1. AAE450 Spring 2009 LEO Atmospheric Drag Analysis and Lunar Orbit Circularization [Andrew Damon] [Mission Ops] February 19, 2009 1

2. AAE450 Spring 2009 [Andrew Damon] [Mission Ops] Atmospheric Drag for Circular Parking Orbits 2 Circular Parking Orbit Altitude (km) Drag (mN) T/D Assume Thrust of 110 mN 20076.4 1.44 30017.86.18 4004.126.83 5000.96114.6 Assume Thrust of 110 mN Assume C D = 1.0 Analysis based on cross section area of: Solar Panels ~ 8 m 2 OTV ~ 4 m 2 Total Area ~ 12 m 2 Recommend: Parking Orbit of 400 km – Drag drops to less than 5% of Thrust, Within capabilities of Dnepr Launch Vehicle

3. AAE450 Spring 2009 Lunar Orbit Circularization  “Step-down” of lunar orbit by thrusting near periapsis (braking)  Goal of 110 km circular parking orbit  EP thruster fired from -45 o to 45 o  Modeled as impulsive maneuver to approximate benefit  ΔV ≈.38 m/s delivered near perilune with EP system  Circularization time on the order of 4 years – not acceptable Solutions: - Raise parking orbit - Extend Earth outbound spiral - Use chemical system to deliver some ΔV [Andrew Damon] [Mission Ops] 3

4. AAE450 Spring 2009 Drag Calculations F D ~ Newtons ρ ~ kg/m 3 C D ~ dimensionless v ~ m/s A ~ m 2 **Can be incorporated as part of EOMs [Andrew Damon] [Mission Ops] Backup Slides 4 Altitude (km) Circular Velocity (km/s) 2007.78 3007.73 4007.67 5007.61 Curve fit for density based on altitude: Where h is altitude in km and ρ is in ng/m 3

5. AAE450 Spring 2009 EP ΔV approximation -TOF for -45 o to -45 o determined - m o is known from time history - m dot assumed to be constant for EP - m f = m o - m dot (TOF) Just apply ideal rocket equation… Isp for system is known -ΔV = Isp*go*ln(m o / m f ) -Because ΔV was applied symmetric to periapsis and this TOF was a small portion of the orbital period, the ΔV was considered impulsive for this “step-down” analysis [Andrew Damon] [Mission Ops] 5