But that's a lot of material you could have just used for space habitats.

It also becomes kind of awkward to dock space ships, as they have to basically hook on to a spinning ceiling to dock. On the plus side, they get to keep some of their speed that they'll be able to put to good use when leaving. on the downside, spinning up a dwarf planet would cost so much energy that nobody is really going to care about the little bits of it docking ships now save. On the even downer side, near future realistic spacecraft navigate in orbits. A ship wanting to dock with Ceres will come up on the inside orbit, with a slightly higher angular velocity but a slightly lower absolute velocity. It doesn't have any excess speed compared to Ceres. So now they have to do some sort of crazy unrealistic maneuver to speed up or else they can't dock. And the extra speed will only be useful when leaving towards some destinations. Until space ships have enough power to sort of freely boost through the solar system it kind of doesn't work at all. Luckily for us we won't have a rocket capable of spinning Ceres up during that period either, the energy requirement is quite silly on a scale of things humans have experience with. As scary as say something like a nuclear bomb is, it doesn't actually release all that much energy compared to say a hurricane. It's just a lot better at depositing all its energy in the same time and place. A hurricane isn't enough to noticeably change a planet's orbital speed, so neither is anything humans have control over.

Personally I think a hollowed out Ceres is a super cool setting in general, because Ceres is cool, spinning things up for gravity is cool and large scale engineering projects are cool. I've actually thought about using the setting for a story of my own. But yeah, I have a bit of trouble wrapping my head around the realistic applicability of the idea.

[Knaight]

Given that the Earth is vastly bigger and denser than Ceres, and so has much more gravity holding it together, it's possible that Ceres does not need to spin nearly that fast, to rip apart.

Bigger works in a few directions here. Notably, for uniform circular motion at a given distance the relevant equation is:


F=mω²r


That's expressed in angular velocity. Note that an increase in radius increases the force experienced when spinning, which makes sense - the actual linear velocity is higher the further you are away, and thus must change faster in the same period. That amount of force is the amount of force that must be applied to not fall apart, which is where things get interesting. On the one hand there's what happens if you look at gravity alone. Some quick equations*:

F=GmM/r²
M=ρV
V=4πr³/3

Solved:

F/m=ω²r=4Gρπr/3

The radius actually cancels out here, the vast majority of the rest can be reduced to a constant, and because of the meaning of F in the two equations you see the maximum angular velocity become a function of density for a gravity only system.

Obviously a lot of these are variable through the system, but there are things we can learn from this highly simplified model. One is that increasing radius doesn't directly increase viable spin speed based on gravity, and that we'd want to look at other factors for a correlation there. The big one is that density itself is gravity dependent to a degree, which we really see with gas giants**, where less massive gas bodies can't maintain the density to stay together even at much lower angular velocities. This sort of density shifting fluid-like behavior is also exhibited by materials we generally think of as solid, hence the self formation of planets into rough spheroids, but the actual changes in density are vastly smaller.

So, we turn to the other forces involved that aren't gravity dependent. These would largely be the intermolecular forces holding different molecules of material together, which we can nicely abstract out to material strength. These we actually see behaving far better at small sizes. Ceres's size works to its advantage here.

Whether it works enough is a different question entirely, and is essentially at least two different questions. The rocky Ceres seen in the Expanse has a very different material composition to the icier actual Ceres and is much more likely to stay in one place. It's also heterogeneous enough either way to make simple tensile strength analysis dubious, so I can't comment on the final question of whether it would actually stay together. That's beyond the scope of the models in question; they just show that being smaller is pretty helpful on the material side and relatively irrelevant on the gravitational side.

*With some weird formatting. Getting greek letters to display right on this forum structure is weirdly difficult.

