Torus planets

[Moontanman]

What would it be like to live on a toroidal planet? Not likely to form but it would be very interesting place!

 

 

http://www.aleph.se/andart/archives/2014/02/torusearth.html

[Endy0816]

Definitely sounds that way. Good find.

[Nicholas Kang]

Please provide me the Physics of this planet or its specification.

 

Please explain is it possible that this planet can form in our current observable universe by the current knowledge of astronomy and astrophysics.

 

Thanks.

 

Regards,

 

Nicholas Kang

Edited June 2, 2014 by Nicholas Kang

[pwagen]

It looks like a toroid planet is not forbidden by the laws of physics. It is just darn unlikely to ever form naturally, and likely will go unstable over geological timescales because of outside disturbances. So if we decide to assume it just is there, perhaps due to an advanced civilization with more aesthetics than sanity, what are its properties?

From the link in the OP.

[imatfaal]

I wonder if the weather patterns drawn on the artists impression are correct. I cannot quite get my head around the interaction of the coriolis effect and hadley cells on a torus.

 

Thinking aloud - if the sun is roughly on the line of the equator then the inner equator will be very very cold and I think you could almost map to a sphere/globe by mapping the inner equator to arctic circle / antarctic. But hadley cells rotate the air because hot air rises - but on the "inside" surface would hot air rise enough to create circulation? It is this circulation that allows coriolis to create major wind systerms etc

 

I am pretty sure that gravity would always be attractive towards the core of the ring - apart from a completely unstable point of zero gravity at the very centre of the hole (contrary to shell theorem for a sphere).

[Delta1212]

I wonder if the weather patterns drawn on the artists impression are correct. I cannot quite get my head around the interaction of the coriolis effect and hadley cells on a torus.

 

Thinking aloud - if the sun is roughly on the line of the equator then the inner equator will be very very cold and I think you could almost map to a sphere/globe by mapping the inner equator to arctic circle / antarctic. But hadley cells rotate the air because hot air rises - but on the "inside" surface would hot air rise enough to create circulation? It is this circulation that allows coriolis to create major wind systerms etc

 

I am pretty sure that gravity would always be attractive towards the core of the ring - apart from a completely unstable point of zero gravity at the very centre of the hole (contrary to shell theorem for a sphere).

I think the "donut hole" should have zero g as long as you're in line with a plane running through the equator. The surface along the inner equator would have an apparent gravity pointing toward the core from the spin, though. I think.

[imatfaal]

I think the "donut hole" should have zero g as long as you're in line with a plane running through the equator. The surface along the inner equator would have an apparent gravity pointing toward the core from the spin, though. I think.

 

Not sure you are right there.

 

Only the very centre of the hole would have zero g - the inner surface would have g. A spherical shell cancels out as a particle internal to the sphere is influenced by an area on each side of it and the influence is governed by the inverse square law (area and inverse square match) - whereas in a ring a test particle is influence by a length/arc of the ring but still governed by the inverse square law (the two factors no longer have same dimension). Thus in a sphere as you move toward one side (r falling) the influence rises with 1/r^2 and the area/mass which causes that falls with r^2 and vice versa = equilibrium. But in a ring the influence still rises with 1/r^2 but the length/mass only falls with 1/r.

 

Obviously the above is an exaggeration with a very thin ring - but the principle applies to fatter rings

[Moontanman]

I remember reading a science fiction book about a very rapidly spinning planet that was on effect shaped like an oval, gravity at the poles was intense but very low at the equator.

 

http://en.wikipedia.org/wiki/Mission_of_Gravity

[imatfaal]

I remember reading a science fiction book about a very rapidly spinning planet that was on effect shaped like an oval, gravity at the poles was intense but very low at the equator.

 

http://en.wikipedia.org/wiki/Mission_of_Gravity

 

It would be the shape of an m&m with the axis through the narrowest section - if you are spinning enough to counter massive gravity then the planet would bulge massively around the equator. I would hate to do the maths

[Moontanman]

 

It would be the shape of an m&m with the axis through the narrowest section - if you are spinning enough to counter massive gravity then the planet would bulge massively around the equator. I would hate to do the maths

 

 

The book was written in 1958 by Hal Clement, he made it as factual as possible, it was an interesting read, I think I might still have a copy someplace.. 700g at the poles 3g at the equator.. http://en.wikipedia.org/wiki/Hal_Clement evidently he later recalculated the gravity at the poles as 250g...

