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Assume realistic strength of materials, like that of steel or stone, or even something with "good" properties like carbon fiber, or advanced ceramics. If one was to put together a hollow sphere in space where the bulk of sphere was hollow (the thickness of the shell is much less than the radius of the sphere) what would the largest possible sphere be. No external forces from the sun, heating from sunlight, gravity from other planets etc.

When would gravity become limiting? I suppose there is the static case, and then a more dynamic case when one could consider that there could be elastic waves in the shell... and if that was the case would lead to the shell buckling before the static case.

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  • $\begingroup$ I don't think that gravity would be biggest problem here. Most likely mega-structures will be build in a modular way, hollow sphere surface fragment part-by-part, and as such the most biggest issue would be to calibrate all parts to fit the "big" picture. As such all factors would be important then,- temperature fluctuations of surface, even smallest mis-alignment (additional microscopic space) under one fragment would result in the failure of overall structure, due to the fact that errors add-up. So certainly, there is a mega-structure size limit, but it's more an engineering problem. $\endgroup$ Commented May 1, 2022 at 21:33
  • $\begingroup$ @ I agree, but if the pieces are big enough I was wondering if there would be a problem with the pieces would gravitationally fall together in a big lump. And if big enough would it start solidify under the pressure. That got me thinking how big a hollow space you could have for a big structure. $\endgroup$
    – UVphoton
    Commented May 1, 2022 at 23:00

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Any size works.

The mass of your spherical shell grows like its area, i.e. like radius $r^2$. But gravity drops like $1/r^2$, and the gravitational field of any spherically symmetric mass distribution is that of a point mass at its origin. Thus, the two factors cancel out, and gravity never becomes a problem.

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    $\begingroup$ How about the pressure gradient? As the the shell gets thicker the pressure should still build up as one goes from the surface deeper into the shell. At some point the pressure will be very high. $\endgroup$
    – UVphoton
    Commented May 1, 2022 at 22:53
  • $\begingroup$ Sure. In the limit that the sphere is completely filled, that's otherwise also known as a star... $\endgroup$
    – rfl
    Commented May 2, 2022 at 1:25

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