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The Space Elevator and what we need to built it Photo source: space-elevator-and-become-an-interplanetary-civilization/ Skylar Kerzner Physics 141A, UC Berkeley

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First Thoughts 1895 – Konstantin Tsiolkovsky proposes a tower up to geostationary orbit 1959 – Artsutanov suggests a geostationary base that lowers a cable 1966 – Isaacs, Vine, Bradner, Bachus determine that the strength required is at least twice that of any existing material Faculty.randolphcollege.edu

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Elevator Physics Force is downward below geostationary, upward above it Geostationary point experiences greatest tension Orbital velocity at 2/3 to Geostationary $100/lb instead of $11k/lb diagram--corrected_for_scale%2BCM%2Betc.TIF

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Strength of Materials Stress (σ) = Force / Cross-sectional Area Stress (σ) = Youngs Modulus (E) * Strain (ε = ΔL/L) to proportionality limit Yield strength - elastic vs. plastic deformation Tensile Strength Brittle vs ductile Stress%E2%80%93strain _curve

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A: Engineering Stress = Force / Original Area B: True Stress = Force / Area _strain_brittle_2.png ain_A36_2.svg

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Specific Strength Specific Strength = Strength / density [N * m / kg] Cable Material needs MN*m/kg Breaking Length – Can suspend its own weight under Earths gravity = Specific Strength / g Required breaking length: 4960km

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Theoretical Strength Limit Atoms are in a harmonic potential well of depth E b = 10eV Interatomic distance d = width of well = 0.2nm E b = kd 2 / 2 k = 2E b / d 2 Pushing on a slab: F = kΔd * A/ d 2 Δd/d = ΔL/L F = E*A*ΔL/L Result: E = 2E b / d 3 If Δd can d then T ~ E = 300Gpa

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Typical Materials Stainless Steel – 2GPa Quartz - 48MPa Tensile Strength (1GPa compressive) Diamond – 60MPa Tensile Strength (but expensive) MaterialStrength (Mpa) Specific Strength (kY) Breaking Length (km) Glass Micro-Melt 10 Tough Treated Tool Steel 5171(yield)69471 Kevlar Diamond60,000 observed

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Orbital Hybridization Bond strength Covalent>ionic>metallic Bonding situation causes excitation New Schrodinger has hybridized solutions New Schrodinger has hybridized solutions N(s + 3pσ) Methane sp 3 orbitals Ethene sp 2 orbitals (+ free p z ) mcdebeer.wordpress.com en.citizendium.org al_hybridisation

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Orbital Hybridization Graphene sp 2 - sp 2 overlap sp 2 and sp 3 energy Pi bonds for strength and conductivity raphene-pi-orbitals.html en.citizendium.org

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Carbon Nanotubes SWNT, MWNT (n, m) indices 1.4g/cc Individual CNT shell 100,000 MPa 48,000 kY 4900 km Breaking Length Armchair SWNT theoretically up to 126 GPa MWNT observed up to 150 GPa

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Other Considerations Climbing Time Powering the climber Radiation Objects in orbit Launching objects

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References Slide 7: Slide 8: Atomic Physics: An Exploration Through Problems and Solutions 2 nd Edition - Budker Slide 9: Slide 12: Slide 13: Slide 14:

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