Toroidal planet

While no firm theoretical understanding as to how toroidal planets could form naturally is necessarily known, the shape itself is potentially quasistable,[1] and is analogous to the physical parameters of a speculatively constructible megastructure in self-suspension, such as a Dyson sphere, ringworld, Stanford torus or Bishop Ring.

[2] A rotating mass in the form of a torus allows an effective balance between the gravitational attraction and the force due to centrifugal acceleration, when the angular momentum is adequately large.

Ring-shaped masses without a relatively massive central nuclei in equilibrium have been analyzed in the past by Henri Poincaré (1885),[3] Frank W. Dyson (1892), and Sophie Kowalewsky (1885), wherein a condition is allowable for a toroidal rotating mass to be stable with respect to a displacement leading to another toroid.

In the simple model of parallel sections, beaded instability commences when the aspect ratio of major to minor radius exceeds 3.

is unstable against displacements leading to toroidal shapes and that this Newtonian instability is excited by the effects of general relativity.

[8] While an integral expression for gravitational potential of an idealized homogeneous circular torus composed of infinitely thin rings is available,[9] more precise equations are required to describe the expected inhomogeneities in the mass-distribution per the differentiated composition of a toroidal planet.

Since the existence of toroidal planets is strictly hypothetical, no empirical basis for protoplanetary formation has been established.

One homolog is a synestia, a loosely connected doughnut-shaped mass of vaporized rock, proposed by Simon J.

Lock and Sarah T. Stewart-Mukhopadhyay to have been responsible for the isotopic similarity in composition, particularly the difference in volatiles, of the Earth-Moon system that occurred during the early-stage process of formation, according to the leading giant-impact hypothesis.

Given how improbable their occurrence, it is extremely unlikely any will ever be observationally confirmed to exist even within our cosmological horizon; the corresponding search field being approximately

Artist's depiction of an earthlike toroidal planet. The odds of any toroidal planet forming might be infinitesimally small yet nonzero; allowing for an infinite universe , not only would a 'donut-shaped planet' almost certainly be bound to occur during the stelliferous era , it would occur infinitely often. [ Note 1 ]