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Orbital Mechanics Dominic Ernst, Omar Abdel-Wahab
Orbital MechanicsDominic Ernst, Omar Abdel-Wahab
Orbital mechanics
IntroductionInto OrbitTo Marsand beyond…
Why Orbital Mechanics? Introduction Into Orbit To Mars and beyond…
Understanding of celestial movementsIt’s awesome!For Science!…and convenience
Orbital velocity Introduction Into Orbit To Mars and beyond…
How fast are you moving?A: 0 km/hB: 1600 km/h C: 25 km/sD: 225 km/sE: well, it depends…à Concept of relative velocity
Kepler’s LawsIntroduction Into Orbit To Mars and beyond…
The Orbit of an Object is an ellipse with the heavy body in one centerSpeed is proportional to distance from centerOrbital period is proportional to orbital radius
Conservation of EnergyIntroduction Into Orbit To Mars and beyond…
Orbital mechanics
IntroductionInto OrbitTo Marsand beyond…
Into Orbit Introduction Into Orbit To Mars and beyond…
Vertical componentHorizontal componentOrbitsRocket 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 componentHorizontal componentOrbitsRocket Launch
Horizontal component Introduction Into Orbit To Mars and beyond…
But Earth‘s surface iscurved!
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 Orbitaround Earth
Into Orbit Introduction Into Orbit To Mars and beyond…
Vertical componentHorizontal componentOrbitsRocket Launch
OrbitsIntroduction Into Orbit To Mars and beyond…
Low Earth Orbit – LEOMedium Earth Orbit – MEOGeostationary Earth Orbit – GEOothers...
OrbitsIntroduction Into Orbit To Mars and beyond…
Low Earth Orbit – LEOMedium Earth Orbit – MEOGeostationary Orbit – GEOothers...
https://en.wikipedia.org/wiki/Low_Earth_orbit#/media/File:Orbitalaltitudes.jpg
OrbitsIntroduction Into Orbit To Mars and beyond…
Low Earth Orbit – LEOMedium Earth Orbit – MEOGeostationary Orbit – GEOothers...
https://en.wikipedia.org/wiki/Low_Earth_orbit#/media/File:Orbitalaltitudes.jpg
OrbitsIntroduction Into Orbit To Mars and beyond…
Orbit Height Velocity Period Used for
LEO 200 - 1'500 km 7.1 - 7.8 km/s
1.5 - 5 h Earth observationSpace stations (ISS)Communication
MEO 6'000 - 12'000 km
5.6 - 4.7 km/s
5 - 12 h Navigation (GPS)Communication
GEO 35'786 km 3.07 km/s 23h 56min 4s
Communication Weather observation TV broadcast (Astra, Eutelsat)
Graveyard Orbit
ca. GEO + 300km < GEO > GEO Disposed satellites
OrbitsIntroduction Into Orbit To Mars and beyond…
Orbit Height Velocity Period Used for
LEO 200 - 1'500 km 7.8 - 7.1 km/s
1.5 - 5 h Earth observationSpace stations (ISS)Communication
MEO 6'000 - 12'000 km
5.6 - 4.7 km/s
5 - 12 h Navigation (GPS)Communication
GEO 35'786 km 3.07 km/s 23h 56min 4s
Communication Weather observation TV broadcast (Astra, Eutelsat)
Graveyard Orbit
ca. GEO + 300km < GEO > GEO Disposed satellites
Into Orbit Introduction Into Orbit To Mars and beyond…
Vertical componentHorizontal componentOrbitsRocket Launch
Rocket LaunchIntroduction Into Orbit To Mars and beyond…
https://www.grc.nasa.gov/www/k-12/rocket/rktrflght.html
Orbital mechanics
IntroductionInto OrbitTo Marsand 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 monthWhen can we go?
Other problems Introduction Into Orbit To Mars and beyond…
Orbit of Mars is inclined & elliptical
Orbital mechanics
IntroductionInto OrbitTo Marsand beyond…
and beyond…Introduction Into Orbit To Mars and beyond…
Limits by:CostFeasibilityTime
and beyond…Introduction Into Orbit To Mars and beyond…
MethodsHohmann transfersGravitational slingshotFuzzy orbits
Hohmann transferIntroduction 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 assist1961: Michael MinovitchFirst application:
Mariner 10 (1973): to Mercury via Venus
Gravitational Slingshot Introduction Into Orbit To Mars and beyond…
Steal orbital energy of a planetChange 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…
https://saturn.jpl.nasa.gov/resources/1776/
Cassini-Huygens
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 orbitsIntroduction Into Orbit To Mars and beyond…
Even lower-cost-paths possiblePaths between Lagrange points of planets
Low cost, but often very slowLot of computation necessaryFuture: high-volume, low-value goods
https://en.wikipedia.org/wiki/Interplanetary_Transport_Network#/media/File:Interplanetary_Superhighway.jpg
Orbital mechanics
Questions?
Want to learn more?
Play «Kerbal Space Program»https://kerbalspaceprogram.com/en/
