Hello everyone! Congrats to all the J2s who have just finished their A levels recently! Weve had a brief hiatus lately, and meanwhile some questions have come in! First off: Q: Explain the concept of a space elevator. A: Hello! Thanks for the interesting question! In summary, a space elevator is a concept for space teleportation that has been around since 1895. The idea of the final structure is simple, but the actual construction of the elevator (the process by which to reach the final structure) is a whole different story. The essential idea (of the final structure) is this: from an anchor on the equator, there will be a cable straight up, all the way past geostationary radius, and ending in a mass somewhere above geostationary radius. With this structure, loads can be transported up and down this cable easily (like an elevator, hence its name). Now, lets take a look at the physics behind this structure and how it is stable. Recall from your physics lessons that a geostationary satellite is a satellite that orbits the Earth at the same angular velocity as the Earth rotates on its own axis, and orbiting in the plane of the equator, such that the satellite stays at the same spot in the sky when seen from the Earth. Remember that there is a fixed geostationary radius from the Earth that the satellite is able to accomplish this, where the net force of Earths gravity corresponds to the needed centripetal force acting on the satellite (G M m / r^2 = m w^2 r; where w represents omega, the angular velocity of the satellite, which is the same as that of the Earth). Now, what if the satellite is at bigger radius than this geostationary radius, but still moving with the same angular velocity (as the Earth)? Well, the gravitational force would be reduced, but the needed centripetal force is increased, ergo, for such a situation to happen, an additional force would have to act on the satellite towards the Earth. Similarly, if the satellite is at a smaller radius than this geostationary radius, but still moving with the same angular velocity, then the gravitational force is increased but the needed centripetal force is reduced, ergo, for this situation to occur, an additional force would have to act on the satellite away from the Earth. With these concepts in mind, let us look at the idea of the space elevator. If we consider each small part of the cable with a mass (and being a satellite in itself), then from our earlier deduction, the parts of the cable below the geostationary radius require an additional force upwards (to stay intact in the structure of the space elevator), while the parts of the cable above the geostationary radius (and the mass) require an additional force downwards. These forces are easily provided by the tension in the cable, i.e. tension in the cable increases from the anchor in the ground to the geostationary radius, and decreases thereafter. Hence, with a cable that is able to sustain such tensions, the structure of the space elevator is stable! Of course, while the idea of the final structure seems promising, there are many complications in trying to construct such a structure, including how to find a cable that has sufficient tensile strength, and how to build the structure up piece by piece (the intermediate structures are unstable, if you think about it). Carbon nanotubes is a promising material that has been considered lately, but we will leave these questions for another discussion. If you are interested, do read up on your own about these issues and possible solutions to them! #OQPhysics
Posted on: Mon, 02 Dec 2013 13:36:11 +0000
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