**Gas giants also notably have much slower surface rotational speeds than you'd expect from day length calculations. Those tend to be based on magnetic field rotation, which corresponds to the rotation speed of more solid cores. If the outer layers of Jupiter actually traversed around the planet in a Jovian day they'd absolutely escape just fine and the planet couldn't hold together. This counteracts the material stability side, where gases have very little. A similar thing applies to spinning stars, though plasma physics are all sorts of weird.

\omega Eit

[DavidSh]

**Gas giants also notably have much slower surface rotational speeds than you'd expect from day length calculations. Those tend to be based on magnetic field rotation, which corresponds to the rotation speed of more solid cores. If the outer layers of Jupiter actually traversed around the planet in a Jovian day they'd absolutely escape just fine and the planet couldn't hold together. This counteracts the material stability side, where gases have very little. A similar thing applies to spinning stars, though plasma physics are all sorts of weird.

What rotational periods are you seeing for Jupiter? Everything I see says about 9 hours and 55 minutes for the planet with atmospheric rotational periods, depending on latitude, with 5 minutes of this. (That is between 9h 50m and 9h 55m)
If i understand the scaling factors appropriately, the minimum rotational period of a pile of rubble of fixed density before it flies apart is independent of the size. For rock, this is about 2.2 hours, as has been observed in asteroids.

[Knaight]

What rotational periods are you seeing for Jupiter? Everything I see says about 9 hours and 55 minutes for the planet with atmospheric rotational periods, depending on latitude, with 5 minutes of this. (That is between 9h 50m and 9h 55m)
If i understand the scaling factors appropriately, the minimum rotational period of a pile of rubble of fixed density before it flies apart is independent of the size. For rock, this is about 2.2 hours, as has been observed in asteroids.

I will say that I trust the dimensional analysis (which I have actual meaningful training in) much more than the statement about minimum rotational period for gas escape and the extent of delay, which was working from memory. There was an angular velocity by radius graph which I'm trying to track down, but I remember there being a substantial slowing by the far upper atmosphere. So, for rocky or icy bodies, where density is basically a constant, yes, the minimum rotational period is independent of the size.

Gas giants do weird stuff, starting with drastic density changes as you go up which absolutely do depend on the mass of the body. For speeds, I remember seeing a model of angular velocity by radius for Jupiter which had a significant dropoff, but I can't find it at the moment. Looking it up now I'm seeing that same 5 minute variation though, so it might actually be better behaved than I remember seeing.

[Jimorian]

At the scale of even a small planetoid, the overall structural integrity of the object is basically equivalent to sand.

[Rydiro]

At the scale of even a small planetoid, the overall structural integrity of the object is basically equivalent to sand.

Yeah, every gas, liquid and rock splinter would fly right off.

Not to mention Earths mantle, which would probably pop like a juicy grape.

[Mastikator]

If the rotation was so fast that the surface velocity of the equator was equal to its escape velocity it would start to rip apart at the equator.

The escape velocity of ceres is 510 meters/second.
The diameter is 939.4km, so the circumference is 2951km

divide 2951km / 0.51km/s = 1.6 hours

If Ceres completes a full rotation every 1.6 hours anyone standing at the equator would fly off, including the surface itself (which I assume has virtually no tensile strength, only compressible strength, being made of sand, rocks and ice).

If you want more of the planet to fly off you have to speed it up even more.

[Corvus]

From what I understand/have heard, you don't actually need to spin Ceres itself. Just build something like an O'Neill Cylinder under the surface somewhere and spin that.

Though it does beg the question that if you could build an O'Neill Cylinder why would you need to stick it in Ceres.

[Knaight]

From what I understand/have heard, you don't actually need to spin Ceres itself. Just build something like an O'Neill Cylinder under the surface somewhere and spin that.

Though it does beg the question that if you could build an O'Neill Cylinder why would you need to stick it in Ceres.

It's a giant pile of radiation shielding you don't have to build at the very least, along with protection from the occasional stray micrometeorite and the like. Though from an energy and friction perspective spinning something inside Ceres without spinning Ceres runs into issues in terms of energy expenditure to keep spinning.

