Gas giant question

[Ford Prefect]

This is a fairly unusual question. I have been thinking about an engineering effort that results in encapsulating a gas giant, like Jupiter, in a shell. As I understand it, if the shell has the right diametre, then it would be possible to have earth equivalent gravity, only with oodles more area. However, I don't know how to work out what that diametre would be. Could anyone show me how to work this out?

[Dooey Jo]

You mean at what distance the gravity is the same as that on Earth? Seems to me that you'd just use the usual
F = G * (M * m) / r^2
and solve for r, setting F equal to m*g...

[Kuroneko]

Just using Newton's law will work more than well enough as an approximation; this yields a 2.27e8m diameter shell. This is somewhat less exact because Jupiter has a non-negligible ellipticity, so if the shell is spherical, there will be higher variations in gravity than on Earth.

[Steel]

If Rs is the radius of the shell, Mj is mass of gas giant jupiter, Me is mass of earth and Re is radius of earth, then for equivalent gravity from a shell around jupiter you need

Rs= Re*sqrt(Mj/Me)

Mj/Me = 317 and Re = 6400km =6.4x10^6 m

So (approximately)

Rs = 18*6.4e6 = 1.1x10^8 m radius shell, so the diameter is

2.2x10^8m

[Paolo]

The shell would be roughly four times the semi-major axis of the Jovian system. It's construction would make for an interesting mini-Dyson swarm story.

[Darth Wong]

If memory serves, Jupiter's diameter is around 1.5E8m, so the shell would be bigger than Jupiter. Therefore, if someone breached the shell, the atmosphere on the outside of the shell would rush into the hole and fall down into the gas giant. Ouch.

[RedImperator]

Besides being awesome, what would be the purpose of this construct? A Dyson swarm makes sense for capturing solar energy. Jupiter is a net radiator, but I don't think it's enough to justify the expense of such a construction project, and it's too far away from the sun for the outer surface of such a construct to be habitable. Are you thinking of a hypothetical alien solar system with a gas giant in the habitable zone?

[Darth Raptor]

While it may not be a star, couldn't a mini-Dyson built around a Jovian be used to exploit the local electromagnetic and tidal forces? If so, it could be a giant power plant and/or a "proof of concept" model for the real thing.

[Darth Wong]

Besides being awesome, what would be the purpose of this construct? A Dyson swarm makes sense for capturing solar energy. Jupiter is a net radiator, but I don't think it's enough to justify the expense of such a construction project, and it's too far away from the sun for the outer surface of such a construct to be habitable. Are you thinking of a hypothetical alien solar system with a gas giant in the habitable zone?

It would be ultra-cool as something left behind by ultra-powerful and inconceivably ancient progenitors as a habitat or experiment. And then somebody tries to figure out the geology of their anomalously large Earth-like planet, and discovers that several kilometres below the surface is a completely artificial construct ...

[Paolo]

Woops, off by three orders of magnitude.

[RedImperator]

While it may not be a star, couldn't a mini-Dyson built around a Jovian be used to exploit the local electromagnetic and tidal forces? If so, it could be a giant power plant and/or a "proof of concept" model for the real thing.

I was thinking about that, but I don't think you'd need to englobe Jupiter to do it. I've heard of schemes to tap the Io flux tube, for example, that wouldn't involve englobing anything.

It would be ultra-cool as something left behind by ultra-powerful and inconceivably ancient progenitors as a habitat or experiment. And then somebody tries to figure out the geology of their anomalously large Earth-like planet, and discovers that several kilometres below the surface is a completely artificial construct ...

That's the teaser for an entire novel right there.

[Prozac the Robert]

There's also the mass of the shell to consider.

If the thickness is 1m and the material is as dense as steel then that puts r on the order of 10^11m (assuming I haven't done something silly). I have no idea what material you'd actually need, or how dense such a material would be, but it shows that the mass of the sphere probably can't be neglected.

[Paolo]

Commericial PV run at efficiencies around 10 percent. So, complete capture of Jupiter's exitance alone would give you about three quarters power of sunlight available to capture on Earth (almost nine thousand times the world's total power output today). Of course you'll be lucky to capture a percent of that with orbiting cloud of collectors, but you have almost an order of magnitude more power coming from the Sun you can still exploit (up to an ideal 5 times solar output incident back home).

The question is whether or not it's cost effective to deploy a 1.2e8 m shell given the amount of power you can exploit. Commercial collectors usually mass around 10 kg per square meter, so today we're talking about a shell at at minimum clocks in at around the mass of 433 Eros, an NEA. So given these rough figures, this project might be within the engineering reach of space civilization that relies considerably on solar power.

[RedImperator]

You know, the more I think about this, the more exciting a story concept it becomes. I really wish I'd thought of it first, Ford.

[Sikon]

Such a shell of hundreds of thousands of kilometers circumference around Jupiter is structurally impossible. By quite a number of orders of magnitude, it can't be constructed from anything in the periodic table.

Making a structural member withstand bending stresses over a limited number of meters like real-world buildings is one thing, but doing that over spans of many millions of meters (e.g. however many millions of MPa stress) is so many orders of magnitude different as not to be plausible.

(It's like having an imaginary future car crash unharmed through solid rock at thousands of miles per hour; such may sound cool, but everything suggests that it is orders of magnitude beyond what's possible).

For a spherical shell, rotating it can cause centrifugal force counteracting the force of gravity but only along a ring segment; e.g. the stress due to gravity can be neutralized at its "equator" but not at its "poles" simultaneously. Given sufficient industrial output like self-replicating factories, it is technically possible to make rings around a planet but never a single continuous hollow shell.

More useful and practical is just to make as many astronomical number of individual habitats as desired and slowly rotate them for artificial gravity. With possible materials, such optionally can each be as huge as up to tens of kilometers or a bit larger in dimension (but not many orders of magnitude larger like the imaginary Jupiter shell).

Likewise, the common portrayal in soft sci-fi of Dyson spheres with a continuous shell around a star doesn't correspond to Freeman Dyson's suggestion. As a physicist with an understanding of the importance of quantitative evaluation of a concept in science and engineering, he did not actually suggest something so impossible. Rather, he proposed a swarm of independent constructs. In total, they would have about the same effect of intersecting a star's light as an imaginary solid shell, but no nonexistent materials are required.

[Darth Wong]

Such a shell of hundreds of thousands of kilometers circumference around Jupiter is structurally impossible. By quite a number of orders of magnitude, it can't be constructed from anything in the periodic table.

Of course. I've written similarly on my website. But sci-fi often involves constructs which require some kind of impossible super-material just to hold together, so it's not really unusual for the genre (Star Trek had an actual hard-shell Dyson Sphere, after all).

In this particular case, you can't rotate the construct at enough velocity to counteract gravity because the idea is to have atmosphere and Earth-normal gravity on the outside surface (so that it looks like a giant Earth-like panet), so you kind of need it to be rigid.

[CaptainChewbacca]

So, I imagine if you were an ancient super-race, you'd either do a complete sphere, or a 'framework' of your 'super materials' which hold your energy collectors, stabilizers, forcefield generators, and of course your 'Ancient Hall of Awesome' (TM).

Over that, you put 10-15 kilometers of soil and rock, as well as your oceans. Might have to use some of that energy to shape/control erosion so that a river or ocean doesn't eat through.

Has anyone crunched the numbers to find out how many Earth Surface Areas such a world would be equivalent to?

Also, is the size of this thing still sufficiently small that you could have multiple galilean moons, also supporting life, orbiting around it? THAT would be cool.

[Surlethe]

Has anyone crunched the numbers to find out how many Earth Surface Areas such a world would be equivalent to?

