Is the Sky-Hook Configuration Stable?

Abstract

The sky-hook, that is a string forming a connection from the surface of the Earth to a satellite in geostationary orbit, which may be used as track for an Earth to space elevator, is an old dream of mankind, originating about 100 years ago in Russia. Besides the question of feasibility from a technological point of view also the question concerning the stability of such a configuration has not yet been completely solved. Under the assumption that a proper material (carbon nanotubes) is available making the connection possible technologically, we address the question of stability of the radial relative equilibrium of a tapered string reaching from the surface of the Earth to a satellite on a circular geosynchronous orbit around the Earth.

Novel Payload Dynamics on Space Elevator Systems

“…It can be seen that the chain will be in equilibrium for a given length (22.7 Earth radii). If the chain is longer than this equilibrium length the chain will rise, while if the chain is shorter the chain will fall, resulting in an unstable equilibrium 7 as expected from the analysis of a single mass. The orbital siphon effect described here utilises the excess centripetal force acting on the chain of masses above synchronous orbit to lift new payloads from the surface of the Earth.…”

Advances in dynamics and control of tethered satellite systems

“…Two ambitious examples in case are gravity-gradientstabilized space elevators [14], and three-dimensional tethered formations for Earth observation application, which may use the gravity-gradient forces to stabilize the spin axis along nadir [24].…”

“…The concept seemed futuristic in 1960s because no material available had the required mechanical properties to build such a space elevator. Noticeably, interest on the space elevator has been recently revived [11][12][13][14][15] due to the discovery of super mechanical properties of carbon nanotubes [16].…”

A finite element based stability test for equilibria of flexible structures in circular orbits

“…One day this structure could enable astronauts to climb up a 36,000 km long tether connecting the earth's surface with a geostationary orbit. However, it turns out that an orbiting tether becomes unstable beyond a critical length [(7), (6)]. …”