Walking on a neutronium Dyson Sphere

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Eebster the Great
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Walking on a neutronium Dyson Sphere

Postby Eebster the Great » Thu Feb 09, 2017 6:56 am UTC

When considering the preposterous scenarios presented to us in science fiction, we are frequently confronted with magnitudes that defy ordinary reason. Consider for instance "The Masterpiece Society" in Star Trek: The Next Generation. In this episode, the Enterprise encounters a Dyson sphere 1 AU in diameter constructed of a "neutronium-carbon alloy" (whatever that means). If we suppose this is similar to actual neutronium, is it plausible that a human could stand on it?

The answer is contingent on a couple of factors: specifically the thickness of the spherical shell and the density of the material. These values are so poorly constrained by the context of the episode and so poorly understood by modern physics, that a range of values spanning a good 8 orders of magnitude or so are possible. Values in which standing up without assistance is possible are, surprisingly, well within that range. Is there something wrong with my analysis here? Is there any way astrophysics could constrain such a value (without pointing out that neutronium is obviously not stable when not under immense pressure, or that acquiring so much of it is effectively impossible)?

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Re: Walking on a neutronium Dyson Sphere

Postby commodorejohn » Thu Feb 09, 2017 7:21 am UTC

Think I've found a title for that 30-minute Krautrock instrumental I've always wanted to write!
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Re: Walking on a neutronium Dyson Sphere

Postby Nicias » Thu Feb 09, 2017 3:03 pm UTC

A little alpha'ing gave this:

https://www.wolframalpha.com/input/?i=(standard+Gravity)%2F(Gravitational+Constant)%2F(4+Pi)%2F(1000+meters)

If the shell is 1 km thick it has to be as dense as the densest white dwarfs.

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Re: Walking on a neutronium Dyson Sphere

Postby Eebster the Great » Thu Feb 09, 2017 4:29 pm UTC

Neutron stars are an awful lot denser than white dwarfs. And the shell was nowhere near a kilometer thick, just a few meters.

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Re: Walking on a neutronium Dyson Sphere

Postby speising » Thu Feb 09, 2017 6:40 pm UTC

I think you mean the episode Relics?
The dyson sphere there was quite a bit thicker than a few meters:
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That small thing in the middle is the Enterprise.

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Re: Walking on a neutronium Dyson Sphere

Postby Soupspoon » Thu Feb 09, 2017 9:37 pm UTC

In the Trekverse, it's rather hard to be all Hard Science about local gravity, as between the "gravity plating" (as anachronistically installed by Sisko in his recreated historic bajoran solar-flier for ease of filming crew comfort) and the slightly laggy inertial dampening fields, everyone tends to experience plot-conducive gravitational intensity and orientation at all times...

(Note: Star Wars also plays with expectations "as convenient".)

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Re: Walking on a neutronium Dyson Sphere

Postby gmalivuk » Thu Feb 09, 2017 10:22 pm UTC

Nicias wrote:A little alpha'ing gave this:

https://www.wolframalpha.com/input/?i=(standard+Gravity)%2F(Gravitational+Constant)%2F(4+Pi)%2F(1000+meters)

If the shell is 1 km thick it has to be as dense as the densest white dwarfs.

What is it that you think that equation shows?
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Re: Walking on a neutronium Dyson Sphere

Postby Moose Anus » Thu Feb 09, 2017 10:29 pm UTC

Wouldn't there be no natural gravity exerted by the Dyson Sphere because of the shell theorem?
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Re: Walking on a neutronium Dyson Sphere

Postby gmalivuk » Thu Feb 09, 2017 10:36 pm UTC

Presumably we're talking about the exterior of the sphere.
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Re: Walking on a neutronium Dyson Sphere

