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

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

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

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

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

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

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

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

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

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

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

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

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: