At those kinds of speeds, the nanobots would require enormous amounts of energy. They would also absorb immense amounts of frictional heating from the atmosphere and their own motors. Think about the shuttle’s tiles glowing red-hot. Now imagine something going 100 times that speed.
I won’t say that it’s *impossible without thinking about it some more, but certainly it would require a technology that is not going to be available in the lifetimes of us or our grandchildren, for that matter. Hell, I’ll go out on a limb and say it’s impossible.
But more to the point, if we had the kind of energy and technology to make million mph nanobots that can build a beanstalk in a matter of seconds, then we’ll already be so advanced that a beanstalk will be a trivial problem anyway. So forget the nanobots.
If this thing is going to be built in our lifetimes, it would have to deal with atmospheric forces. That’s extremely difficult for a satellite in orbit to do. The math isn’t that hard, but it’s tedious. You’d have to figure out the cross-sectional area of the tether at each altitude, the speed and average density of the air at each altitude, then come up with a figure for drag forces. Then figure out how long this thing will be hanging in the atmosphere before it’s anchored, and you can figure out the reaction mass required in your satellite to compensate for the motion.
But then you have another problem - the tether going out into space will oscillate if you move the satellite around underneath it, and start whipping around. So you’d have to engineer a system that can compensate for changes in drag pretty much instantly.
The most cost-effective solution might involve extruding the tether down into the very thinnest altitude, then flying up another tether from the ground that’s already made and connecting the two. Once they are connected, you start paying out the tether in the opposite direction to put the whole thing under tension, and now you’re in business.
That would minimize the time the tether is causing satellite problems. But these are the kinds of engineering problems that would have to be analyzed and solved before we could do this. That’s one reason why the 15 year timeframe is ridiculous.
Remember a book called “Colonies in Space” by TA Heppenheimer? Or the original goal of the L5 society? I still remember when I was a kid, and hearing scientists seriously talking about how we could have 20,000 people living in floating space colonies by the year 2000. This was back around 1975 or so. Here we are in 2002, and I don’t see them. This 15 years-to-build-a-tether idea falls in the same category - something that only sounds do-able until you start looking at the fine print and coming to grips with the sheer amount of engineering work required.