Space elevators are one of the hot topics in space exploration because they promise vitrually free transportation to space.  To me, they have always sounded a little too easy, but a good argument did not occur to me until recently.  For the moment, I will not try to explain the whole concept of how a space elevator is supposed to work or limit the technicality of my discussion, but just concentrate on why I think it won't work in physics terms.  My other caveat is that I only have a BA in physics, so I don't claim to be an expert, and would appreciate if anyone can give me a reason why my argument won't work. 

The basic concept of the space elevator is that there is a satellite with its center of mass in geostationary orbit.  A cable runs down from the satellite to a tower on Earth's equator, with an "elevator" that can ride up the cable.  This allows cargo to ride up the cable simply for the amount of energy needed to climb against gravity, which is much lower than that needed to attain orbital velocity.

The problem:  as the load rides up the cable, it gains transverse kinetic energy which is not counterbalanced by the cable, which can only exert a force perpendicular to gravity.  At the surface of the Earth, the load is moving at ~500 m/s due to the rotation of the Earth.  In the course of its travel up the cable, it must have a transverse acceleration of ~2500 m/s in order to reach the transverse velocity of the satellite at 3000 m/s.  This means an energy change of 3000^2-500^2 = 8.75 * 10^6 J per kilogram of load.  For a load of ~1000 kg this would be ~10^11 J, enough to slow a satellite of 10^11 kg (or 100,000,000 tons) by 1 m/s.  Since most proposed satellites would be smaller than this, the speed drop would be even greater.  As the speed of the satellite dropped, its orbit would become unstable and it would fall to Earth. 

The only solution to this problem that I can see is to fire a rocket in the transverse direction, either from the elevator car or from the satellite, in order to make up the velocity deficit.  Of course, this defeats the benefit of the elevator, especially since you would need to accelerate the fuel, etc.  Maybe it would make sense with a very high efficiency engine such as a solar or nuclear electric drive, but it would be very doubtful. 

As I said at the outset, if anyone can give me a reason why this argument is not valid, please let me know.

Last Updated 3/10/05