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I know that atomic bombs when exploded in or under or not too far above the ground, mushroom clouds are the shape that gets made by expansion, but it has the ground as a mirror, or whatever, depending on altitude. But if an atomic bomb is exploded at great altitude, what pattern or shape would the cloud take? Is it known?

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Several nuclear devices have been detonated at high altitude i.e. effectively in space. The best known is probably the Starfish Prime test. A video of the detonation is available on Youtube.

In vacuum the explosion is basically spherical, though turbulence develops in the expanding wavefront and that creates fine structure that makes it look like a hairy sphere rather than a smooth one.

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