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# sln8 - EAS4510 Homework#8 Solution Note Chapter 4 of...

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EAS4510 Homework #8 Solution Note: Chapter 4 of Orbital Mechanics by Prussing and Conway is helpful. #1) P1 is the periapsis position and P2 is the top of the minor axis for an orbit with eccentricity 0.1 e = . Use terminal velocity vectors to show that 1 00 T PQW p vv ⎡⎤ = ⎣⎦ and [ ] 2 T PQW cir =− where (1 ) ) p e v ae µ + = and cir v a = . Terminal velocity vectors: () 1 2 1 2 cr vB A eB A e A A e =+ +− −− ±± where 12 4 4 A rrc a B ++ 1 2 ) ra e ra = and ( ) 2 2 22 11 2 ca e a ea e + + = Î ( ) ( ) 2 2 2 2 0.228152 44 2 1.33926 2 A aa a ee e B a e µµ ⎛⎞ = = ⎜⎟ −+ − −++ − ⎝⎠ = = −− − −+− − l l l l l ( ) l l l 1 2 2 2 2 21 1 1 r r c eP Q e P Q e P a e P eQ P rr e c e = == = ± ± ± So now solving the equations for 1 v and 2 v , we get: l l l l l l 13 1 13 2 10 1.10554 0 0 0 vP Q W a vPQ W a + =− − + and 1 1.10554 1 p e v a + Î [] 1 2 0 1.10554 0 0 0 T T PQW p T T PQW cir a a ⎢⎥ QED

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#2) a) Show that the Lagrange Parameters for the minimum energy trajectory between P1 and P2 satisfy min α π = and min 0 β = .
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sln8 - EAS4510 Homework#8 Solution Note Chapter 4 of...

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