 

Hal Clement, Asimov, and Heinlein were my favorite writers when I was a little boy..

The idea of a torus shaped planet is very intriguing, The more i look the more interesting it becomes.

 

I have been working a story around the type of planets found in the book by Robert Forward http://en.wikipedia.org/wiki/Rocheworld, I wanted to give it a bit of a twist so that both planets are earth mass and share an atmosphere so that flying animals can migrate from one planet to the other much like flying animals migrate from the poles to the equator on Earth.

 

I have been told that such a configuration would not be stable over geologic time but it's a story...

[Fuzzwood]

One thing I see happening on this planet is that you have to provide the location where your weight was taken for your identification card.

[MigL]

Don't see how this configuration could be stable. As Imatfaal points out gravity is always towards the centre, and zero at the centre, in effect the exact same as for a sperical configuration, along with the same forces trying to collapse it spherically. There is no reason why a 'donut hole' would form, rather if the spin was excessive, after flattening it would start coming apart at the outer edges where the forces are highest.

 

You also still have all those old yellowed paperback sci-fi books from the 50s and up, Moontanman ?

The first book of the type I ever read was 'Galactic Derelict' by Andre Norton ( actually a crazy cat woman ) and I was hooked. Read all of her stuff and moved on to other writers. My favourite R.L. Foreward is still 'Dragon's Egg', but I've read some of his others.

[Moontanman]

Don't see how this configuration could be stable. As Imatfaal points out gravity is always towards the centre, and zero at the centre, in effect the exact same as for a sperical configuration, along with the same forces trying to collapse it spherically. There is no reason why a 'donut hole' would form, rather if the spin was excessive, after flattening it would start coming apart at the outer edges where the forces are highest.

 

You also still have all those old yellowed paperback sci-fi books from the 50s and up, Moontanman ?

The first book of the type I ever read was 'Galactic Derelict' by Andre Norton ( actually a crazy cat woman ) and I was hooked. Read all of her stuff and moved on to other writers. My favourite R.L. Foreward is still 'Dragon's Egg', but I've read some of his others.

 

 

Andre Norton was one of my favs as well. Forerunner was the first of hers i read..

[J.C.MacSwell]

Any material not on the equatorial plane would have a gravitational component toward it, that could not possibly be balanced by angular momentum.

 

That statement may not be exact for variations in density, but would hold for material furthest from the equatorial plane in any case.

 

Even on the equatorial plane balance cannot be achieved, since the angular velocity must be less the farther from the centre.

 

So it is not balanced, never mind stable, and is not possible for any mass the size of a planet, composed of known materials. The shape would be dominated by gravitational pressure...tending toward a sphere..and angular momentum...which would flatten it toward the poles

Edited June 3, 2014 by J.C.MacSwell

[arc]

Taking inspiration from the science fiction perspective, could we beef up the structure of this planet? Can a different origin be contrived for a solid iron ring to form the core of the toroid. Maybe a remnant of a core from a cold dead star, broken into pieces by some type of collision or ? The ring shaped piece of iron with an uneven surface resembling irregular facets drifted through the cosmos and was caught up with other star dust into a newly forming solar systems accretion disc.

 

Now, with this heavily magnetised toroidal iron ring in place could a crustal layer form. Maybe a completely watered planet producing inductive heating from the salt laden waters circulating the heavily magnetized core ring. This should solve the stress issues. It would not flatten toward the poles and the salt water circulating in one direction may in time smooth the ocean floor surface while the rotating water helps stabilize the planet's rotation. In time the core could reshape into a more uniform ring and produce in the thick mud a new deep water life based around electrosynthesis.

[Moontanman]

Taking inspiration from the science fiction perspective, could we beef up the structure of this planet? Can a different origin be contrived for a solid iron ring to form the core of the toroid. Maybe a remnant of a core from a cold dead star, broken into pieces by some type of collision or ? The ring shaped piece of iron with an uneven surface resembling irregular facets drifted through the cosmos and was caught up with other star dust into a newly forming solar systems accretion disc.

 

Now, with this heavily magnetised toroidal iron ring in place could a crustal layer form. Maybe a completely watered planet producing inductive heating from the salt laden waters circulating the heavily magnetized core ring. This should solve the stress issues. It would not flatten toward the poles and the salt water circulating in one direction may in time smooth the ocean floor surface while the rotating water helps stabilize the planet's rotation. In time the core could reshape into a more uniform ring and produce in the thick mud a new deep water life based around electrosynthesis.

