There has been quite a bit of press about construction of a space elevator by Obayashi Corp, a Japanese construction company, lately. As exciting as an elevator to space would be, let’s just look at some of the hurdles that such a project would have to overcome from a scientific point of view.

What may not be obvious to non-physicists is how you would keep an elevator to space from falling back down to Earth. It would, in some sense, be the tallest thing mankind would have ever constructed, but you can’t just build a really tall building into space. Instead, you would have to assemble a giant platform in geosynchronous orbit (altitude 36,000km) and then lower the elevator cable from space. This would allow you to build the elevator from the top down. However, the plans proposed by Obayashi propose extending the elevator to 96,000km. This means that if the top of the elevator were not connected to Earth in any way, it would orbit slower than the Earth rotates. When you connect the two, the Earth would actively pull on the top platform, speeding it up to match the rotational speed of the Earth. This makes sense from a construction point of view; having the platform want to fly away from the Earth means that you can pull on the cable in order to climb it without pulling the elevator down on top of you.

Even though the top of the elevator has to be pulling on the Earth to keep tension in the cable, it is a productive exercise to figure out just how much tension would be produced from something at that altitude. First, we need to make a few assumptions. Let’s assume the counterweight at the top of the elevator has about the same mass as the International Space Station (450,000kg) and for now let’s ignore the mass of the cable connecting the counterweight and the Earth.

It is easy enough to write down the force on the counterweight due to the gravity of the Earth. Newton figured it out centuries ago:

F_{earth} = -G M m/r^{2}

where G is the gravitational constant, M is the mass of the Earth, m is the mass of the counterweight, and r is the distance to the center of the Earth.

Meanwhile, the force from the Earth accelerating the counterweight to match the rotation speed of the Earth is given by:

F_{rotation} = m ω^{2} r

where ω is the rotation velocity of the Earth.

The sum of these two forces is what acts on the counterweight:

F_{total} = -G M m/r^{2} + m ω^{2} r

At an elevation of r=102,400km (the altitude plus the radius of the Earth), F_{total} = 227,799 Newtons. This is equivalent to the weight at Earths surface of a 25 ton object. In construction terms however, that is not too bad; many things weigh much more than that are suspended by cables. However, the cables used to make such an elevator would have to stretch almost 100,000 km; about 100 times longer than any current cable in existence! Not only that, but when you factor in the weight of the cable itself, it is not feasible unless the material it is made of has a much higher tensile strength/mass ratio than steel. Currently the only material that has such a high ratio is carbon nanotubes, but the longest continuous piece of carbon nanotubes was 2cm long made at MIT, not even close to useful lengths.

So, due to the limited manufacturing capability of carbon nanotubes, the space elevator is likely to remain a lofty dream for the foreseeable future. This doesn’t mean we can’t imagine what it would be like to visit the top of the space elevator. For instance, if you were way up at the counterweight, you would not be weightless like the astronauts in the ISS. Instead, you would actually feel a weak force pushing you away from the Earth, about 1/20th that of gravity on the surface of the Earth. This means that in order to not fly away and off into space, you would either have to stand with the top of your head facing the Earth or somehow tether yourself to the counterweight. This would have to be considered when building the elevator car. When you start your journey on the Earth, you would experience normal gravity. However, that gravity would slowly decrease until you reached and elevation of 36,000km where you would be weightless. Then, as you climbed more, you would experience a force pushing you into the ceiling. That means what started as the ceiling became the floor and when you travel back down to the planet, you would have to switch one more time. So, controls, storage, facilities, etc. in the elevator car would need to be able to operate regardless of the apparent direction of the force of gravity.