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What would a toroidal planet be like?

by EskWIRED
Tags: planet, toroidal
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EskWIRED
#1
Jan16-13, 07:13 PM
P: 97
You know, donut shaped.

ISTM that the rivers would run towards the center, rather than towards lower altitudes.

Depending upon the proportions of the planet, anything on the surface of the "hole" in the middle of Planet Toroid could experience negative gravity and float towards the center of mass in mid-air (or mid-vacuum). It would get crowded there after a while.


The geometry might be WAY different. On some toroiplanets significantly shorter routes could be had by veering towards the center, if you were equipped for any nasty gravity effects. Only the bravest and most intrepid would stray TOO far from the outer circumference.

What else?
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phinds
#2
Jan16-13, 07:29 PM
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Since the actual formation of such a planet would be impossible, it would have to be man-made and that would be QUITE an undertaking for no good reason.

If you posit its existence, however, it WOULD lead to some weird results, as you postulate.
EskWIRED
#3
Jan16-13, 07:39 PM
P: 97
Quote Quote by phinds View Post
Since the actual formation of such a planet would be impossible, it would have to be man-made and that would be QUITE an undertaking for no good reason.

If you posit its existence, however, it WOULD lead to some weird results, as you postulate.
I thought of another one - with the right dimensions and topography, some planets would allow vacationers to gently float upwards if they traveled to high altitudes in the central regions. They could tether themselves in place, bobbing and floating in the breeze.

Ryan_m_b
#4
Jan17-13, 05:32 AM
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What would a toroidal planet be like?

I may be wrong here but I'm pretty sure such a planet would be impossible without some unobtanium. To get a torus you'd have to spin it to stop all the mass collapsing into a sphere but if you spin it to the extent that a hole forms in the middle then hasn't the centrifugal force completely overcome the gravitational binding energy? In other words if the spin is fast enough to propel all the mass of a planet away from the centre then why would it stop and stabilise at a higher altitude to form a torus?

I could be completely wrong as I say but it seems to me you'd need to make a ring of impossibly strong material and dump a planets worth of mass on the outside to get what you're proposing.
EskWIRED
#5
Jan17-13, 08:43 AM
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Quote Quote by Ryan_m_b View Post

I could be completely wrong as I say but it seems to me
Using your "it seems to me" test, it seems to me that you are completely correct. Bummer.


But what if you took an existing planet that did not have a molten center, lopped off the polar regions and bored a hole through the axis? Would there be structural issues with such a thing, other than the risk of the center collapsing inwards? If you started with a giant slowly rotating sphere of metal and rock then there would be no issue with the material getting flung off into an accretion disk, ISTM.
Ryan_m_b
#6
Jan17-13, 08:49 AM
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Quote Quote by EskWIRED View Post
But what if you took an existing planet that did not have a molten center, lopped off the polar regions and bored a hole through the axis? Would there be structural issues with such a thing, other than the risk of the center collapsing inwards? If you started with a giant slowly rotating sphere of metal and rock then there would be no issue with the material getting flung off into an accretion disk instead of forming a solid torus, no?
The problem is within the very definition of planet which IIRC is a celestial body of sufficient mass to collapse to a spheroid. If you cored a world like an apple it would just collapse in on itself, nothing would be strong enough to hold the planet up.
EskWIRED
#7
Jan17-13, 08:59 AM
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Quote Quote by Ryan_m_b View Post
The problem is within the very definition of planet which IIRC is a celestial body of sufficient mass to collapse to a spheroid. If you cored a world like an apple it would just collapse in on itself, nothing would be strong enough to hold the planet up.

I see what you are saying. It's very interesting. I find it very disappointing, however :)

Thanks.
meldraft
#8
Jan17-13, 10:20 AM
P: 280
Xmmmm but shouldn't there be an ideal inner to outer radius ratio and angular momentum combination for which it doesn't collapse on itself? So to speak if you had a cosmic mold to create the planet and just put it there and spin it, it would stay there.

