A simple model of a payload ascending or descending a space elevator is developed to explore the underlying dynamics of the problem. It shown that an unconstrained payload at rest on a space elevator at synchronous radius is in an unstable equilibrium, and that this instability can be used to motivate the development of new ideas for payload transfer. In particular, it will be shown that a chain of connected payloads can be assembled which will lift new payloads at the bottom of the chain, while releasing payloads from the top of the chain. The system therefore acts as an 'orbital siphon', transporting mass from the surface of the Earth to escape speed without the need for external work to be done.
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