 

 

I was thinking along similar lines but more of an artificial word, with a torus core of some artificial material along the lines of Niven's ring world. It wouldn't have to spin as fast, make the torus 12,000 miles thick and 36 thousand miles across, the hole in the doughnut would be 12,000 miles across. Spin so it would have a 36 hour day, I'm not sure how to calculate the surface area of a torus but I'm betting it would be equal to several Earths. Gravity should be around Earth normal or a bit above...

 

Makes for some interesting possible story lines..

[MigL]

Niven's 'Ringworld' is stable because it encircles its sun, i.e. it is a ring occupying the total orbit of its terraformed former planet.

What we are discussing here is a toroidal planet orbiting its sun. Definitely not stable.

[Janus]

Niven's 'Ringworld' is stable because it encircles its sun, i.e. it is a ring occupying the total orbit of its terraformed former planet.

What we are discussing here is a toroidal planet orbiting its sun. Definitely not stable.

The "Ringworld" isn't really stable either. It would take just the slightest nudge and the structure would drift into its star. (for the same reason James Maxwell proved that Saturn's rings could not be solid.)

 

After having this pointed out, Niven corrected for this by including "attitude jets" which would correct for said drift in the later novels ( One of the plots revolved around the idea that one of the civilizations on the ringworld has cannibalized the attitude jets to make spacecraft, leaving the ringworld with too few to do the job.)

[MigL]

Thanks for pointing that out Janus.

But at least Ringworld has the slight possibility of acheiving stability for a brief instant, like a pencil falling to the ground and landing on its tip.

Torusplanet, on the other hand, cannot even form, like a pencil that's glued to your hand and can't drop.

[md65536]

Torusplanet, on the other hand, cannot even form, like a pencil that's glued to your hand and can't drop.

What would happen if you had say a very dense planet, with a very dense thin ring around it (like neutron star density or something). Then add an accretion disk of "normal" matter. I imagine the matter would form a thick even shell around the dense thin ring, if gravitational pull was effectively always toward the nearest point on the ring. If you knocked out the center planet with a collision of another massive object, while the ring-world is solidifying but before it hits the planet, couldn't you end up with such a toroid?

 

Edit: Or would the formation of the core ring be impossible if it was that significantly massive?

Edited June 5, 2014 by md65536

[arc]

Torusplanet, on the other hand, cannot even form, like . . . .

Considering how vast the cosmos is . . . . . . . . I can't commit to that term.

[MigL]

Your edit was accurate md65536,

 

Considering how vast the cosmos is arc.........gravity acts the same all over,

[arc]

Your edit was accurate md65536,

 

Considering how vast the cosmos is arc.........gravity acts the same all over,

 

You, I am sure, are correct. I am not adequately educated in these matters. But I always try to take the safe position and view things in regards to its probability with the standard "very unlikely" or "highly unlikely" or everyones favorite - most probably very highly unlikely. I just have seen in the past history of science, and generally with anything regarding human understanding of nature, there have been some real surprises. And you have to admit we have not seen anything yet when it comes to "what's out there".

 

I would appreciate your opinion on why a more durable core as mention by me and others, would not help this planet's structure survive the forces involved, even if for a short while longer, regardless of how short of time it is. Can you conceive of any circumstances that could produce a viable result. A great science fiction plot could be at stake!

[Acme]

...Torusplanet, on the other hand, cannot even form, like a pencil that's glued to your hand and can't drop.

According to the calculations by the authors of the paper linked to in the OP, it could form. The work is copyright protected so I can only direct readers to page 687 in Summary and Discussion that gives the conditions for formation.

 

Toroidal figures of equilibrium. Wong, C.-Y. Astrophysical Journal, Vol. 190, p. 675 - 694

[hoola]

I can imagine the torus planet could be built, and would probably have to be stabilized by internal structures not occuring naturally, and also a large moon(s) in orbit around it, just as our moon stabilizes our planet...I could also see the atmosphere having a thinner but loftier ceiling at the torus center hole...perhaps losing atmosphere into space at the center unless some mechanism is used to stop the loss..(giant sealed bubble halves jutting out from center?).and being a really cool region to go hang gliding with the lowered gravity...if you could keep atmospheric pressure pumped up...with a no gravity region at dead center..

Edited June 6, 2014 by hoola