The destruction of a continuous ring revolving around a gravitating center

Abstract

In article by Morozov and Fridman (1984) the general equation of motion of an elastic thread in an external gravitational field was formulated and also instability of an elastic thread rotating around a gravitating center was established.

On this basis, in the present article we show that the classical model of a hypothetical continous ice ring around Saturn, proposed by Laplace and Maxwell, was incorrectly interpreted by them. Specifically, supposing the ring to be infinitely hard and firm, they came to the conclusion that it will fall on the planet's surface. However, in reality such a ring would be destroyed due to internal stresses under displacements which are three orders of magnitude smaller than the distance between the ring and the planet. We also note that accounting for this effect is important under discussions of cosmogonical models.

In conclusion, estimates are given which show that the steel ring (thread) revolving the Earth and rotating around it at the distance of 200 km from the surface would be torn, due to its instability before it falls on the Earth. Meanwhile, for threads of firm aluminium fusions the opposite picture is to be expected. It is noted that the instabilities indicated may be stabilized by using follow-up (‘cybernetic’) systems with power plants.