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.
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