What a fascinating premise. Kudos to the author for doing such a thoughtful analysis. His technique for arriving at the cross-sectional shape is especially interesting. I would have never considered that the optimal cross-sectional shape to have been anything other than a circle.<p>I wonder if it would be possible to orbit the ring in the axial plane, around a single arm of the torus? Or even in a lemniscate, intersecting the inner Lagrange point?
<i>”There is a central unstable Lagrange point at the middle of the hole”</i><p>So, why would Ringworld (an enormous toroidal planet with a relatively small sun (a sun similar to our sun, which weighs 6E24 kg, Ringworld would weigh 300 times that, at 2E27 kg) at its center) be stable?
I wonder how many millennia it will be before we can trivially terraform one of these from another planet for fun. Just deploy a hoard of self-replicating autonomous robots and sit back for ten years. Might need some carefully-orchestrated nuclear detonations to increase the average gravitational potential, though.
Fascinating, and great to imagine that given the sheer number of start in the known universe, there is a chance that somewhere out there such a thing exists right now.