The surface area of this monster is some 1.5E17 m^2, while the surface area of Earth is a mere 5.1E8 m^2. Th gas-giant sphere is all of 290 million Earths, plus change.

As far as the atmosphere problem, you might solve that by dividing the surface into cells, so if a meteor or something punched a hole in the structure you would only lose the air in one portion of it.

[Paolo]

Quick plot of configurations with densities between 100 (average density of commercial 1 m^2, 5 cm thick solar panels) and 8000 kg/m^3 (steel) yield in plane stresses ranging from 115 GPa to 4.5 TPa. As pointed out, in plane stress is insensitive to thickness for a spherical pressure vessel given a constant density.

[RedImperator]

Has anyone crunched the numbers to find out how many Earth Surface Areas such a world would be equivalent to?

The surface area of this monster is some 1.5E17 m^2, while the surface area of Earth is a mere 5.1E8 m^2. Th gas-giant sphere is all of 290 million Earths, plus change.

As far as the atmosphere problem, you might solve that by dividing the surface into cells, so if a meteor or something punched a hole in the structure you would only lose the air in one portion of it.

As long as we're building the thing out of wanktanium, we might as well make it self-healing. Or have the Mysterious Ancient Maintenance Droids still active.

[CaptainChewbacca]

Has anyone crunched the numbers to find out how many Earth Surface Areas such a world would be equivalent to?

The surface area of this monster is some 1.5E17 m^2, while the surface area of Earth is a mere 5.1E8 m^2. Th gas-giant sphere is all of 290 million Earths, plus change.

As far as the atmosphere problem, you might solve that by dividing the surface into cells, so if a meteor or something punched a hole in the structure you would only lose the air in one portion of it.

Hm... in my looking I found a rule-of-thumb that if you're going for earthlike gravity on the surface, the surface area will be equal to the gravity disparity times earth's surface, i.e. a body with 100 earth masses surrounded by a shell with a surface gravity of 1 g will have a surface area equal to 100 earth areas.

[Ford Prefect]

Ah, thank you very much everybody. I was well aware of the engineering complexity involved. However, I was enamoured by the sheer scale of such a construct, from the sheer endlessness of a city constructed across its surface, down to the tendril-like shafts spiralling down to suck out the Jovian's precious planetery fluids. Admittedly, I can't reasonably make a bit of it fall in, so to speak, and have characters staring down in awe at the storm-wracked giant at the core of their home.

[CaptainChewbacca]

Ah, thank you very much everybody. I was well aware of the engineering complexity involved. However, I was enamoured by the sheer scale of such a construct, from the sheer endlessness of a city constructed across its surface, down to the tendril-like shafts spiralling down to suck out the Jovian's precious planetery fluids. Admittedly, I can't reasonably make a bit of it fall in, so to speak, and have characters staring down in awe at the storm-wracked giant at the core of their home.

You could have them find an 'access hatch' to some secondary control chamber which is equipped with a window and service corridor over 'ventilation span AR2190-B', which is a giant swirling vortext 1000 miles across.

That'd be cool.

[Darth Wong]

Once you get inside the superstructure, you can presumably find monitoring stations and all manner of other equipment which allows you to see down, or airlocks.

If it were made into a movie, the sight of a guy going out on an airlock and losing his grip would be quite dramatic. Falling thousands of kilometres toward an inevitable fate of being crushed by the atmosphere of the giant. He would have time to talk to the others via radio as he falls.

[Ender]

Charles Stross did it in Accelerando, though it was Saturn there. It wasn't a solid shell - it was a series of huge multi km hexagons linked together, with a kind of shell holding the atmosphere in. Think wrapping the planet in pieces of bubblewrap for a mental image. They were IIRC, diamondoid construction with huge bags of hydrogen beneath them to keep them aloft. Always meant to run the numbers and see if they would float, never bothered.

Anyway, it occurs to me that in any big space opera setting this would be superior to the usual "agri-world" in that it has greater land area and the controlled environment means that once could control things like the weather.