1. Space Elevator Submitted by:- Paras Joshi R180207035

2. Introduction • A Space Elevator is a proposed space launch structure without the use of rockets which can be used to transport material from earth’s surface into space. • It is essentially a long cable extending from our planet's surface into space with its centre of mass at geostationary Earth orbit (GEO), 35,786 km in altitude. • It is basically the concept of Konstantin Tsiolkovsky, considered to be the founding father of rocketry and astronautics. • The centrifugal force of earth's rotation is the main principle behind the elevator.

3. Introduction Cont. • The concept most often refers to a cable that reaches from the surface of the Earth on or near the Equator to geostationary orbit (GSO) and a counter-mass outside of the atmosphere. • This structure would be held in tension between Earth and the counterweight in space like a guitar string held taut.

4. Mathematical background • While considering Space elevator apparent gravitational field comes into play which is given by- g= -K.M/r²+w².r Whereas near the earth’s surface, it’ll be given as- g=K.M/r² Where g=acceleration along radius K=gravitational constant M=mass of the earth r=distance from that point to earth’s center

5. Math. Background Cont. • The main technical problem is the long cable's own weight. It can be strong enough to hold 35,000 km of itself. • The solution is to build it in such a way that at any given point, its cross section area is proportional to the force it has to withstand and as per given formula- g= acceleration along the radius S=cross-area of the cable at any given point r dS=its variation ρ=density of the material used for the cable σ =traction a given area can bear without splitting

6. Counter Weight • The emphasis is given to the counter weight as it is the main support to hold the elevator and the climber. • Some of the proposals are:- • A heavy asteroid • A space station, space dock or space port beyond geostationary orbit • An extension of the cable itself far beyond geostationary orbit. • The third proposal is considered to be the better one due to its simplicity and the fact that payload may slip into the interplanetary space because of gained velocity when reached the extreme end of the cable.

7. Material Used • Carbon nanotubes would be the best option for the purpose as it is the strongest and stiffest material yet discovered in terms of tensile strength and elastic modulus respectively. • Carbon nanotubes are allotropes of carbon with a cylindrical nanostructure. • Nanotubes have been constructed with length-to-diameter ratio of up to 132,000,000:1.

8. Tether Technology • A tether is a cord or fixture that anchors something movable to a reference point which may be fixed or moving. • In tether technology, cables, miles long, are stationed in an orbit around the earth. On one end there is a shuttle and on the other end of the tether would be a counter mass. • This system picks up spacecraft in low orbits and hurls them into higher orbits or towards other planets.

9. Power Beam Technology • It is an electromagnetic radiation through a process of optical amplification based on the stimulated emission of photons. • Power Beam is revolutionizing the mode of power transmission by integrating optical technology to produce safe, reliable and abundant wireless power. • Power Beam operates at a wave length which is 1400nm or greater.  These waves create the beam.  The beam is collimated giving us the ability to achieve great distances without loss in power or efficiency.

10. Risks Involved Some of the risks which need to be considered are:- • All satellites with perigees below the top of the elevator would eventually collide with the elevator cable. • Meteoroids present another problem, they would not be predictable and much less time would be available to detect and track them as they approach Earth. • Corrosion is thought by some to be a risk to any thinly built tether. • Material defect would be one of the causes as because large structures have more defects than small structures

11. Conclusion • Space Elevator is best option to transport material into the space as it uses a fraction of current cost. • As of 2000, conventional rocket designs cost about $11,000 per pound ($25,000 per kilogram) for transfer to geostationary orbit. Current proposals envision payload prices starting as low as $100 per pound ($220 per kilogram). • As we are planning to explore the universe therefore it can be a better option to use this approach so as to be economical and time efficient.

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