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

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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?