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It would be awesome to have space elevators all over the globe and create a LEO network for factories and logistics.

A man can dream.

LEO is not accessible by space elevator at all. If you got off at ISS height you would just fall down. Good for basejumping though. And no you wouldn't even need heatshield, just rugged EVA suite.

The elevator itself would need to extend past LEO into geostationary orbit, but you should be able to get off the elevator in LEO space.

As you're going up the space elevator, you would also be picking up horizontal velocity as you ascend. At ISS altitudes there would be enough atmospheric particles to slow you down once you got off, but it would take a while; probably on the order of years. Base jumping would not be a good idea.

I have always wondered if one could be strapped into a Falcon 9 fairing half and ride that down in an EVA suit. Coolest ride I can imagine.

A cowboy hat is mandatory attire for this scenario.

basically, "starship troopers", the book

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