The physics of a toroidal planet

I love the idea of futuristic or alien civilizations using advanced technology to create planetary scale art.

I wonder if such an advanced civilization would be able to create a toroidal planet. It would have to be spinning pretty fast for it not to fall into the central hole - fast enough that the effective gravitational field at the outermost ring of the surface would be quite weak and the gravitational field at the innermost ring would be quite strong. The gravitational "down" direction would vary across the surface of the planet and wouldn't be normal to the average surface except on those two rings. I think if you slipped you probably wouldn't fall off (unless the effective gravity was very low) but you would generally fall towards the outermost ring. Any oceans and atmosphere would also be concentrated at the outermost ring. It would be as if there was a planet-sized mountain with its top at the innermost ring and its bottom at the outermost. It would therefore have to be made of something very strong if the minor radius was reasonably large - rock (and probably even diamond) tends to act as a liquid at distance scales much larger than mountains.

I need to try to remember to google my ideas before writing about them. Having written this, I've just discovered that lots of people have thought about this before.

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