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

2. 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

3. 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

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

5. 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

6. 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
500
750
1000
2000
5000
10000
Note:
Periapsis is at an altitude of 400 km
[Levi Brown] [Mission Ops] 6

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

8. Sizing Results
TOF (days)
mdot (mg/s)
Apoapsis Altitude
a (km)
Energy
Mo (kg)
Power (Kw)
351
5.6
400
679.8
2.5846
500
679.6
2.5646
750
679.3
2.5209
1000
678.9
2.4696
2000
677.7
2.3109
5000
675.1
1.9507
10000
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

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

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

11. 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

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

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

14. 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
147.3
3397
[Levi Brown]
[Mission Ops] 14

15. Increasing to 15000 km circular orbit saved 50 kg and 1.5 kW
More Notes
Increasing to 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: km depart vs 400 km saved approximately 1 kW
196 days TOF: 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