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I was doing some back-of-the-envelope calculations to see what happens to a body dumped from Challenger, and discovered that the Memorial Shuttle's travel times are way off.

See, it turns out that a counterweight at 70,000 km whipping around once every 24 hours (tangent speed 5.6 km/s) is in fact well above escape velocity (3.2 km/s). So while corpses will fly out into solar orbit just fine, a "slow boat" simply letting go at the right time will have you on Luna in about a day. For that matter, Mars is only 3.6 km/s away, so you don't even need to use any fuel for that until you arrive (excepting course correction maneuvers.)

And that's not even taking advantage of the Beanstalk as a magnetic accelerator, which could put you on course at a scorching 32 km/s without exceeding 1.5 g! That is frankly way too fast for anything local, considering you have to stop at the other end. It's nearly solar escape velocity, and ten times the velocity necessary to reach Mars!

Er... Thank you for coming to my TED Talk.

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Seems you are right. While the escape velocity from earth's surface is 11.2 km/s, at 70000 km from the earth's center it's something around 3.4 km/s according to my calculation.

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I guess this all makes sense, considering it's the Midway Station that is at the geo-synchronous orbit altitude (where you would be at the exact velocity needed to stay in stable orbit). Wouldn't that mean it makes more sense for ships to leave from Midway Station if they intend to stay in-orbit of earth? ie. Intending to get to Luna? 

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I tried to talk the math, acceleration physics, orbital dynamics, duration of travel and got verbally shredded, bluntly told to STFU and to mind my own business...

.... I'm still taking the anti-rad tabs.

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