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Orbital Mechanics Orbital Mechanics Dominic Ernst, Omar Abdel-Wahab Orbital Mechanics Orbital mechanics Introduction Into Orbit To Mars and beyond… Why Orbital Mechanics? Introduction Into Orbit To Mars and beyond… Understanding of celestial movements It’s awesome! For Science! …and convenience Orbital velocity Introduction Into Orbit To Mars and beyond… How fast are you moving? A: 0 km/h B: 1600 km/h C: 25 km/s D: 225 km/s E: well, it depends… à Concept of relative velocity Kepler’s Laws Introduction Into Orbit To Mars and beyond… The Orbit of an Object is an ellipse with the heavy body in one center Speed is proportional to distance from center Orbital period is proportional to orbital radius Conservation of Energy Introduction Into Orbit To Mars and beyond… Orbital mechanics Introduction Into Orbit To Mars and beyond… Into Orbit Introduction Into Orbit To Mars and beyond… Vertical component Horizontal component Orbits Rocket Launch Vertical component Introduction Into Orbit To Mars and beyond… https://www.kennedyspacecenter.com/events/events-calendar/see-a-rocket-launch Into Orbit Introduction Into Orbit To Mars and beyond… Vertical component Horizontal component Orbits Rocket Launch Horizontal component Introduction Into Orbit To Mars and beyond… But Earth‘s surface is curved! Horizontal component Introduction Into Orbit To Mars and beyond… Horizontal component Introduction Into Orbit To Mars and beyond… Horizontal component Introduction Into Orbit To Mars and beyond… Gravitational force Centripetal force Horizontal component Introduction Into Orbit To Mars and beyond… Velocity needed for Orbit around Earth Into Orbit Introduction Into Orbit To Mars and beyond… Vertical component Horizontal component Orbits Rocket Launch Orbits Introduction Into Orbit To Mars and beyond… Low Earth Orbit – LEO Medium Earth Orbit – MEO Geostationary Earth Orbit – GEO others... Orbits Introduction Into Orbit To Mars and beyond… Low Earth Orbit – LEO Medium Earth Orbit – MEO Geostationary Orbit – GEO others... https://en.wikipedia.org/wiki/Low_Earth_orbit#/media/File:Orbitalaltitudes.jpg Orbits Introduction Into Orbit To Mars and beyond… Low Earth Orbit – LEO Medium Earth Orbit – MEO Geostationary Orbit – GEO others... https://en.wikipedia.org/wiki/Low_Earth_orbit#/media/File:Orbitalaltitudes.jpg Orbits Introduction Into Orbit To Mars and beyond… Orbit Height Velocity Period Used for LEO 200 - 1'500 km 7.1 - 7.8 km/ 1.5 - 5 h Earth observation s Space stations (ISS) Communication MEO 6'000 - 12'000 5.6 - 4.7 km/ 5 - 12 h Navigation (GPS) km s Communication GEO 35'786 km 3.07 km/s 23h 56min Communication 4s Weather observation TV broadcast (Astra, Eutelsat) Graveyard ca. GEO + 300km < GEO > GEO Disposed satellites Orbit Orbits Introduction Into Orbit To Mars and beyond… Orbit Height Velocity Period Used for LEO 200 - 1'500 km 7.8 - 7.1 km/ 1.5 - 5 h Earth observation s Space stations (ISS) Communication MEO 6'000 - 12'000 5.6 - 4.7 km/ 5 - 12 h Navigation (GPS) km s Communication GEO 35'786 km 3.07 km/s 23h 56min Communication 4s Weather observation TV broadcast (Astra, Eutelsat) Graveyard ca. GEO + 300km < GEO > GEO Disposed satellites Orbit Into Orbit Introduction Into Orbit To Mars and beyond… Vertical component Horizontal component Orbits Rocket Launch Rocket Launch Introduction Into Orbit To Mars and beyond… https://www.grc.nasa.gov/www/k-12/rocket/rktrflght.html Orbital mechanics Introduction Into Orbit To Mars and beyond… Hohmann Transfer Introduction Into Orbit To Mars and beyond… Orbital maneuver with minimal energy requirement (Δv) Increase Apoapsis to target Orbit Hohmann Transfer Introduction Into Orbit To Mars and beyond… Going from Earth to Mars takes ~8 month When can we go? Other problems Introduction Into Orbit To Mars and beyond… Orbit of Mars is inclined & elliptical Orbital mechanics Introduction Into Orbit To Mars and beyond… and beyond… Introduction Into Orbit To Mars and beyond… Limits by: Cost Feasibility Time and beyond… Introduction Into Orbit To Mars and beyond… Methods Hohmann transfers Gravitational slingshot Fuzzy orbits Hohmann transfer Introduction Into Orbit To Mars and beyond… https://de.wikipedia.org/wiki/Hohmann-Transfer Gravitational Slingshot Introduction Into Orbit To Mars and beyond… Also: Swing-by or Gravity assist 1961: Michael Minovitch First application: Mariner 10 (1973): to Mercury via Venus Gravitational Slingshot Introduction Into Orbit To Mars and beyond… Steal orbital energy of a planet Change speed and trajectory of spacecraft (Almost) no fuel needed Gravitational Slingshot Introduction Into Orbit To Mars and beyond… https://en.wikipedia.org/wiki/Gravity_assist Gravitational Slingshot Introduction Into Orbit To Mars and beyond… Cassini-Huygens https://saturn.jpl.nasa.gov/resources/1776/ Gravitational Slingshot Introduction Into Orbit To Mars and beyond… https://en.wikipedia.org/wiki/Gravity_assist#/media/File:Cassini%27s_speed_related_to_Sun.png Fuzzy orbits Introduction Into Orbit To Mars and beyond… Even lower-cost-paths possible Paths between Lagrange points of planets Low cost, but often very slow Lot of computation necessary Future: high-volume, low-value goods https://en.wikipedia.org/wiki/Interplanetary_Transport_Network#/media/File:Interplanetary_Superhighway.jpg Orbital mechanics Questions? 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