[factotum]

Basically, due to friction, if you have something spinning inside Ceres, eventually the asteroid itself will pick up the spin--could take decades, but the Ceres of the Expanse has been inhabited for that sort of period of time, so it's almost a moot point. In any case, as far as I know (not having read the books) the idea is definitely that the entire asteroid is being spun, not some small part deep inside it.

[Rydiro]

Basically, due to friction, if you have something spinning inside Ceres, eventually the asteroid itself will pick up the spin

Dont think so. Conservation of angular momentum means you cant change the spinning of ceres from the inside.

[factotum]

Dont think so. Conservation of angular momentum means you cant change the spinning of ceres from the inside.

Of course you can? If the thing spinning inside slows down due to friction, conservation of angular momentum means what is lost has to go *somewhere*, and in this case, it will go to the main body of the asteroid. Or, if you prefer to look at it another way: if there's some sort of motor attached to the spinning thing to keep its speed constant, any force exerted by the that motor will result in an equal and opposite force being exerted on the body of the asteroid. Since we're in space and there's no atmospheric friction to prevent it, this means the asteroid will start to spin in the opposite direction to the object inside it. Obviously the asteroid has much greater mass and so this effect will take a while to become significant, but it will definitely happen.

[Knaight]

Obviously the asteroid has much greater mass and so this effect will take a while to become significant, but it will definitely happen.

Of course, the two components spinning in opposite directions have friction at the point of spin, which means you need constant energy input just to keep them spinning. The same doesn't really apply to just spinning Ceres as a whole.

[Lvl 2 Expert]

So if you want to have a habitat big and heavy enough to do that, build two cilinders spinning in opposite directions. All you'll generate is heat, right?

[Telok]

So if you want to have a habitat big and heavy enough to do that, build two cilinders spinning in opposite directions. All you'll generate is heat, right?

Ceres is irregular in shape, the centers of mass of the cylinders are not in the same place, at least one cylinder center of mass is not at Ceres center of mass. I'm pretty certain that you're going to induce some nasty tumbling that way.

[Lvl 2 Expert]

Ceres is irregular in shape, the centers of mass of the cylinders are not in the same place, at least one cylinder center of mass is not at Ceres center of mass. I'm pretty certain that you're going to induce some nasty tumbling that way.

Even if you stick them close together or on exact opposites of the center of mass?

Ceres is not that irregular, and it weights about 10^20 kg. That's ten thousand times less than Earth, but a trillion times more than Mount Everest. It has some inertia to work with.

[gomipile]

If the rotation was so fast that the surface velocity of the equator was equal to its escape velocity it would start to rip apart at the equator.

The escape velocity of ceres is 510 meters/second.
The diameter is 939.4km, so the circumference is 2951km

divide 2951km / 0.51km/s = 1.6 hours

If Ceres completes a full rotation every 1.6 hours anyone standing at the equator would fly off, including the surface itself (which I assume has virtually no tensile strength, only compressible strength, being made of sand, rocks and ice).

If you want more of the planet to fly off you have to speed it up even more.

That's what it would take to get bits to start flying off "to infinity." Getting it to start flying apart is easier. All you need is to counter the gravitational force at the surface on the equator. Alternatively, you need just enough speed to put a rock on the equator into an orbit around Ceres the same radius as the equator.

If my math is right (which might not be true, since I'm tired,) that comes to a rotational period of about two and one quarter hours.

[Mastikator]

That's what it would take to get bits to start flying off "to infinity." Getting it to start flying apart is easier. All you need is to counter the gravitational force at the surface on the equator. Alternatively, you need just enough speed to put a rock on the equator into an orbit around Ceres the same radius as the equator.

If my math is right (which might not be true, since I'm tired,) that comes to a rotational period of about two and one quarter hours.

...I showed you my math now show me yours.

