# Can a donut-shape planet or star be formed?

How stable is that configuration and under what conditions such object may form ? Is there any evidence suggesting that such objects might exist ?

• By “donut shape” you mean a ring of matter with a void at the centre (of gravity)? What would act to keep matter away from the centre? – Chappo Says SE Dudded Monica Sep 11 '18 at 5:10
• @Chappo centrifugal force – user3715778 Sep 11 '18 at 5:30
• The centrifugal force only exists in a rotating reference frame. If I’m at rest at the centre of gravity in an inertial reference frame, what force is acting on me? – Chappo Says SE Dudded Monica Sep 11 '18 at 5:41
• The authors of RingWorld were reliably informed by some MIT profs that a torus-world rotating about a central sun would be unstable as well. This is different from your question, but in general toruses are not "natural" – Carl Witthoft Sep 12 '18 at 15:22
• @Carl Authors? Did Larry Niven clone himself? ;) – PM 2Ring Sep 12 '18 at 16:20

No, such a configuration would not be stable. Matter tends to clump together and as the mass increases the rotation slows.

If the rotation were too fast for the material at any given size then the stresses would be too great for it to remain as a cohesive body. In these cases you would get something more like a rubble pile. If the rotation were somehow sufficiently high enough to theoretically form a donut shape, I think the gravitational force of the matter would not be enough for it to coalesce into any sort of cohesive body.

Consider, for conservation of angular momentum the angular velocity decreases as the distance from the centre of rotation increases. That is, stuff closer to the centre rotates faster than stuff farther away. But for a solid body the angular rotation is the same at all distances from the centre. This means that the angular velocity (in degrees per unit of time) is the same at all distances, and in this case the stuff closer to the centre rotates more slowly than the stuff farther away.

So to form a solid body the stuff in the centre needs to slow down as it accretes matter - it rotates more slowly as it gets bigger. This would prevent forming a donut because the centripetal forces don't outweigh the gravitational forces. Fluid bodies like stars or planets with liquid/molten cores are more complex but the same idea applies.