Cost Comparison of Higher Parking Orbit Scale up for Arbitrary Payload February 26, 2009 [Levi Brown] [Mission Ops] 1

Raising Departure Orbit 1. Depart from higher circular parking orbit Decrease lunar transfer/Increase launch 2. Determine total cost effects Limitations in launch vehicle capability 3. Investigate eccentric orbits Create curve of launch vehicle performance with orbit energy 4. Determine mass and power for varying altitudes Use sizing code from propulsion 5. Best fit curve relationships 6. Cost with varying orbit energy Result: Launch from lowest altitude (400 km) Use longest time of flight (1 year) [Levi Brown] [Mission Ops] 2

Scale Up for Arbitrary Payload Assume OTV is deliverable mass to 400 km for that launch vehicle Sized OTV using same code as previously Determined Power required, payload mass to lunar orbit (LLO) and relative cost to LLO Launch Vehicle Relative Cost to LLO (Thousand $/kg) Relative Cost to LEO (Thousand $/kg) Falcon 9 (Loaded) 16.1 3.7 Dnepr 16.8 4.4 Falcon 9 (Partial) 20.2 6.1 Rockot 22.0 74 Soyuz 22.3 7.5 Delta IV 27.2 10.7 Delta II 40.6 17.9 Note: Assumed used same thruster as for the small payload Looking into higher thrust and more efficient engines Result: Minimize relative cost by minimizing relative cost to LEO [Levi Brown] [Mission Ops] 3

Back-up Slides [Levi Brown] [Mission Ops] 4

Initial Analysis Results Using a circular departure orbit Departure Altitude (km) Initial Mass (kg) Thrust Required (mN) Power (kW) Solar Array Mass (kg) Power Cost (Million $) 200 650 123 2.2 14.6 2000 630 102 1.7 11.3 15000 600 55 0.7 4.7 0.4 36000 580 31 2.7 Note: Analysis performed for a mass flow rate of 7.1 mg/s and 150 day time of flight This analysis was performed prior to the change of using a minimum Parking orbit of 400 km [Levi Brown] [Mission Ops] 5

Dnepr Launch Vehicle Capability Circular Altitude (km) Eccentric Orbit Energy Levels Dnepr ($ 15 million) Circular Altitude (km) Deliverable Mass (kg) 200 4400 300 3700 400 3400 500 2750 600 1900 700 1200 800 650 900 Apoapsis Altitude (km) Semi-Major Axis Energy (km^2/s^2) 400 6778.14 -29.4034 500 6828.14 -29.1881 750 6953.14 -28.6633 1000 7078.14 -28.1571 2000 7578.14 -26.2994 5000 9078.14 -21.9539 10000 11578.14 -17.2135 Note: Periapsis is at an altitude of 400 km [Levi Brown] [Mission Ops] 6

Launch Vehicle Capability Curve [Levi Brown] [Mission Ops] 7

Sizing Results TOF (days) mdot (mg/s) Apoapsis Altitude a (km) Energy Mo (kg) Power (Kw) 351 5.6 400 6778.14 -29.4033792 679.8 2.5846 500 6828.14 -29.1880689 679.6 2.5646 750 6953.14 -28.6633407 679.3 2.5209 1000 7078.14 -28.1571459 678.9 2.4696 2000 7578.14 -26.2993585 677.7 2.3109 5000 9078.14 -21.9538607 675.1 1.9507 10000 11578.14 -17.2134921 672 1.5236 196 621.5 6.5534 621.1 6.5007 620.2 6.3709 619.2 6.2373 615.9 5.7801 608.1 4.727 600.3 3.6605 Note: This analysis was performed using previous payload mass of 320 kg [Levi Brown] [Mission Ops] 8

Initial OTV Mass with Varied Orbit Energy mdot=5.6 mg/s [Levi Brown] [Mission Ops] 9

Power Required with Varied Orbit Energy mdot=5.6 mg/s [Levi Brown] [Mission Ops] 10

Cost Model 11 ms/c = spacecraft mass required to reach LLO CLaunch Vehicle = Total cost of launch vehicle (LV) mLV Capability = mass LV can put into orbit Ps/c = power required to reach LLO Prate = $1000/Watt Mprop= propellant mass required to reach LLO Xerate = Cost of Xe ($1200/kg) [Levi Brown] [Mission Ops] 11

Falcon 9 Total Cost for Varying Apoapsis 196 and 351 Day TOF [Levi Brown] [Mission Ops] 12

Confirmation of Results Lowest cost at 400 km Orbit and 351 days [Levi Brown] [Mission Ops] 13

Scale up for Arbitrary Payload Results Launch Vehicle Mass to 400 km (kg) Thrust (mN) Number of Thrusters Mpay (kg) Power Required (kW) Mprop (kg) Dnepr 3400 680 3 2130.5 20.3 509.4 Falcon 9 9953 2001 9 6060.6 59 1528.4 6000 1205 5 3717.9 37.6 849.1 Rockot 1825 357 2 1038.9 9.03 339.7 Delta II 3065 606 1780.4 16.7 509.5 Soyuz 5025 1000 4 3143 32.05 679.3 Delta IV 23757 4760 20 14853.5 147.3 3397 [Levi Brown] [Mission Ops] 14

Increasing to 15000 km circular orbit saved 50 kg and 1.5 kW More Notes Increasing to 15000 km circular orbit saved 50 kg and 1.5 kW It was hoped that using a larger launch vehicle with higher capability would decrease overall cost. The cost/kg would only increase slightly, but it would allow a significant decrease in power costs. 1 Year TOF: 10000 km depart vs 400 km saved approximately 1 kW 196 days TOF: 10000 km depart vs 400 km saved approximately 3 kW For this reason, the minimum total cost for shorter TOF occurred at a median altitude of Around 4000 km vs the minimum total for longer TOF occurred at low altitudes However the increase in power to have the shorter TOF still outweighs the savings So the minimum cost still occurs at long TOF with at low altitudes [Levi Brown] [Mission Ops] 15