# Planets in unusual shapes

I am writing a science fiction story about a strange universe. I have a few questions which fall in the same general category.

1) What sort of gravity would allow a planet to maintain the shape of a dodecahedron?

2) If there exists a planet, where the physical laws are the same as in this universe, can such a planet maintain the shape of a doughnut (or more scientifically, a toroid)? Would gravity or centrifugal forces cause it to collapse into something more spherical?

3) What sorts of problems, given the known laws of this universe would there be in creating some kind of force field (electro-magnetic or otherwise) in a bubble surrounding yourself, and using that bubble to fly?

4) Since the electro-magnetic force is more powerful than gravity, is it possible to somehow convert electro-magnetic energy directly into gravity and make an effective anti-gravity device?

Naty1
1,2, One way to approach your questions would be to consider that a planetary body cooled into a shape of your choosing.

I believe there is still disagreement about whther the large circumference/diameter of the Earth at the equator resulted from hardening of the mantle or whther it is an effect of current motion...

3, mainly a problem of sufficient energy to overcome gravity...but with some antimatter you could hypothesize antigravity...

4. not in the sense you likely mean...but sufficient electromagnetic repulsion can surely overcome gravity...even a magnet is strong enough to lift a paper clip against the entire gravitational attraction of the planet earth...
while we do NOT currently understand the connection between electromagnetism and gravity, you could hypothesize a new discovery that is common to both...and can be used to generate both...

oops! I do not know if we are supposed to discuss science fiction here...so I will stop...

Gold Member
I am writing a science fiction story about a strange universe. I have a few questions which fall in the same general category.

1) What sort of gravity would allow a planet to maintain the shape of a dodecahedron?
There is no natural phemonenon that could create or maintain such a thing; it would have to be built artificially and maintained either through sheer strength or through artificial means.

2) If there exists a planet, where the physical laws are the same as in this universe, can such a planet maintain the shape of a doughnut (or more scientifically, a toroid)? Would gravity or centrifugal forces cause it to collapse into something more spherical?
No. Any mass large enough will eventually collapse into a spheroid. Smaller masses will collapse into less spherical spheroids. Closest we've seen is asteroids shaped like dumbbells.

3) What sorts of problems, given the known laws of this universe would there be in creating some kind of force field (electro-magnetic or otherwise) in a bubble surrounding yourself, and using that bubble to fly?

4) Since the electro-magnetic force is more powerful than gravity, is it possible to somehow convert electro-magnetic energy directly into gravity and make an effective anti-gravity device?
If you'd like. Power your device with Handwavium.

oops! I do not know if we are supposed to discuss science fiction here...so I will stop...

Why not? Shouldn't a decent science fiction author check with what we currently know about physics once in a while to see what's likely and what's not?

As far as the planet in the shape of a dodecahedron, what if gravity works differently on that planet?

Gold Member
Why not? Shouldn't a decent science fiction author check with what we currently know about physics once in a while to see what's likely and what's not?
Yes, and regards to known physics, you already have your answer, which is simply: no it cannot be done.

You want to speculate about unknown ideas, and that is where lines will be crossed.

As far as the planet in the shape of a dodecahedron, what if gravity works differently on that planet?
Sure, but you're not talking sci-fi; you're talking fantasy.

You can have it whatever way you want simply by premising a technology advanced enough.

In Larry Niven's Protector, the protagonist whimsically manipulated gravity to produce a sculpture in the shape of a Mobius strip upon whose surface his guests could stroll.

But why start with the effect (a dodecahedral planet) and trying to make up a cause? If you want to write sci-fi, consider setting up a cause (in the form of known physics or plausible technology) and determine an effect?

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Mentor
(Thread moved to the General Discussion forum)

slider142
1) What sort of gravity would allow a planet to maintain the shape of a dodecahedron?

The primary cause of liquids and loose mass coalescing into roughly spherical shapes is the metric being Euclidean, assuming you want to keep gravity dependent on distance between masses. A different metric, ie., the taxicab metric, would give you different rest shapes, such as cube-like shapes. Other metrics will give other shapes. This relies on your universe being intrinsically different from ours.

elect_eng
1) What sort of gravity would allow a planet to maintain the shape of a dodecahedron?

