The main challenge in building a tower which extends past the upper reaches of Earth’s atmosphere is there are currently no known materials that would be strong enough not to buckle under their own weight. However, this hasn’t stopped many scientists and engineers devising ways that it could be possible, along with high-profile bodies such as NASA investing in research into how it could be done. The accepted view of how this might work involves building from the top down, where the top would be a large mass in geosynchronous orbit around Earth (orbiting the planet yet staying in the same position at all times). The ‘tower’ would most likely be a thin yet strong cable or tether that could be climbed by mechanical means to deliver payloads into space. Building from the top down (towards the ground) would need to be balanced by building up (away from Earth), where the upwards building would act as a counterweight to keep the geosynchronous orbit in check. Exciting developments in the manufacture of new materials such as carbon nanotubes – extremely strong for how little they weigh – could be the perfect candidate. However, finding the huge amount of carbon that we would need is the next hurdle to overcome.
Answered by Rik Sargent.