Stationary motion of a self gravitating toroidal incompressible liquid layer

TL;DR

This paper demonstrates the existence of stationary, rotating, and self-rolling motions of an infinitesimally thin, self-gravitating incompressible fluid torus, where particles follow helix-like paths around the torus.

Contribution

It establishes the existence of stationary solutions for a self-gravitating fluid torus with infinitesimal thickness, rotating and rolling on itself, under Newtonian attraction.

Findings

Stationary motions exist for a self-gravitating fluid torus.

Particles follow helix-like trajectories around the torus.

The torus maintains an approximately round shape during motion.

Abstract

We consider an incompressible fluid contained in a toroidal stratum which is only subjected to Newtonian self-attraction. Under the assumption of infinitesimal tickness of the stratum we show the existence of stationary motions during which the stratum is approximatly a round torus (with radii r, R and R>>r) that rotates around its axis and at the same time rolls on itself. Therefore each particle of the stratum describes an helix-like trajectory around the circumference of radius R that connects the centers of the cross sections of the torus.