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Low-Thrust Transfers from GEO to Earth-Moon Lagrange Point Orbits

Low-Thrust Transfers from GEO to Earth-Moon Lagrange Point Orbits. Andrew Abraham Moravian College, 2013. Newton’s Laws. If then & the object moves in a straight line Action = Reaction: . Orbits: Inertial Reference Frame. Orbits: Inertial Reference Frame. Orbital Trajectories.

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Low-Thrust Transfers from GEO to Earth-Moon Lagrange Point Orbits

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  1. Low-Thrust Transfers from GEO to Earth-Moon Lagrange Point Orbits Andrew Abraham Moravian College, 2013

  2. Newton’s Laws If then & the object moves in a straight line Action = Reaction:

  3. Orbits: Inertial Reference Frame

  4. Orbits: Inertial Reference Frame

  5. Orbital Trajectories

  6. Circular Orbit

  7. Applications of Various Orbits

  8. Low Earth Orbit (LEO)

  9. Medium Earth Orbit (MEO)

  10. Geosynchronous Earth Orbit (GEO)

  11. Molniya Orbit (HEO) Russia Visible 83% of the time

  12. Non-Chemical vs. Chemical Ions + Electric/Magnetic Fields Fuel + Oxidizer

  13. Atmospheric Operation Ion Engine Chemical Engine

  14. Rocket RE-ACTION ACTION

  15. Rocket Equation Rocket Equation = Change in Spacecraft’s Velocity = Efficiency of Rocket = 9.81m/s2 = Final Spacecraft Mass = Initial Spacecraft Mass

  16. Mass vs. Specific Impulse (Isp) Low Thrust: Isp= 3000s %Mass = 89.5% Chemical Propellant: Isp= 200 - 300s %Mass = 25.0%

  17. Ion Engine

  18. Ion Engine • Constant Thrust of 500-700mN • About the weight of 8 quarters or 0.1lbs • Consumes 2-8KW of electrical power from solar arrays

  19. Orbit Maneuvers:High vs. Low Thrust Low Thrust (Ion) High Thrust (Chemical)

  20. Example: LEO to GEO • LEO ……………….Green • Low Thrust ……Red • GEO ………………Blue • 1000Kg • 855.5Kg • Time of Flight: 102 days

  21. Add the Moon!?

  22. The 3 Body Problem Velocity…………Gray Force of …...Red Force of ……Green Force of ……Blue

  23. Make Simplifying Assumptions Assume: Circular Restricted 3 Body Problem & are only influenced by each other and orbit their common center of mass in perfectly circular orbits

  24. Circular Restricted 3-Body Problem (CR3BP) WARNING!!! Non-Inertial Reference Frame (Rotating) Define: Synodic Reference Frame

  25. CR3BP Equations of Motion

  26. CR3BP: 5 Equilibrium (Lagrange) Points

  27. Characterization of Lagrange Points m Inverted Pendulum (Unstable) Pendulum (Stable) m

  28. Unstable Lagrange Point L2 Applications: Communications Navigation (GPS) Observation

  29. Lyapunov, Halo, and Lissajous Orbits Halo L1 Moon Earth Lyapunov Lissajous L1 Moon Earth Image Credit: NASA

  30. Merging Low-Thrust & Halo Orbits in the Earth-Moon System L4 L3 moon L2 L1 L5

  31. Merging Low-Thrust & Halo Orbits in the Earth-Moon System L3 L5 L1 moon L2 L4 Different View

  32. One More View 1000kg Spacecraft 69kg of fuel used for 60 day flight GEO-like orbit to Halo orbit

  33. NASA Space Station Resupply Mission(s)

  34. Thank You! • Questions?

  35. Applications: Sun-Earth System Solar & Heliospheric Observatory (SOHO) @ Sun-Earth L1 WMAP, James Webb Telescope, Plank @ Sun-Earth L2 Planet-X @ Sun-Earth L3 Trojan Asteroids @ Sun-Earth L4 & L5 Wilkinson Microwave Anisotropy Probe (WMAP)

  36. Centrifugal Force

  37. “Weightlessness”(Non-Inertial Reference Frame) y Fg Fc x v F = ma F = Fg + Fc= 0

  38. Orbits: Inertial Reference Frame y Fg v x

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