oW THRUST TO ESCAPE: RESULTS OF NUMERICAL COMPUTATIONS DEFINITIONS: Sesc =S(E=0 (linear distance travelled) △V ds丿 0 06 0.89079 28 063 0.86 0.8850.79 LO 0.63 0.80 10 78 0.6 09650,0000.88071 to a good approximation 1-0.79 0.88 =0.63 Edelbaum's Sub-Optimal Climb and Plane Change Instead of optimizing the tilt profile a(0), Edelbaum(1961, 1973)just kept J a constant during each orbit, then optimized |a I(R) 16.522, Space P pessan Lecture 3 Prof. Manuel martinez Page 4 of 916.522, Space Propulsion Lecture 3 Prof. Manuel Martinez-Sanchez Page 4 of 9 LOW THRUST TO ESCAPE: RESULTS OF NUMERICAL COMPUTATIONS DEFINITIONS: ( ) 2 0 F = m r ν ⎛ ⎞ µ ⎜ ⎟ ⎝ ⎠ co 0 v = r µ ( ) ( ) 2 co esc. 0 v s =s E=0 = = 2r F 2a M µ (linear distance travelled) F a = M ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ ν esc 0 T r esc. dr ds ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ co V v ∆ esc. 0 s r esc. 0 r r ν co 1 4 V 1 - v ∆ ν 10-2 8.9 0.63 0.75 50 0.89 0.79 10-3 28 0.63 0.86 500 0.885 0.79 10-4 88 0.63 0.92 5,000 0.88 0.80 10-5 278 0.64 0.96 50,000 0.88 0.71 So, to a good approximation, ( ) 1 esc 4 co V 1 - 0.79 v ∆  ν esc 0 r 0.88 r ν  esc dr 0.63 ds ⎛ ⎞ ⎜ ⎟ ⎝ ⎠  Edelbaum’s Sub-Optimal Climb and Plane Change Instead of optimizing the tilt profile α(θ) , Edelbaum (1961, 1973) just kept α constant during each orbit, then optimized α (R )