# How do I prevent my turtle from collapsing under its own gravity?

Suppose the universe contained a species of planet sized turtles1 that can travers at least interstellar space. How can I explain (without invoking magic) that these turtles are not spherical?

If this is not possible within the laws of physics as they are, what can be changed minimally about them (the laws of physics) that could allow such an organism to structurally sustain itself? Important here is its relative size to "normal" living organisms.

The answers to this question should not focus on how/whether this organism could survive (sources of food), travel or even evolve. For the scope of this question, all other issues with this organism may be considered to be solved.

1: not necessarily a representative image of the turtle as imagined by the author, the world on its back especially I can only assume was a fabrication by the illustrator.

• Ok it is strange we asked these about the same time! worldbuilding.stackexchange.com/questions/1360/… – kaine Oct 9 '14 at 13:39
• @kaine well this is specific about turtles, although there is some overlap. – mechalynx Oct 9 '14 at 13:41
• Yeah, I tried keeping mine on a small scope, I think tehy don't egt into eachother's water too much. We'll see how it plays out. – overactor Oct 9 '14 at 13:42
• I'm not worried about overlap; i expect that the gravitation force will limit your creature to comparitively (like half the size of pluto or something) while mine is less rigid (in alot of ways). I just thought the simular topic within 1 minute of each other was funny. – kaine Oct 9 '14 at 13:48
• This (and even more so, the answer's diagram) reminds me of an old Russian science joke: "... furthermore, lets' assume that cows are perfectly spherical..." – user4239 Oct 10 '14 at 1:17

### You have a different problem (and it’s not that bad)

Planets only become spherical because they are either made of material that behaves like a fluid (gas, dust, magma) or behaved like that during their creation. Moreover, planets cannot self-repair, turtles can.

What you have to worry about with cosmological turtles is that their tissue bursts or breaks under their gravitational forces. So, let’s make a very rough estimate of the orders of magnitude relevant for your turtle:

The blue pieces represent the major masses (say, body and head) and the red piece represents some weight-bearing structure (say, the neck). $x$ is a variable length. All parts have the same depth as height, i.e., the blue pieces are cubes and the red piece is $x × \frac{x}{5} × \frac{x}{5}$.

We then have (with some further assumptions):

• If we assume that each of the blue pieces has the same density as water (1 kg/ℓ), they each weigh $M = 1000\,\frac{\text{kg}}{m^3}·x^3$.
• If we assume each blue piece to be a point mass, the distance on which their gravitational forces act is $2·x$ and the gravitational force between them is $$F = \frac{G·M^2}{(2·x)^2} = x^4 · 1.7·10^{−5} \frac{\text{N}}{\text{m}^4}.$$
• If we assume the red piece to have the same compressive strength as bone (170 MPa), it can bear forces of $$170\,\text{MPa}·\left(\frac{x}{5}\right)^2 = x^2·6.8·10^6\frac{\text{N}}{\text{m}^2}.$$
• The two forces equal for $x=6.4·10^5\,\text{m}$ or 640 km, which means that the structure collapses for higher $x$ and is stable for lower $x$. For comparison: The earth’s diameter is 1.3·10⁷ m or 13000 km; the moon’s diameter is 3.8·10⁶ m or 3800 km.

Of course, there are other destructive mechanisms (tension, shearing, torsion, …) and other tissues involved and the turtle will be organised differently, but the order of magnitude of the forces and strengths will remain the same, unless you have totally different materials involved.

