Torus Planet

[Werner]

Centerline radius: 247,000 km
Thickness: 12,800 km
Mass: 200 Earth masses
Rotational rate at self orbital velocity: 24 hours
Surface Area: 121 times Earth

This object has about twice the mass of Saturn with the surface area of Jupiter. It orbits a G-class star within its habitable zone.

 

[BackworldTraveller]

What stops it collapsing into a sphere?

 

[Werner]

Centrifugal force, same thing that prevents the Earth from falling into the Sun.

 

[whulorigan]

Centrifugal force, same thing that prevents the Earth from falling into the Sun.

How fast was it spinning when it was molten and forming in order to become oblate enough to form a torus, and why has it lost that angular momentum since?

 

[Werner]

How fast was it spinning when it was molten and forming in order to become oblate enough to form a torus, and why has it lost that angular momentum since?

Why do you assume that it has? Do ringworlds stop spinning?

 

[whulorigan]

Why do you assume that it has? Do ringworlds stop spinning?

Not stopped, but rather slowed its rotation rate. Otherwise, what will be its effective surface gravity when you compare its natural gravity due to mass combined with its centrifugal force due to rotation?

Also, unlike a sphere gravity will not be directed uniformly towards the "interior" of the torus-mass either. The interior-facing surface of the torus will be at a different gravitational potential than the outer-facing surface (and so will the "upper" and "lower" surfaces that are perpendicular to the interior and exterior surfaces). That will make for interesting atmospheric dynamics, presuming it has one. Gravity for a toroid from its center of rotation to its outer-surface can be roughly approximated as directed toward the center-point along the axis of rotation, and will fall off from the center point as 1/R (not 1/R²). The magnitude of the gravity will be based on the amount of mass enclosed by a notional cylinder symmetric about the axis of rotation, out to a radius "r" defined by the point at which you wish to measure it. This likely means that the interior-facing surface of rotation will be in microgravity; full gravity will be encountered along the outer-facing surface of rotation.

Discussion: https://www.reddit.com/r/askscience/comments/6isvfm/physics_how_does_gravity_work_on_a_torus_world/

Ringworlds are not naturally formed, but are artificially constructed of super/ultra-dense materials, and use rotation to create a habitat along the inner surface with "gravity" due to centrifugal force. The ringworld needs the ultra-dense construction material in order to withstand the stresses associated with the rotation of an object of that size.


I am of course assuming that you are envisioning this world as a "rocky/solid" world with the outer-surface of the torus to live upon, and not either a toroidal "gas-giant" or a solid torus with habitats bored into the interior (please correct me if my presupposition is incorrect).

 

[coliver988]

or perhaps something more like Niven's the Integral Trees: "the story is heavily influenced by the setting: a gas torus, a ring of air around a neutron star."

 

[whulorigan]

or perhaps something more like Niven's the Integral Trees: "the story is heavily influenced by the setting: a gas torus, a ring of air around a neutron star."

I do not know if I have read that one. Is it in one of his anthologies?

 

[BackworldTraveller]

Not stopped, but rather slowed its rotation rate. Otherwise, what will be its effective surface gravity when you compare its natural gravity due to mass combined with its centrifugal force due to rotation?

With it's stated spin speed, it's slowed a lot...but it won't have cooled enough to be solid so it still collapses!

So what could have slowed it? No nearby moon to spin up.

 

[BackworldTraveller]

I do not know if I have read that one. Is it in one of his anthologies?

https://www.google.co.uk/url?sa=t&r...tegral_Trees&usg=AOvVaw2CD4U3VLlr3am4F6tcEAxj

 

[whulorigan]

With it's stated spin speed, it's slowed a lot...but it won't have cooled enough to be solid so it still collapses!

So what could have slowed it? No nearby moon to spin up.

Could it be close-orbiting a massive Gas Giant or Brown Dwarf? What if it is in orbital resonance with some other body but with retrograde rotation? (I am "spit-balling" - don't know if that would help or not).

 

[Werner]

Not stopped, but rather slowed its rotation rate. Otherwise, what will be its effective surface gravity when you compare its natural gravity due to mass combined with its centrifugal force due to rotation?

Also, unlike a sphere gravity will not be directed uniformly towards the "interior" of the torus-mass either. The interior-facing surface of the torus will be at a different gravitational potential than the outer-facing surface (and so will the "upper" and "lower" surfaces that are perpendicular to the interior and exterior surfaces). That will make for interesting atmospheric dynamics, presuming it has one. Gravity for a toroid from its center of rotation to its outer-surface can be roughly approximated as directed toward the center-point along the axis of rotation, and will fall off from the center point as 1/R (not 1/R²). The magnitude of the gravity will be based on the amount of mass enclosed by a notional cylinder symmetric about the axis of rotation, out to a radius "r" defined by the point at which you wish to measure it. This likely means that the interior-facing surface of rotation will be in microgravity; full gravity will be encountered along the outer-facing surface of rotation.

Discussion: https://www.reddit.com/r/askscience/comments/6isvfm/physics_how_does_gravity_work_on_a_torus_world/

Ringworlds are not naturally formed, but are artificially constructed of super/ultra-dense materials, and use rotation to create a habitat along the inner surface with "gravity" due to centrifugal force. The ringworld needs the ultra-dense construction material in order to withstand the stresses associated with the rotation of an object of that size.


