1. AAE450 Spring 2009 Preliminary Trans-Lunar Analysis [Levi Brown] [Mission Ops] January 29, 2009 1

2. AAE450 Spring 2009 [Levi Brown] [Mission Ops] Bielliptic Transfer Two Body Problem (Point Mass Central Bodies) Coplanar transfer between Earth (200 km) and lunar (110 km) parking orbits Method of patched conics For Calculation: Use intermediate radius 1,000,000 km beyond the moon’s orbit HohmannBielliptic Delta V (km/s)4.04.2 Time of Flight (days) ~481 Bielliptic consistently slightly larger for reasonable flight times Impulse Thrust = Hohmann 2

3. AAE450 Spring 2009 Low Thrust Transfer [Levi Brown] [Mission Ops] Electric propulsion sizing analysis from Space Propulsion Analysis and Design Circular spiral transfer: ΔV = ΔV 2 – ΔV 1 ≈ 7 km/s Isp varied 1000-4000 seconds Efficiency of 0.55 Results: Time of Flight 1-8 months Requires 55-500 mN and 2-5 kW 3

4. AAE450 Spring 2009 Back-up Slides [Levi Brown] [Mission Ops] 4

5. AAE450 Spring 2009 [Levi Brown] [Mission Ops] Comparisons for Other Orbits Earth Parking Orbit (km) Lunar Parking Orbit (km) Intermediate radius (km) ParameterHohmann (Approx.) Bielliptic 2001101,000,000 Delta V(km/s)4.04.2 Time of Flight~5 days81 days 2001103,750,000 Delta V(km/s)4.03 Time of Flight1 yr 36,0001101,000,000 Delta V(km/s)1.82.11 Time of Flight6 days83 days 36,0001103,750,000 Delta V(km/s)2.03 Time of Flight1 yr 2005001,000,000 Delta V(km/s)3.94.1 Time of Flight5 days81 days 5

6. AAE450 Spring 2009 [Levi Brown] [Mission Ops] Comparisons for Other Orbits Earth Parking Orbit (km) Lunar Parking Orbit (km) Intermediate radius (km) ParameterHohmann (Approx.) Bielliptic 2005003,750,000 Delta V(km/s)3.9 Time of Flight1 yr 36,0005001,000,000 Delta V(km/s)1.72.05 Time of Flight6 days83 days 36,0005003,750,000 Delta V(km/s)1.9 Time of Flight1 yr 6

7. AAE450 Spring 2009 Reference Humble, Ronald W., Henry, Gary N., Larson, Wiley J. Space Propulsion Analysis and Design. McGraw-Hill Companies, 1995, Pg 518, 619. [Levi Brown] [Mission Ops] 7