• The math you used comes out to 640km which isn't too shabby. if you use a larger MPa you can get it better. A main issue, however, still seems to be the mass of the neck. – kaine Oct 9 '14 at 17:23
• @kaine: Reworked. I am not sure what your problem is with the mass of the neck. Hydrostatic pressure is not a problem, as bones are not liquidous. The gravitational force of the bone is negligible, because though it’s closer, it’s also much lighter – you can imagine every smaller structure as a smaller version of the large model (which is thus more stable). – Wrzlprmft Oct 9 '14 at 17:32
• By my math is decreases your answer by another couple hundred kilometers and it bothers me that one such a simple model something so apparent is ignored. The additional pressure is almost 40 some MPa on top of the 170MPa. That is ignored. The bone to bone is just 4MPa but the bone to water is 16 MPa each way. – kaine Oct 9 '14 at 17:58
• FWIW: The discworld (the fictional world represented by the doll linked in the OP) is approximately 16,000km in diameter. This measurement does not account for Great A'Tuin (the Giant Star Turtle, Chelys galactica) nor the four giant elephants (Berilia, Tubul, Great T'Phon, and Jerakeen). Chelys galactica are largely composed of the element "chelonium". Giant Star Turtles hatch with a quartet of elephants and a disc on their backs. – Brian S Oct 10 '14 at 18:27
• The turtle will hit issues with the scaling of forces long before it gets to that size. Steel seems underly rigid on scales of less than 30m but about that it starts behaving in a more and more flexible manner. By the time you reach the scale of the larger ships, steel begins to behave more like paper twisting flexing and bending in surprising ways. The same effect would hit biological materials. Bone on the scale of more than a few dozen meters, will likely behave like partially cooked pasta. Whale bones flex a lot. Stress waves will simple pulverize sections of bones were they build up. – TechZen Oct 16 '14 at 19:33

I'm having a few problems with the concept, particularly around what the innards of such a creature would end up looking like under that much pressure. And while I write that Wrzlprmft puts up a well thought post that describes that.

Alternate theory for you...

There is the potential for the Redwood forest in California and Oregon to be one single living organism...one tree that branched off into several trees and so on until it formed one giant living mass of a forest. Drawing on that...I could see your 'turtle' forming in a similar manner. A single life mass with modest beginnings that feeds directly off the planet itself (be it a process similar to lichen that breaks down rocks and feeds from that is a potential...using the planets thermal energy is another potential). This biomass continually grows, overtaking any other living body on the planet until the planet is covered in one giant biomass. Through whatever means, this biomass becomes intelligent (aka it develops a 'brain' somewhere on or in the planet).

This really gets around the soft flesh of a creature being crushed under it's own weight. You now have an intelligent planet sized creature that at it's core is infact a planet, however it's coated in a single living intelligent being that is capable of manipulations on a global level. It's self 'feeding' in that it draws it's energy from the planet inside of it (maybe consuming a moon here and there for additional mass?). Reproduction becomes this planet sized creature locating other planets and seeding it so that it's new seed can grow in the same way it did.

In this manner, I think you could get a 'turtle' to pretty much whatever size you want and not have to worry about the creature collapsing in on itself

To make the mass look like a turtle...a space weather event could hit this planetoid forcing it to defend itself and having the outter mass grow a shell. I doubt flippers would be a valid locomotion technique as they'd just flail around in space with nothing to push off of. Instead, it's ability to move would be more like a squids...'breathing' in and contracting (exhale?) which shoots mass (rocks, water?) off the planet through pores in it's shell. In this case, it would be constantly searching for new 'mass' from asteroids, moons, or other planets (gives it the 'need to feed' on other stellar bodies).

• Note, if he doesn't need the shell, couldn't that be exposed planetary surface? Maybe some sensory outposts to give it some color? – kaine Oct 9 '14 at 19:48
• @kaine Heh, a desert patch on it's "skin" would give it a look like it had a rash :) I didn't think of sensory organs...though something of this size could develop senses that we couldn't fathom. A giant interior lake could function as a 'ear drum' capable of hearing interstellar neutrons that normally travel through matter..or sense dark matter even. – Twelfth Oct 9 '14 at 20:01

In order to make a creature of this size resembling a turtle, (though it very unlikely to form) it cannot collapse under its own weight.