Sorry I couldn't resist

At 1.6 hour rotation period only the top layer of the equator would escape into solar orbit. Much of the equatorial crust would fly into orbit (a tiny fraction escapes), almost all of the dwarf planet would remain as a ball. Eventually you'd end up with rings.

[Fat Rooster]

That's what it would take to get bits to start flying off "to infinity." Getting it to start flying apart is easier. All you need is to counter the gravitational force at the surface on the equator. Alternatively, you need just enough speed to put a rock on the equator into an orbit around Ceres the same radius as the equator.

If my math is right (which might not be true, since I'm tired,) that comes to a rotational period of about two and one quarter hours.

It would actually be less than that, because it would deform significantly well before you get to that sort of rotational period. As you speed up the rotation the surface at the equator gets higher.

Structurally, at those scales everything behaves a bit like a fluid. If you consider the weight of the top 10km of material is about 600 tons per square meter even in Ceres gravity, you begin to see that the sheer quantity of material makes the forces available along any 2 dimensional interface look a bit puny next to pressure. If an idea involves relying on natural tensile strength or shear forces, you can basically just chuck it.


Best solution for a station there would probably be an O'Neil cylinder in orbit around Ceres surrounded by a non rotating shield. Because they are in zero G respective to each other there are basically no friction losses inherent to the system, and not having to support the 'weight' of the shield against the artificial gravity makes the structure considerably easier. You might end up accepting some air resistance friction and using the non rotating outer shield as the pressure vessel, but that does risk spinning up the outer shell and damaging it. That shouldn't be much of an issue though if the outer shell is considerably more massive than the inner cylinder, and in many ways it is a more scalable design. Being able to move from rotating sections to zero G labs, or between rotating sections, without having to pass through rotating seals or air lock systems could massively simplify the design. Rotating seals would always be a nightmare.
The 9 hour rotational period of Ceres means that an elevator system is pretty simple to build. If you had enough, you could actually build it out of balsa wood without tapering. Even if you were just filling a cavity with rocks from Ceres as your shield getting mass into orbit is not a big deal. It would probably be easier than mining out a structurally sound cavity and building a bearing that can deal with the weight of a rotating cylinder, even if you did place it at the pole to avoid any gyroscopic loads. Putting them at the center… is possible, but... yeah why? The pressures might be comparable to digging at a depth of ~5km on earth*, but we also believe that a significant part of that will be through metallic iron. You can either go 300m/s for up, or drill 500km including through iron if you are determined to go down. Going up seems simpler to me, and probably involves moving less material.

Ceres is on the upper bounds of building a centrifuge artificial gravity system inside regular gravity, but my guess is that it isn't worth it for the majority of habitation. If Ceres were not spinning, maybe, but the relatively rapid spin makes elevator designs extremely easy, and that makes surface habitation less of a necessity. You can regard it more like oil rig habitation, with the actual city that supports the industry remaining in orbit.

Another thing that nobody has mentioned is the need to keep the cylinders vertical if they are in Ceres' gravity. While not 100% certain, I would guess that gravity varying by 5% over a rotation would be significantly disorientating. You might get used to it, but it would be like working on a ship perpetually in rough seas. You certainly aren't going to be playing pool in it.

*Conservative fermi estimate. If Ceres has a significant Iron Core gravity will not fall off as fast, and may actually increase with depth, resulting in much higher pressures.

[Rydiro]

Of course you can? If the thing spinning inside slows down due to friction, conservation of angular momentum means what is lost has to go *somewhere*, and in this case, it will go to the main body of the asteroid. Or, if you prefer to look at it another way: if there's some sort of motor attached to the spinning thing to keep its speed constant, any force exerted by the that motor will result in an equal and opposite force being exerted on the body of the asteroid. Since we're in space and there's no atmospheric friction to prevent it, this means the asteroid will start to spin in the opposite direction to the object inside it. Obviously the asteroid has much greater mass and so this effect will take a while to become significant, but it will definitely happen.