I am of course assuming that you are envisioning this world as a "rocky/solid" world with the outer-surface of the torus to live upon, and not either a toroidal "gas-giant" or a solid torus with habitats bored into the interior (please correct me if my presupposition is incorrect).

Okay its 247,000 km in radius, and 12,800 km thick. The radius is measured at the centerline of the tube, that means you subtract 6400 km to get the inner radius 240,600 km, and you add 6400 km to get the outer radius 253,400 km. The distance between opposite ends of B the torus is twice the radius 494,000 km. The diameter of the hole is 18.8 Earth diameters across. Gravity on the inner surface should be around 1-g - 1/37.5 -g or about 0.973333-g.

 

[Werner]

Could it be close-orbiting a massive Gas Giant or Brown Dwarf? What if it is in orbital resonance with some other body but with retrograde rotation? (I am "spit-balling" - don't know if that would help or not).

A torus world is in all likelihood not a natural planet, it is easier to build than a ringworld or a banks orbital but it does have to be build, nature will not do it for us. Why? If the torus world started out as molten the liquid rock in the torus will tend to ball up in on spot, a torus world needs to start off as solid so liquid rock cannot flow.

 

[willtron3030]

Are we discussing a natural torus, or a planetary-scale construct? Because the first thing that occurred to me was Heaven's River, the "Bobiverse" novel by Dennis E. Taylor. The artifact is a topopolis. [wikipedia link]

 

[BackworldTraveller]

A torus world is in all likelihood not a natural planet, it is easier to build than a ringworld or a banks orbital but it does have to be build, nature will not do it for us. Why? If the torus world started out as molten the liquid rock in the torus will tend to ball up in on spot, a torus world needs to start off as solid so liquid rock cannot flow.

Issues...
How to assemble it cold. Infalling rocks generate heat when they meet the central body.

At the masses and pressures in this model the term "Solid" is somewhat academic. Even "solids" flow under enough pressure. The total mass is huge. 1.0 Mj. n.b. This is more high-density rock in one place than the entire solar system! At just 12km deep, the solid rock is sufficiently plastic to close a borehole while it's being drilled.

Even circling at once per 24 hours, the inward pressure due to gravity is still large enough that the rock on the inner edge will be plastic...which allows the inner edge circumference to become smaller. The shrinkage will generate heat (which makes the whole more plastic) and rotational energy. Which continues until a sphere is reached and the whole is spun up to quite a speed (no I can't be bothered with the maths).

 

[Enoki]

Not to be a wet blanket, but it begs the question, Why build it at all? What advantage(s) accrues from spending that much effort and material on it's construction?

Once you have jump capable ships or even just the ability to terraform--something you'd have to have to build the toroid--and ships capable of moving between system planets in a week or less, why not just terraform those, or even make a few more if you need to rather than build this huge structure?

Is there anything preventing a civilization capable of building a ring planet from simply accruing enough material to build another planet-planet in the same orbit as one they already inhabit? Wouldn't that be simpler?

 

[Werner]

Issues...
How to assemble it cold. Infalling rocks generate heat when they meet the central body.

At the masses and pressures in this model the term "Solid" is somewhat academic. Even "solids" flow under enough pressure. The total mass is huge. 1.0 Mj. n.b. This is more high-density rock in one place than the entire solar system! At just 12km deep, the solid rock is sufficiently plastic to close a borehole while it's being drilled.

Even circling at once per 24 hours, the inward pressure due to gravity is still large enough that the rock on the inner edge will be plastic...which allows the inner edge circumference to become smaller. The shrinkage will generate heat (which makes the whole more plastic) and rotational energy. Which continues until a sphere is reached and the whole is spun up to quite a speed (no I can't be bothered with the maths).

You first construct a framework and then you fill it in. A torus has more surface area to radiate heat out of than does a sphere, it will cool faster for a given amount of volume. You can also segregate the flow of molten material inside,

 

[Grav_Moped]

Not to be a wet blanket, but it begs the question, Why build it at all? What advantage(s) accrues from spending that much effort and material on it's construction?

Once you have jump capable ships or even just the ability to terraform--something you'd have to have to build the toroid--and ships capable of moving between system planets in a week or less, why not just terraform those, or even make a few more if you need to rather than build this huge structure?

Is there anything preventing a civilization capable of building a ring planet from simply accruing enough material to build another planet-planet in the same orbit as one they already inhabit? Wouldn't that be simpler?

Because aliens have alien motivations, I guess.

 

[AtlanticFriend]

Not to be a wet blanket, but it begs the question, Why build it at all? What advantage(s) accrues from spending that much effort and material on it's construction?

To show that it can be done? To acquire data on the project's feasibility/infeasibility? To be able to say to Grandfather Yaskoyday "Here Grandad, it's a bit oddly shaped but I did it all by myself" ? (and for what we know, maybe that is what drove Grandfather off the edge ).

 

[Werner]

To show that it can be done? To acquire data on the project's feasibility/infeasibility? To be able to say to Grandfather Yaskoyday "Here Grandad, it's a bit oddly shaped but I did it all by myself" ? (and for what we know, maybe that is what drove Grandfather off the edge ).

It is more comprehensible than ringworld, only 121 Earths of living space, not 3 million!