Postby morriswalters » Fri Feb 10, 2017 3:26 am UTC

Such a shell would have no net gravitational interaction with its englobed star (see shell theorem), and could drift in relation to the central star. If such movements went uncorrected, they could eventually result in a collision between the sphere and the star—most likely with disastrous results. Such structures would need either some form of propulsion to counteract any drift, or some way to repel the surface of the sphere away from the star.[12]
Also if assuming a radius of one AU, then there may not be sufficient building material in the Solar System to construct a Dyson shell. Anders Sandberg estimates that there is 1.82×1026 kg of easily usable building material in the Solar System, enough for a 1-AU shell with a mass of 600 kg/m2—about 8–20 cm thick on average, depending on the density of the material. This includes the hard-to-access cores of the gas giants; the inner planets alone provide only 11.79×1024 kg, enough for a 1-AU shell with a mass of just 42 kg/m2.[13]
That is from the Wikipedia article on Dyson Spheres. And there is this little tidbit.
would have a surface area of approximately 2.8×1017 km2 (1.1×1017 sq mi), or about 550 million times the surface area of Earth
In one conceptual model I see 550 million earth masses to make Dyson a Sphere with a surface gravity of 1 G. That sounds wrong somehow. Niven's Ring World novels play with a variant of the Dyson Sphere that talks about these ideas.

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Re: Walking on a neutronium Dyson Sphere

Postby gmalivuk » Fri Feb 10, 2017 3:34 am UTC

Yeah, acceleration due to gravity is G*M/r^2, or G*M/(surface area / 4pi), so if the surface area increases by a factor of 550 million, then so must M.
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Re: Walking on a neutronium Dyson Sphere

Postby speising » Fri Feb 10, 2017 7:24 am UTC

Do not forget that there's a sun in the middle. I don't know its gravity at 1 au, but is isn't insignificant.

Edit: ok, only 0.5875 m/s^2 according to wolfram alpha.

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Re: Walking on a neutronium Dyson Sphere

Postby Nicias » Mon Feb 13, 2017 4:47 pm UTC

gmalivuk wrote:
Nicias wrote:A little alpha'ing gave this:

https://www.wolframalpha.com/input/?i=(standard+Gravity)%2F(Gravitational+Constant)%2F(4+Pi)%2F(1000+meters)

If the shell is 1 km thick it has to be as dense as the densest white dwarfs.

What is it that you think that equation shows?


If you look at the surface gravity of a thin shell, the inverse square term in the law of gravitation is cancelled by the r^2 term in the mass of a spherical shell. Thus you get a=(area density) * G * (4 pi). So setting a=g gives

area density= g/(4pi G).

Dividing by thinkness of 1 km gives

volume density = g/(4pi G 1000m)

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Re: Walking on a neutronium Dyson Sphere

Postby gmalivuk » Mon Feb 13, 2017 5:12 pm UTC

Ah, right. I was mentally adding parentheses around the last quotient and trying to figure out why you'd stick the thickness on the top of the fraction.
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Re: Walking on a neutronium Dyson Sphere

Postby thoughtfully » Thu Feb 16, 2017 2:20 pm UTC

It doesn't involve a Dyson Sphere, but another SciFi reference is Dragon's Egg by Robert L. Forward, a physicist whose SciFi is fairly hard. Humans orbit a neutron star and send a robot to the surface to interact with a technological civilization there.
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Re: Walking on a neutronium Dyson Sphere

Postby Hypnosifl » Mon Mar 27, 2017 4:29 am UTC

It's been hypothesized by physicists that there might be a possible type of nucleonic matter, called "strange matter", which could exist stably without the need for enormous external pressures as in neutron stars. I posted some stuff on this on the worldbuilding stack exchange website--see this post for the basic info I could find on strange matter, and this post where I dug up a paper that gave some theoretical estimates of the density and strength of stable strange matter, and used it to try to figure out the smallest possible dyson sphere that could maintain structural integrity around a given central mass (and hence the highest surface gravity that could be felt at the radius of the dyson sphere for that central mass).


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