I have to agree with others here that a dodecahedron shaped planet is very difficult to explain scientifically.

Just to throw out an idea, - would your purposes be served if the planet only appeared to be a dodecahedron from space? What if a new technology could reflect light rays in a controlled way from a distance. Light from a sun/star could be controlled to perfectly reflect from a virtual dodecahedron that is larger than the planet. An external observer would see what appears to be a dodecahedron. If the light is reflected as from a smooth surface then the dodecahedron would appear to be perfect mirrored surfaces. If the light is allowed to scatter, then it would appear pure white. Either way, what an impressive jewel that would be!

As to why a species would deliberately reflect sunlight? That would depend on your story. Maybe the effect is meant to make a moon look esthetically pleasing in a planet's sky. Or maybe, a sun has gone to a gas giant stage and the reflectors make the planet habitable by reflecting most of the radiation and letting just the right amount and spectral content through to the planet's surface.

I know of no scientific principle by which this would work, but sci-fi is allowed to take some poetic license in cases like this. You would need to offer some description of how this effect is based on science and technology and not magic or other mystical means.

Staff Emeritus
Gold Member
No. Any mass large enough will eventually collapse into a spheroid.
Dave, do you have a proof for this? With sufficient angular velocity and tensile strength, I don't see any obvious reason that a toroid will not be stable.

Gold Member
You would need to offer some description of how this effect is based on science and technology and not magic or other mystical means.
"[URL [Broken] Clarke[/URL] wouldst disagree.

"Any sufficiently advanced technology is indistinguishable from magic."

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TheStatutoryApe
Designer planets? Artificial means seems like the best explanation for such a thing. Even if you have some explanation as to why it could happen naturally I don't think it would go over very well with an audience. A bit of writer's advice I read somewhere said that if something is unbelievable it is unbelievable. It does not even matter if you can find a logical and realistic explanation for how it could happen, if your audience does not believe it then they will not believe it end of story.

Staff Emeritus
Gold Member
"[URL [Broken] Clarke[/URL] wouldst disagree.
[Off-topic detour in Nazism] 'Wouldst' is a verb (past tense of 'will') used for a second person pronoun, such as 'thou'; it does not work with a third person pronoun, such as 'Mr. Clarke'. [/detour]

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MotoH
[Off-topic detour in Nazism] 'Wouldst' is a verb (past tense of 'will') used for a second person pronoun, such as 'thou'; it does not work with a third person pronoun, such as 'Mr. Clarke'. [/detour]

Sieg heil.

Most of the Scifi/fantasy books I have read will simply state that this is the way it is. You don't need an explanation IMO for anything in your book. It should be about plot and characters, not the science behind how your planet is a dodecahedron or some other wibly buzz.

Gold Member
[Off-topic detour in Nazism] 'Wouldst' is a verb (past tense of 'will') used for a second person pronoun, such as 'thou'; it does not work with a third person pronoun, such as 'Mr. Clarke'. [/detour]
I did not know that. Thank you.

-a fellow grammar nerd

elect_eng
"[URL [Broken] Clarke[/URL] wouldst disagree.

"Any sufficiently advanced technology is indistinguishable from magic."

Well, yes, he was a master. Even in 2001, where no clear explanation was given to the (very mystical) powers of the monolith, I never had a problem accepting his work as science fiction. Science fiction does allow a wide range of poetic license, and the better the poet, the more license is allowed.

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TheStatutoryApe
Well, yes, he was a master. Even in 2001, where no clear explanation was given to the (very mystical) powers of the monolith, I never had a problem accepting his work as science fiction. Science fiction does allow a wide range of poetic license, and the better the poet, the more license is allowed.