Nope, you are missing that friction also imposes an opposing force on the asteroid. Which will cancel out your motor spinning. Because thats what the motor does, it reverses the effects of friction, setting asteroid AND cylinder to the respective rotation they had before friction came in.
Cylinder+asteroid are a closed system, thus their total angular momentum cannot be changed by interacting inside of it.

[factotum]

Nope, you are missing that friction also imposes an opposing force on the asteroid. Which will cancel out your motor spinning. Because thats what the motor does, it reverses the effects of friction, setting asteroid AND cylinder to the respective rotation they had before friction came in.
Cylinder+asteroid are a closed system, thus their total angular momentum cannot be changed by interacting inside of it.

I just don't believe that. Let's say that, instead of allowing the cylinder to run down via friction in the bearings, you put a brake on it to stop it near instantly. Are you still claiming its spin won't be transferred to the asteroid?

[Seppl]

Nope, you are missing that friction also imposes an opposing force on the asteroid. Which will cancel out your motor spinning. Because thats what the motor does, it reverses the effects of friction, setting asteroid AND cylinder to the respective rotation they had before friction came in.
Cylinder+asteroid are a closed system, thus their total angular momentum cannot be changed by interacting inside of it.

While it is true that you cannot change the total angular momentum (or any momentum) from the inside, the important word here is "total". You can set the outside shell into rotation in one direction and have an inner core rotating into the opposite direction to counteract that. Which is what is relevant regarding the question how fast you can spin that outer shell before it starts disintegrating.

[monomer]

Nope, you are missing that friction also imposes an opposing force on the asteroid. Which will cancel out your motor spinning. Because thats what the motor does, it reverses the effects of friction, setting asteroid AND cylinder to the respective rotation they had before friction came in.
Cylinder+asteroid are a closed system, thus their total angular momentum cannot be changed by interacting inside of it.

They are not a closed system, you are adding in energy to spin the cylinder, which will then get transferred to the asteroid through friction.

[Rydiro]

I just don't believe that. Let's say that, instead of allowing the cylinder to run down via friction in the bearings, you put a brake on it to stop it near instantly. Are you still claiming its spin won't be transferred to the asteroid?

Yes it will. Lets say your cylinder rotates clockwise wrt asteroid. Lets call it state 1. You brake. Now the asteroid rotates a little extra clockwise and the cylinder is still wrt asteroid. State 2. Now you start your motor to rotate the cylinder clockwise wrt asteroid again. This pushes the asteroid counter clockwise. You are now back to state 1 again.
The breaking and accellereating both act upon the asteroid, but in different directions. They cancel each other out.

[Rydiro]

They are not a closed system, you are adding in energy to spin the cylinder, which will then get transferred to the asteroid through friction.

Thats called heat, not angular momentum.
Unless your energy had angular momentum in the first place, like spinning photons hitting your solar collectors. Which would be weird.

[monomer]

Thats called heat, not angular momentum.
Unless your energy had angular momentum in the first place, like spinning photons hitting your solar collectors. Which would be weird.

You are converting energy (which come from an outside source, say chemical rockets or electricity) to angular momentum thus changing the angular momentum of the entire system.

[Seppl]

You are converting energy (which come from an outside source, say chemical rockets or electricity) to angular momentum thus changing the angular momentum of the entire system.

No, you cannot do that. Not by flying some kind of fuel or other energy storage to the asteroid and using it for some kind of motor. Angular momentum has to come from the outside in the form of other angular momentum, or be in someway removed from the asteroid to spin it up in the opposite direction. It's a fundamental conservation law (for this kind of system). There is no such thing as an energy to angular momentum conversion.

You could spin up the asteroid by flying a rocket into it at an angle, thus transferring that momentum to the asteroid. Or by building some kind of giant cannon on the asteroid and firing something off at an angle at escape velocity, thus gaining angular momentum by removing the momentum of the projectile.