You've most likely heard that planets can exist in the shape of a donut, also known as a torus. These toroidal worlds could even support human life, as long as it spun fast enough to balance out it's own gravity, and contained some form of water, air, and food.
I'm wondering if there are any possible ways a celestial body could naturally form this way?
It is not obvious whether they are stable, yet thin ones (Hoops, having a large hole at their center) are not. It is permissible by physics, but the conditions creating them are very unlikely. This is a case study of such configuration.
There is a certain range of axial rotation speed which could turn a fast-spinning planet into an ellipsoid, and a narrow range which "stretches" it further into a torus. It is interesting to find-out how axial rotation can be increased to allow that. Maybe a series of asteroids coolisions can do the trick? The site refers to the shape as somewhat sensitive to wobbles which make the torus tear apart into two spherical planets orbiting each other, so the series of collisions is a too delicate operation?.
The ring may itself be unstable, in particular to a “bead” instability where more and more mass accumulates at some meridians than others, leading to breakup into two or more orbiting blobs.
It looks like a toroid planet is not forbidden by the laws of physics. It is just darn unlikely to ever form naturally, and likely will go unstable over geological timescales because of outside disturbances.
Nothing donut shaped is going to be stable and probably wouldn't be natural either, you might get something that looks a bit like a red blood cell but that's probably not going to be on a planet scale unless it's artificial. Anything with enough mass to be a planet will fall in on itself as a spheroid, anything spinning fast enough to flatten out to something approaching toroidal would exceed the Roche Limit for known planetary compositions.
All planets go through a phase in which they are fluid. Being fluid mean that gravity and hydrostatic forces shape them in the most energy convenient configuration, which is a sphere.
A torus would have no mass in its center of mass, and sooner or later mass would start impinging there, turning it into a sphere.
The only way to have something toroid shaped is to make it small enough that the material strength overcomes gravitational forces. The name planet would then not be applicable. At best it can be an asteroid.