Non-spherical cosmic bodies obviously exist but they are either:

• small enough that physical rigidity prevents it from collapsing under its own gravity
• Low enough density that it does not collapse on itself

In order for this to work, therefore, you need something with incredible rigidity and low density.

Ananke has a mass of 3*10^16 kg and is not spherical. I could accept that an intelligent or evolved internal structure could keep it turtle shaped at that size. If you were willing to accept that size, it would be fine. Your planet's surface would be about 30 miles diameter. Phobos and Deimos are smaller.

Lets decrease this density a bit. Aerographite has reported density of .2 milligrams per cubic centimeter. If we use nanobots it make it more structured and stronger than we physically can in the real world, I still don't think that the average density can be below 2 milligrams to prevent collapse and keep its shape from in space conditions. If we say it can be nonspherical if the surface gravity of the sphere would be the same as Ananke if it were a sphere, then you get an average distance from the core to the skin of: 36000 km diameter

Is that a sufficient diameter? Maybe you could increase it by another order magnitude but it is already not very realistic. This density plays a huge role in it and is tiny. The hardness of the structure is not really that tough so the outermost regions would be essentially just aerogel while the interior is a denser, harder structure (but still very light).

The gravity on the surface of the turtle would be tiny. Any atmosphere would diffuse right into him or escape into the void. If you actually want a livable disc on him... well... I don't know... There is a reason Discworld needs such interesting magic.

I had not looked into it, but being hollow might help.

• You can also reduce density by being hollow. – jm. Oct 9 '14 at 19:39
• @jm I noted that in the answer. Also note my answer is 5× larger than the earth so, yeah, he needs to be heavier and denser now not lighter. – kaine Oct 9 '14 at 19:42
• I kind of focused on getting him as big as possible as I was curious about that for my question. – kaine Oct 9 '14 at 19:43

The answers to this question should not focus on how/whether this organism could survive (sources of food), travel or even evolve.

Well, I was educated as a biologist so it's gibberish to me to think of a model for animal that doesn't start with its environment and its selection pressures.

So, I am going to ignore that restraint in part because doing so makes it easy to imagine why a space turtle would be non-spherical.

1) The turtles aren't spherical because they face selection to form another shape.

Spheres don't make good powered shapes. A lot of people think that real spacecraft remain cylinders because that form is needed for launching through and atmosphere but it's really about stability under power in space.

Stability is a function of the displacement of mass laterally from the line of thrust running up from the engines. The closer the majority of mass is to the line of thrust, the easier to balance the ship on top of the thrust. This is not obvious because in air, water or ground contact, a long cylinder shape encounters resistance and begins to act like a lever knocking the ship off the thrust axis. In vacuum that effect is trivial. The ship's axial center of gravity is more stable.

A sphere displaces more mass around from the thrust line than a long cylinder of equivalent volume. That displaced mass must balance constantly or it will move the ship's center of off the thrust line.

Consider it this way: Inside a ship under acceleration, an astronaunt walks as far along the longest path possible. As he does, his mass alters to the center of gravity to some degree. In a cylinder ship, he will spend most of his time slightly offset from the thrust line and moving parallel to it. On a spherical ship, most of the paths he could take move him farther away from the center of gravity and in the most extreme case, as long as half the diameter of the ship. If he walked side to side at the ship's midpoint perpendicular to the line of thrust, his mass would have a lever effect at the extremities.

So, spheres are great if you have no thrust but otherwise tricky. Just as both animals and vehicles on Earth have the basic head-tail layout despite their radically different origins and materials, likely a space animal would also evolve have a head-tail layout for stability under thrust.

The next issue would be wider than it is thick. Animals on earth evolved under gravity so they form to resist gravity which means they have a top-bottom. A space turtle wouldn't. If it evolved as a head-tail form as above, everything else would be distributed evenly around the outer perimeter.

