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Could you Daisy chain one space elevators together?
Like, one leading from earth to the moon than from the moon to say...Mars.
I haven't bothered to edit this yet and I already know it's retarded.
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Couldn't do it from the Moon to the Earth because the Moon isn't geostationary. The cable would end up being wrapped around the planet. Ditto for Mars, except that the tangle would probably be around the sun, seeing as Earth and Mars have different orbital periods.
But you wouldn't need to. You would use the space elevator to cheaply take the parts for the spaceship in to orbit, assemble them in space, bring the astronauts and various supplied up and then kick off from there. Because the ship won't need fuel and rockets to get past Earth's gravitational pull, it can be much smaller than it otherwise would be.