2008-11-21 mission analysis geometric visibility and manoeuvre calculations tommy yuen
TRANSCRIPT
Lunar Penetrator – 1
2008-11-21
Mission AnalysisGeometric Visibility and Manoeuvre Calculations
Tommy Yuen
Presentation Outline• Requirements• How Are We Getting There?• Geometric Visibility• Theoretical Hohmann Transfer• Verifying STK Results• Conclusion• Future Work
2008-11-21 2Tommy Yuen
RequirementsThe Penetrator shall:
• Penetrate a depth of 2 ± 0.5 m • Have sufficient link time to be able to
transmit segments of data in packets periodically
• Be able to communicate with the relay satellite of Selene I
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How Are We Getting There?Selene I – Satellite information
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Main Orbiter (SELENE I)Circular Orbit
Orbit 100 [km]Inclination 90 [°]
Relay Satellite (OKINA)Elliptical Orbit
Orbit 100 x 2400 [km]Inclination 90 [°]
Simplifications: The apoapsis is at -90° lattitude
Selene I
Okina
Geometric VisibilityIdeal case geometric link time:
• Approximately 7000 s
Ideal case regolith transmission thickness:• Approximately 11.8 m
Worst case geometric link time: • Approximately 80 s
Simplifications: • 90° latitude• Only communicates with Okina
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0.8°
80°
2.5 m0.45 m
80°
Worst and Ideal Case Comparison
Ideal Case
Geometric Visibility
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0 10 20 30 40 50 60 70 80 900
1000
2000
3000
4000
5000
6000
7000
8000
Transmission Angle vs. Link Time
Transmission Angle [°]
Link
Tim
e [s
]
Theoretical Hohmann Transfer
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Circular Orbit
Elliptical Orbit
Change in Velocity Required
Rp
Ra
circularcircular rV
arVa
12
acircular VVV
Theoretical Hohmann Transfer
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0 200 400 600 800 1000 1200 1400 1600 18000
400
800
1200
1600
Hohmann Transfer and Impact Velocity
Change in Velocity Required [m/s]
Spee
d at
Impa
ct [m
/s]
Free Fall Velocity554 m/s
Verifying STK Results• Conservation of Energy:
• Tsiolkovsky's Rocket Equation:
• Simplifications:• Tangential Velocity is Cancelled Prior to Free Fall
• Booster Engines Apply Impulsive Burns and have an Isp of 285 s
• The Mass of the Penetrator is 10 kg
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moon
penmoon
moonaltitude
penmoonimpactpeninitialpen r
MMG
rr
MMGVMVM 22
2
1
2
1
final
initialsp M
MlngIV 0
Verifying STK Results• Scenario 1
– A vertical burn was used to slow the penetrator down to 0 m/s at the desired altitude of about 28.1 km
– Amount of fuel required is about 11.2 kg
• Scenario 2
– A vertical burn was used to slow the penetrator down to 300 m/s at the surface of the moon
– Amount of fuel required is about 9.7 kg
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Conclusion
• Geometric link time is about 80 to 7000 s
• Hohmann transfer is not a plausible option
• STK results agree with back of the envelope calculations
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Future Work
• Refine communication visibility simulations for different impact locations and craters
• Determine post impact mission time line
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Lunar Penetrator – 1
2008-11-21
Questions?