P.S. It would probably need to be smaller than a planet of course as Ryan_m_b points out.
mfb
#9
Jan17-13, 11:02 AM
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Every toroid would have to rely on internal stiffness to keep its shape - if you make it small enough, everything is possible, and the size limit is just given by the materials you can use.

I would expect that r<<R (with the usual radius definitions) gives an attracting surface everywhere, but I did not check this. In this case, there could be a limit ##c=\frac{r}{R}## for the surface gravity on the inside...
ImaLooser
#10
Jan18-13, 11:17 PM
P: 570
Quote Quote by EskWIRED View Post
I see what you are saying. It's very interesting. I find it very disappointing, however :)

Thanks.
Yes, hes' right. It is fun to think about though. If you had a hollow planet there would no gravity in the interior.

Someone mentioned high enough spin, but I'm pretty sure that would be unstable. I feel certain that the forces would be so great that it would be impractical to balance them perfectly, and any little glitch would cause the thing to disintegrate.
mrspeedybob
#11
Jan19-13, 06:44 AM
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Would it be possible for such a "planet" to exist as a ring around another gravitating body? For example, what if the earth were replaced by a torus which occupied all the volume that earth passes through in its orbit around the sun? This torus would revolve around the sun at 1 rev / year.

I'm not saying anything about how such an object could form or be built, but if it were, could it continue to exist?
mfb
#12
Jan19-13, 06:49 AM
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It would be unstable against shifts of its orbit, variations from a perfect circle and internal density variations. It might be possible to build this as artificial object, but it is not stable without (probably unrealistic) internal stiffness, active correction mechanisms or whatever.
EskWIRED
#13
Jan19-13, 09:32 AM
P: 97
Quote Quote by ImaLooser View Post
If you had a hollow planet there would no gravity in the interior.


Is that correct? My understanding is that there would be gravity in the interior, pulling one towards the closest part of the shell. If one were to be in the exact center, one would remain motionless, because the gravity woudl be the same in all directions.

But there would be gravity in the interior.
mfb
#14
Jan19-13, 09:52 AM
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If the mass has a spherical symmetry, gravity from all parts outside of you exactly cancels. You can show this with Gauss law (or integration over the sphere).
phinds
#15
Jan19-13, 10:08 AM
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Quote Quote by EskWIRED View Post
But there would be gravity in the interior.
No, at any point inside a sphere gravity is only a function of the amount of mass inside a sphyerical shell defined by that point. In the case you are talking about, there IS no mass inside such a coordinate sphere. I think that's a layman's way of saying what mfb just said.

EDIT: in other words, as you move towards the center of a solid sphere, gravity decreases until at the center it is zero. In a hollow sphere, you're at zero as soon as you move inside the shell.
ImaLooser
#16
Jan20-13, 02:24 AM
P: 570
Quote Quote by mrspeedybob View Post
Would it be possible for such a "planet" to exist as a ring around another gravitating body? For example, what if the earth were replaced by a torus which occupied all the volume that earth passes through in its orbit around the sun? This torus would revolve around the sun at 1 rev / year.

I'm not saying anything about how such an object could form or be built, but if it were, could it continue to exist?
Larry Niven invented something like that called Ringworld. MIT students figured out it would be unstable and would fall into the Sun.
ImaLooser
#17
Jan20-13, 02:30 AM
P: 570
Quote Quote by mrspeedybob View Post
Would it be possible for such a "planet" to exist as a ring around another gravitating body? For example, what if the earth were replaced by a torus which occupied all the volume that earth passes through in its orbit around the sun? This torus would revolve around the sun at 1 rev / year.

I'm not saying anything about how such an object could form or be built, but if it were, could it continue to exist?

A toroidal planet -- you could have a supernova. Supernovas tend to blow up asymmetrically, and contain lots of iron and some carbon. It could blow out an expanding smoke ring of steel that freezes before it can collapse. Very unlikely but maybe remotely possible. I expect steel is too soft to sustain planetary-style gravity, but it could be fairly large. That's the best I can do so far.


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