How large can planets be?

I don't like the Dyson Swarm, I like the solid outer shell. Once again, it'll take a thousand years just to concieve of one...

 

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As I said, the solid sphere is unstable, and it's due to Newton's shell theorem so sadly no amount of engineering will get past that. It might take a thousand years to build one but it would be a wasted millennium unless you put some engines on it to keep the sun centred.

 

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So it's not possible, yet it's possible- right?

 

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I suspect he means something along these lines:

Since the gravitational field inside of a uniform spherical shell is everywhere zero, the shell can exert no net force on the star, and by the law of action/reaction the integral of the force the star exerts over the shell must also be zero. In other words, there is no restoring force to maintain the central position of the star.

 

Cheaper and more feasible living alternatives will prevail.
Same reason there is not a glass dome over London.
The Dyson phase will more likely be skipped...
Funding will be diverted to Proxima/Alpha Centauri projects.

 

That's exactly it - by the shell theorem a spherical shell must have zero gravitational potential inside the shell. The shell theorem is a consequence of Gauss' law, which states that the gravitational flux through a closed surface is proportional to the mass enclosed within it.

 

Well, actually the gravitational potential (due to the shell) is a constant within the shell and thus the gravitational field vector is zero, but that's basically it.

 

Planetary orbits are stable. If you nudge a planet (i.e. even a small meteor impact) it speeds up or slows down. If it speeds up its orbit expands; larger orbit = slower orbital speed so it stabilizes in a new, slightly larger orbit. If it slows down, it stabilizes in a new, slightly smaller orbit. Over the years the various planets have been nudged by collisions, tidal effects, other gravity sources etc but due to this stabilizing force they tend to remain in stable orbits.

Dyson spheres aren't like that. There's no stabilizing force. Nudge a Dyson sphere with a meteor, a gas cloud, even a rocket launch, and it will start to drift. The star inside will not drift. Eventually the star will wind up in one side of the Dyson sphere. The sphere would likely not survive that.

 

A Dyson shell is completely plausible with three engineering problems:

1. Not enough matter in the solar system to build one.
2. The sun's counter-orbit to the planets.
3. An adequate counter-thrust system capable of doing the hula hoop to counteract.

Considering you will get a billion trillion times as much energy from a Dyson Sphere, these are mere engineering problems.

 

A Dyson sphere has never really made sense to me.

It is impossible for a solid (contiguous) shell to orbit. If you rotate it fast enough to orbit the equator, the north and south high latitudes try to collapse toward the axis _and_ pancake toward the equatorial plane. I can't see how the materials strength problem could ever be solved.

A ringworld makes a lot more sense but iirc also suffers from the sun freely wandering in the equatorial plane, athough there is a restoring force toward (normal to) the plane.

 

Paul Birch 'solved' the solid (contiguous) Dyson sphere problem a few years ago. You could support the sphere by creating a network of rotating orbital rings inside it. These rings require energy to run, but that's not too much of a problem since the star is pumping out plenty of energy.
see
http://en.wikipedia.org/wiki/Orbital_ring

 

Re: OP.

Do we all agree you can have a super Earth 100 or 1000 times the size of the Earth?

 

... No you can't have a solid planet a 100 a 1000 times the size of the earth, you might have one tough with a 100 a 1000 times the mass of our earth

 

To consider this question correctly, we must make a distinction between mass and 'size'. The mass of the planet is important, and a planet 100 times the mass of Earth would be a very dense object indeed, But it wouldn't be 100 times as wide - the radius of a large planet doesn't increase linearly if you add more mass, instead the centre of the planet becomes more compressed.

Given a constant temperature, a planet twice the mass of Jupiter would not be much wider than Jupiter itself- but it would be much denser, especially at the core.

Some hot gas giants (such as HAT-P-1b) are quite a bit larger- but that is because they have expanded due to their temperature, not because of extra mass. If you could cool those large, puffy, hot gas giants down to the temperature of Jupiter they would be no larger than Jupiter itself.

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If you were to find a very massive planet with no atmosphere at all, it would be considerably smaller than Jupiter; the largest a solid planet with no atmosphere could possibly be is probably just a bit smaller than Neptune.

In fact a solid, cold sphere with the same mass as the Sun would be about as big as the Earth. White dwarfs are the closest to this sort of object that we are likely to observe in reality, and when the white dwarfs in our universe eventually cool down they will resemble small, incredibly dense planets.

The upper limit for the mass of such an object is the Chandrasekhar limit, about 1.4 tmes the mass of the Sun, or 466,000 times the mass of the Earth. Any solid object larger than that would collapse into a neutron star.

 

Not really, my point was as I said - the shell theorem states that a spherically symmetric shell has zero gravitational potential inside it. That means there can be no gravitational interactions with a massive object inside the shell, meaning the position of the shell with respect to the star is unstable.

 

Umm... Constant gravitational potential. See my post 28.

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Since you can't directly measure gravitational potential and it is related to the gravitational force by \(\vec{F} = \vec{\nabla} V\) I can add an constant I like and not change the physics. Therefore I choose to make V zero inside the shell.