The difference is that people know a bit about planets and what they are supposed to be like. A mysterious monolith is, by definition, mysterious and giving it mysterious powers does not seem odd or out of place. Describing your story as taking place on a toroid planet with no explanation what ever will, depending on the background and context, just seem silly and entirely ridiculous. The issue arises then of how to explain or contextualize the phenomenon in such a fashion that the audience will accept it. It does not have to be a clear explanation at all. One could simply say that it is a "designer" planet created by some artist through some process unknown to the narrating observer and leave it at that. If the story has already set it self apart as being surreal with multiple odd and inexplicable elements then it may not seem so out of place to simply throw it out there without explanation as it fits in the context. Particularly good writers get away with outlandish things in their writing not because they are simply that good that they do not have to consider such issues but rather because they resolve these issues so elegantly that one does not think to question them.

elect_eng
The difference is that people know a bit about planets and what they are supposed to be like. A mysterious monolith is, by definition, mysterious and giving it mysterious powers does not seem odd or out of place. Describing your story as taking place on a toroid planet with no explanation what ever will, depending on the background and context, just seem silly and entirely ridiculous. The issue arises then of how to explain or contextualize the phenomenon in such a fashion that the audience will accept it. It does not have to be a clear explanation at all. One could simply say that it is a "designer" planet created by some artist through some process unknown to the narrating observer and leave it at that. If the story has already set it self apart as being surreal with multiple odd and inexplicable elements then it may not seem so out of place to simply throw it out there without explanation as it fits in the context. Particularly good writers get away with outlandish things in their writing not because they are simply that good that they do not have to consider such issues but rather because they resolve these issues so elegantly that one does not think to question them.

I don't know why you directed these words to me. I think you took my words out of context. Note my previous comments

elect_eng said:
I have to agree with others here that a dodecahedron shaped planet is very difficult to explain scientifically.

elect_eng said:
You would need to offer some description of how this effect is based on science and technology and not magic or other mystical means.

The comment of mine that you responded to was a response to DaveC's quote from Clarke, directed toward my comment that magic is not allowed in SF. Which of your statements do you think I would be contradicting with my previous comments. I don't really see a glaring difference in our points of view. If you see one, it is likely just an issue of wording and interpretation.

TheStatutoryApe
I don't know why you directed these words to me. I think you took my words out of context. Note my previous comments

Perhaps I mistook your response. You seemed to indicate that there was little need for explanation of the almost magical powers of the monolith in 2001:ASO and that lack of need seemed a reflection of the prowess of the author. I was only clarifying that there was indeed a sort of explanation, if only based in context and storytelling convention, and that the strength of the writer is not in needing little explanation but in making it seem that way.

And no my post was not really meant to be for you but more for the benefit of the OP since he is looking for writing advice.

Homework Helper
Gold Member
Dearly Missed
Well, I'd say if you have a many-worlds idea where the gravity-like force in your world does NOT follow an inverse square law, you might have strong effects upon stable shapes.

Probably, some mathematicians have played around with this, demonstrating various features that would have occurred for non-square laws of attraction.

Homework Helper
I think the idea about changing the metric (but not the inverse-square part as such) for gravity has merit. The Manhattan metric would yield octahedral planets, for example; the $\text{L}^\infty$ metric, cube planets. The $\text{L}^0$ metric may be too bizarre; tendrils of matter would stretch to the limit of the modified-physics space, and Brownian motion and even quantum fluctuations would seriously affect the shape of planets.

Edit: The $\text{L}^p$ norm for non-integer p (well, even for integer p) is, in general, a superellipse -- a 3D Lamé curve. Basic Math'ca code for plotting:
Code:
sq[r_] :=
RegionPlot3D[
Abs[x]^r + Abs[y]^r + Abs[z]^r <= 1, {x, -1, 1}, {y, -1,
1}, {z, -1, 1}]
This assumes that the planet will compactify itself around a single point (as happens with a body of uniform density in the real world with the $\text{L}^2$ norm); I haven't checked the physics to make sure this still holds.

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Homework Helper
Designer planets? ...I don't think it would go over very well with an audience.
Slartibartfast ?

elect_eng
Perhaps I mistook your response. You seemed to indicate that there was little need for explanation of the almost magical powers of the monolith in 2001:ASO and that lack of need seemed a reflection of the prowess of the author. I was only clarifying that there was indeed a sort of explanation, if only based in context and storytelling convention, and that the strength of the writer is not in needing little explanation but in making it seem that way.

