The usual catenary is formed by a hanging chain in a gravity field which is uniform -- i.e., the case for chains which are small relative to the size of the Earth. Is there a closed form solution to "large" catenaries which have a size as large as, or larger than the Earth? In particular, consider a chain whose links are _repulsed_ by a spherical (non-rotating) Earth (e.g., proportional to -1/r^2). What are the shapes of these curves? A large enough chain would go completely around the Earth. I guess there would be solutions where such a closed chain would touch the Earth at just one point. I don't know if there would be stable solutions where the chain would not touch the Earth at all. If rotation is introduced, things probably get a lot weirder.