It won't, because it can't.
I've read miles of this stuff, and there's one factor that no one has taken into account, and it's a killer.
They can't build a space elevator, because it will be ripped apart by the torsional stress from the tidal forces.
For giggles, let's assume they somehow manage to hang one of these suckers into the sky, and, they somehow manage to stick an "elevator cab" on the top of it. (OK, not the "top" top, but the geo-sync altitude "top" portion.)
What happens when they lower the cab?
Picture an ice skater, spinning on one toe, arms spread out.
Then imagine the ice skater pulling in her arms.
Now picture that ice skater being 40 thousand miles tall. :)
The horizontal velocity of that cab -- at geo-sync altitude -- will be staggering, and even though it's "undetectable" at altitude, when you lower the cab, it will be like trying to contain a cannonball with a spiderweb.
"The horizontal velocity of that cab -- at geo-sync altitude -- will be staggering, and even though it's "undetectable" at altitude, when you lower the cab, it will be like trying to contain a cannonball with a spiderweb."
Actually... um...
Only delta-v over time matters - that is, acceleration. If you raise or lower the cab slowly enough, the change in velocity will not be big enough to cause problems.
What if (i.e. not well thought out) you counter ballance weights by moving equal amount up at the same time as down. Perhaps by mining from the moon or astoriods? Send ore down and machines up?
I am having trouble visualizing this.
The lateral velocity of the cab is zero relative to the surface of the Earth, and remains so as it ascends or descends. There is no spinning.
I could see the beanstalk requiring counterweights, but I don't see what your skater has to do with anything.
The response I've seen to this requires letting out a counterbalance weight further into space to counteract the effect of changing the weight distribution as the cab goes down. I don't fully understand it, but I know space elevator theorists have at least addressed that question sufficiently for it to get reported somewhere on the internet.
It will be about 6000mph, which will have to be braked to the 1000 mph surface speed, as the elavator cab travels a distance of 18,000 miles The numbers might be awesome, but I'm not seeing a problem here.
Actually the numbers (about 0.3 mph/mile) are about one percent of the sideways work that has to be done during a carrier aircraft landing because the flight deck is angled 10° to the centreline of the ship - itself not significant, and there it happens in a few seconds, not the 50 hours travel an Earthstalk cab will have.
(In my best Dr. Strangelove voice):
Let's see. Radius = 4K miles(Earth) + 62K miles (elevator) = 66K miles.
Circumference = 2piR = 415K miles/24hrs = 17,000 mph at 62,000 miles.
And that "horizontal" speed must drop to zero by the time the cab reaches the ground. He's talking about an 13 ton elevator -- Where do we get the energy to stop 13 tons moving at 17,000 mph?
Conversely, where do we get the energy to accelerate 13 tons to 17,000 mph?