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

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Presentation transcript:

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

Newton’s Laws

Orbits: Inertial Reference Frame

Orbital Trajectories

Circular Orbit

Applications of Various Orbits

Low Earth Orbit (LEO)

Medium Earth Orbit (MEO)

Geosynchronous Earth Orbit (GEO)

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

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

Atmospheric Operation Ion Engine Chemical Engine

Rocket ACTION RE-ACTION

Rocket Equation

Mass vs. Specific Impulse (I sp ) Chemical Propellant: I sp = s %Mass = 25.0% Low Thrust: I sp = 3000s %Mass = 89.5%

Ion Engine

Constant Thrust of mN About the weight of 8 quarters or 0.1lbs Consumes 2-8KW of electrical power from solar arrays

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

Example: LEO to GEO

Add the Moon!?

The 3 Body Problem

Make Simplifying Assumptions

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

25 CR3BP Equations of Motion

26 CR3BP: 5 Equilibrium (Lagrange) Points

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

28 Unstable Lagrange Point L2L2 Applications: Communications Navigation (GPS) Observation

29 Lyapunov, Halo, and Lissajous Orbits Image Credit: NASA Moon L1L1 L1L1 Earth Halo Lyapunov Lissajous

30 Merging Low-Thrust & Halo Orbits in the Earth-Moon System L4L4 L5L5 L3L3 L1L1 L2L2 moon

31 Merging Low-Thrust & Halo Orbits in the Earth-Moon System L3L3 Different View L5L5 L4L4 L2L2 L1L1 moon

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 Wilkinson Microwave Anisotropy Probe (WMAP) 1.Solar & Heliospheric Observatory Sun-Earth L 1 2.WMAP, James Webb Telescope, Sun-Earth L 2 Sun-Earth L 3 4.Trojan Sun-Earth L 4 & L 5

Centrifugal Force

“Weightlessness” (Non-Inertial Reference Frame) y x FgFg v FcFc F = ma F = F g + F c = 0

Orbits: Inertial Reference Frame y x FgFg v