To get a flat shape, we would need to evoke a selection pressure to make that shape optimal. The obvious one would be that the turtle absorbs sunlight or solar wind plasma for food. In all three cases, a flat shape oriented perpendicular to the line to the star, like a sunflower, would give it the most surface area for absorption.

2) Size: Just because something is big, doesn't mean it has to be a sphere. Gravity is the weakest force so if offset by another force, its tendency to form materials into spheres could be easily offset.

Living things are not static structures, they are dynamic and exert energy all the time to maintain their shape (cells devote 70% of their energy moving around potassium and sodium ions that among other things maintain cell wall shape.)

If we imagine a turtle that produces and controls magnetic fields in its tissues, quite plausible with biological conductors, we could imagine a turtle that constantly manipulates a complex matrix of internal magnetic fields to maintain its shape against gravity and to dampen out the various stress forces propagating throughout it. The magnetic fields would actually be the most rigid part of the system. Instead of trying to simply resist giant scale stress forces with static materials, the turtle would absorb, diffuse and redirect them.

The turtle would be something like an internally complex balloon animal with gravity taking the place of external air pressure and magnetic reinforcement taking the place of internal air pressure. The tissues are the skins of the balloons. The tissues just have to be strong enough to exist at the balance point of each force. The forces actually strengthen the tissues just like air pressure strengthens the skin of balloons.

In that case, the turtle could grow much larger than it would if it relied on just static mass to resist the pull of gravity. However a consequence of dynamic form would mean that as soon as the turtle dies, or just weakens past a certain point and runs out enough energy, it will implode.

Also, growing in a rectilinear turtle shape would distribute mass around in a non-spherical shape which would decrease the overall power of gravity to pull everything to a single point. This would slow the gravitational feedback loop that forms spheres.

I presume at some point gravity would defeat magnetic reinforcement but I don't have any idea how to calculate the mass at which that happens, especially with an irregular shape.

Think in terms of a big ocean ship like an aircraft carrier. It's density is much less than that of steel, because it's mostly empty. That's why it floats. It's density is less than water.

If your turtle was mostly exoskeleton, you could make it as big as you want without danger of collapsing on itself (it might need some structure inside for stiffness, etc). Of course, if the turtle were "born" on planet with gravity, it would need some material that could avoid structural collapse. But out in space, it wouldn't matter.

• Even then, the problem that gravitational forces raise with the fourth power and areas and thus stability raises with the second power of length would eventually hit, though only when the turtle is already larger than a planet. – Wrzlprmft Oct 10 '14 at 7:05

I would have put this in a comment but I dont have enough rep,

The Turtle which you link to in your question - planet sized turtle is actually a representation of the "discworld" - Now these are fantasy books written by Terry Pratchet which do include magic however IIRC while magic is used to explain the existence of the discworld in the books universe "magic" is more like science Quote below from Wikipedia

Magic is the principal force on the Discworld, and operates in a similar vein to real-world elemental forces such as gravity and electromagnetism. The Disc's "standing magical field" is essentially the local breakdown of reality which allows a flat planet on the back of a turtle to even exist. The force called "magic" is really just a function of the relative absence of reality in the local area, much in the same way that the absence of heat is described as "coldness". Magic warps reality in much the same way as the real universe's gravity warps its space-time. The act of performing magic is, essentially, telling the universe what you want it to be like, in terms it can't ignore. This is very draining to magic users, due to Discworld science's Law of Conservation of Reality (which states it takes the same effort to do something with magic as it would to do it mundanely). This is why most Discworld wizards store magic in a staff (with a knob on the end) which is a sort of capacitor for magical energy.

On the Discworld, where magic has more in common with particle physics than Houdini, high-level background magic (most likely a reference to real-world background radiation) occurs when a very powerful spell hits,

• If it is relevant to this question, you could explain why magic is not needed to explain the disc world, as a way to flesh out your answer. – overactor Oct 10 '14 at 8:00