Lunar Descent Trajectory February 5 th 2009 AAE

Lunar Descent Trajectory February 5 th, 2009 AAE 450 Spring 2009 [John Aitchison] [Mission Ops]

Descent Trajectory § Goal – Determine trajectory, attitude, burn time, range & altitude § EOM Derivation Assumptions • Moon/spacecraft system, spherical & does not rotate, point masses • 2 -D problem • T/m varies only with changing propellant mass (no throttling) 2 AAE 450 Spring 2009 [John Aitchison] [Mission Ops]

Useful Numbers Time (s) 0. 0 Action Retro Downrange (km) Altitude (km) 0. 0 15 170. 3 27° 170. 1 5. 7 207. 5 Vertical 175. 4 0. 9 222. 1 Touchdown 175. 4 0. 0 § Variability with: – Vehicle Mass – Thrust Capability – Lunar Parking Orbit 3 AAE 450 Spring 2009 [John Aitchison] [Mission Ops]

Code (pg. 1) 4 AAE 450 Spring 2009 [John Aitchison] [Mission Ops]

Code (pg. 2) 5 AAE 450 Spring 2009 [John Aitchison] [Mission Ops]

Code (pg. 3) 6 AAE 450 Spring 2009 [John Aitchison] [Mission Ops]

Code (pg. 4) 7 AAE 450 Spring 2009 [John Aitchison] [Mission Ops]

Coordinate System 8 AAE 450 Spring 2009 [John Aitchison] [Mission Ops]

Coordinate System Definitions 9 AAE 450 Spring 2009 [John Aitchison] [Mission Ops]

Assumptions 10 AAE 450 Spring 2009 [John Aitchison] [Mission Ops]

Calculations (pg. 1) 11 AAE 450 Spring 2009 [John Aitchison] [Mission Ops]

Calculations (pg. 2) 12 AAE 450 Spring 2009 [John Aitchison] [Mission Ops]

Calculations (pg. 3) 13 AAE 450 Spring 2009 [John Aitchison] [Mission Ops]

Calculations (pg. 4) 14 AAE 450 Spring 2009 [John Aitchison] [Mission Ops]