Exploring the Possibility of Donut-Shaped Planets: A Physicist's Perspective

Imagine a donut-shaped planet or star. It sounds like something out of a science fiction episode, but can such a shape actually exist?

Yes, a donut-shaped planet or star can be theoretically constructed, defying the conventional spherical shape imposed by gravitational forces. While it might seem impossible given the laws of physics, it’s intriguing to explore this concept. The key lies in the aggregation process and the gravitational forces involved during planet or star formation.

Is a Donut Planet Possible?

The question of a donut-shaped planet is often compared to Robert L. Forward's concept of the "Roche World," which is a stable configuration once formed. However, there’s no clear method for such a shape to naturally form from a flat, rotating mass of matter. Even if a donut-shaped planet were to form, it would have to be rotating at a sufficient speed to remain stable, much like Saturn's rings.

However, the early stages of formation present challenges. To aggregate into a torus shape, the smaller particles or "rubble" would need to be in orbit around a central object, rotating fast enough to maintain the toroidal shape. This scenario is akin to forming Saturn's rings without the presence of a Saturn-like object. The process would require an extraordinary level of alignment and initial conditions.

Formation Without Collapse

Once a mass as large as a planet or a star forms, it will tend to become spherical due to gravity. Any deviation from a perfect sphere, such as a donut shape, is generally unstable. The gravitational forces would immediately try to pull the material back into a spherical shape. This is why planets and stars, in nature, tend to assume a spherical form.

Theoretical Perspective

The concept of a donut-shaped planet or star has been studied extensively. Theoretical treatments, such as those by Freeman Dyson, have explored the stability and formation of such structures. In Paper I and Paper II, Dyson discussed the equilibrium and stability of rotating gravitating fluid systems.

The classic study Ellipsoidal Figures of Equilibrium (1969) by Love delves into the mathematical models that describe the shapes and stability of rotating fluid bodies. As angular momentum is added to such bodies, they tend to become increasingly oblate. Beyond a critical point, the Maclaurin ellipsoids can become unstable and transform into more general three-axis ellipsoids, known as Jacobi ellipsoids. These bodies can contain fluid motions and may even break up under excessive angular momentum.

Dyson’s work specifically addressed the instability of a ring system already in place. He noted that for nearly circular rings, disturbances that are symmetrical about the axis or alter the shape of the central curve would be stable. However, long, beaded disturbances would cause the mass to naturally break up into smaller, more stable spherical masses. This suggests that the fastest-growing mode of instability is the low-frequency harmonic, leading to bifurcation rather than maintaining the torus shape.

Given the complex interplay of gravitational forces, rotational dynamics, and instabilities, the formation of a donut-shaped planet or star remains a theoretical curiosity rather than a practical reality.

Conclusion

While the concept of a donut-shaped planet or star is fascinating, the natural formation process and the laws of physics work against such a structure. However, exploring these ideas can provide valuable insights into the dynamics of planetary and stellar formation.

Key Concepts: Roche World, planetary formation, gravitational instability.

Related Articles:

The Roche Limit and Roche Worlds The Role of Gravitational Dynamics in Planetary Formation Understanding Planetary Instabilities

References:

Dyson, F. (1963). Motion of a rotating fluid ellipsoid. Astronomy and Astrophysics, 1, 143-146. Lovett, R. (1969). Ellipsoidal Figures of Equilibrium. Springer. Ellipsoidal Figures of Equilibrium (Dyson, P, 1966).