I understand. I'm basically in perfect agreement with all you have said. My wording must not have been clear. When I said "...science fiction does allow a wide range of poetic license, and the better the poet, the more license is allowed..." I basically was trying to say something similar to what you just said.

Homework Helper
Dave, do you have a proof for this? With sufficient angular velocity and tensile strength, I don't see any obvious reason that a toroid will not be stable.

I've heard a rough estimate for the oblateness of an object to be the centripetal acceleration divided by the acceleration due to gravity at the surface. (It at least gets you in the correct order of magnitude, so a planet like Jupiter is much flatter than a planet like the Earth.)

If you slowly spun the planet up, you'd reach a point where the centripetal acceleration at the surface were equal to the gravitational acceleration. That means the equatorial matter could achieve orbit - even though that orbit might only be an inch above the surface. That's as fast as the matter should ever get, since as soon as it's in orbit, the planet isn't sweeping it along anymore. The spinning up would be a non-conservative process.

The eventual oblateness of a planet spinning this fast should be 1. In other words, the planet should wind up being a flat platter. The planet would continue to flatten, supplying new matter at the critical surface velocity, throwing new matter into orbit. Additionally, as the mass of the old planet decreased, the velocity required to throw matter into orbit would decrease, meaning new matter would be thrown into orbit faster and faster.

The newer matter tossed into orbit would collide with older matter in orbit and you'd wind up with an unstable ring. It would flow along in the shape of a ring. The outer most portion of the ring would be held in place by gravity, but chunks of the inside could break off and drift weightlessly across the inside of the ring, striking the ring in some random place, breaking off new chunks, etc. (Matter would still be held inside the plane of the ring - the weightlessness would only occur inside the ring).

The outer portion of the ring would even have a tenuous structure. The new matter colliding with the earlier matter would knock the earlier matter into a higher elliptical orbit, but the earlier matter would never reach perigee since it would hit the newer matter on the way down. That way, the ring slows as it expands, hopefully enough to hold the outer portion of the ring in contact with the inner portion. I'm not sure whether that would happen or if you'd be stuck with a ring of debris instead of a "planet". You'd have a planet plagued by constant earthquakes from the collisions on the inside if it did hold. The formation into a ring would have to be a conservative process.

But, if the planet's rotation then slowed some more - enough that the outer most objects should find an orbit lower than the ring - then the weight of the outside of the ring would start compressing the inside of the ring, just like the arches of an old Roman bridge. The force of gravity compressing the ring would finally give you the tensile strength you needed. The additional slowing down would have to be a non-conservative process since you're reducing angular velocity and the radius simultaneously.

It would be a strange place. You'd have gravity on the outside of the ring and be weightless on the inside of the ring.

It would also raise the question about what caused the planet to start spinning so fast and what caused its rotation to slow down - all without breaking the laws of conservation of energy and momentum. And whatever caused the planet to spin up would have to cease almost as soon as the ring started forming, since it would have the same effect on the matter in the ring as it did on the matter in old spherical planet. (Actually, a slight delay and a higher orbit for the outer portion of the ring would give you more room to cram all of the mass of your sphere into a toroid.) And, if the planet kept slowing down, it's weight would become so heavy that it would only be a matter of time before one of those compressed chunks on the inside of the ring were just destroyed, starting the decomposition of the entire planet. It would eventually decompose back into a sphere. So whatever was slowing the planet down would have to cease at some point if the planet were to remain stable.

So, while a toroid planet could be stable if it existed, it would take a whole lot of PFM to create it.

(Could a planet actually form in a toroid during its initial formation? I don't think so since part of the matter it accumulates comes from sweeping up debris in its orbital path.)

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Gold Member
It would be a strange place. You'd have gravity on the outside of the ring and be weightless on the inside of the ring.
Ah! It behaves just like a cross section of a hollow sphere or Dyson sphere!

Aquafire
1) What sort of gravity would allow a planet to maintain the shape of a dodecahedron?

Not that this offers an answer, but it reflects Plato's interest in such a solid.

http://www.mathpages.com/HOME/kmath096.htm" [Broken]

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Gold Member
I found that very interesting...

In R4, are there more or less than five platonic solids?
On topic, do what you want, but make it seem realistic.