A space elevator on Earth could permit sending objects and astronauts to space at costs only a fraction of those associated with current means. Constructing one would, however, be a vast project, and the elevator would have to be built of a material that could endure tremendous stress while also being light-weight, cost-effective, and manufactureable. A considerable number of other novel engineering problems would also have to be solved to make a space elevator practical. Today's technology does not meet these requirements. However, optimists say that we could develop the necessary technology by 2008 and finish building the first space elevator by 2018.
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Source: Wikipedia