Low-Thrust Transfers from GEO to Earth-Moon Lagrange Point Orbits Andrew Abraham Moravian College,...
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Transcript of Low-Thrust Transfers from GEO to Earth-Moon Lagrange Point Orbits Andrew Abraham Moravian College,...
Low-Thrust Transfers from GEO to Earth-Moon Lagrange Point Orbits
Andrew AbrahamMoravian College, 2013
Newton’s Laws
1. If then & the object moves in a straight line
2. Action = Reaction:
Orbits: Inertial Reference Frame
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 EngineChemical
Engine
Rocket
ACTIONRE-ACTION
Rocket Equation
𝑚𝑓
𝑚0
=𝑒− Δ𝑉𝐼 𝑠𝑝𝑔0Rocket Equation
= Change in Spacecraft’s Velocity = Efficiency of Rocket = 9.81m/s2
= Final Spacecraft Mass = Initial Spacecraft Mass
Mass vs. Specific Impulse (Isp)
Chemical Propellant: Isp= 200 - 300s %Mass = 25.0%
Low Thrust: Isp = 3000s %Mass = 89.5%
𝑚𝑓
𝑚0
=𝑒− Δ𝑉𝐼 𝑠𝑝𝑔0
Δ𝑉=3𝑘𝑚/ 𝑠
Ion Engine
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
High Thrust (Chemical)
Low Thrust (Ion)
Orbit Maneuvers:High vs. Low Thrust
Example: LEO to GEO
• LEO ……………….Green• Low Thrust ……Red• GEO ………………Blue
• 1000Kg • 855.5Kg
• Time of Flight: 102 days
Add the Moon!?
The 3 Body Problem
Velocity…………GrayForce of …...RedForce of ……GreenForce of ……Blue
𝑚2
𝑚1
𝑚3
Make Simplifying Assumptions
Assume: Circular Restricted 3 Body Problem
1.
2. & are only influenced by each other and orbit their common center of mass in perfectly circular orbits
24
Circular Restricted 3-Body Problem (CR3BP)
Define:µ≡
𝑚2𝑚1+𝑚2
Synodic Reference Frame
WARNING!!!Non-Inertial Reference Frame
(Rotating)
25
CR3BP Equations of Motion
𝑈=𝑉 −12
(𝑥2+𝑦 2 )
26
CR3BP: 5 Equilibrium (Lagrange) Points
27
Characterization of Lagrange Points
m
m
Pendulum (Stable)
Inverted Pendulum (Unstable)
28
Unstable Lagrange Point
L2
Applications:CommunicationsNavigation (GPS)Observation
29
Lyapunov, Halo, and Lissajous Orbits
Image Credit: NASA
Moon
Moon
L1
L1
Earth
Earth
Halo
Lyapunov Lissajous
30
Merging Low-Thrust & Halo Orbits in the Earth-Moon System
L4
L5
L3
L1 L2
moon
31
Merging Low-Thrust & Halo Orbits in the Earth-Moon System
L3
Different View
L5
L4L2
L1
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 (SOHO) @ Sun-Earth L1
2. WMAP, James Webb Telescope, Plank @ Sun-Earth L2
3. Planet-X @ Sun-Earth L3
4. Trojan Asteroids @ Sun-Earth L4 & L5
Centrifugal Force
“Weightlessness”(Non-Inertial Reference Frame)
y
xFg
v
Fc
F = maF = Fg + Fc = 0
Orbits: Inertial Reference Framey
x
Fg v