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# sln6 - EAS 4510 Homework#6 Solutions#1 Problem 3.8 BMW rp1...

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EAS 4510 Homework #6 Solutions #1) Problem 3.8, BMW: 1 1 1.1 .290 p rD U e = = 2 2 5 .412 p U e = = Î 1 1 1.5493 1.99859 a aD U U = = Î 2 2 8.5034 12.0068 a U U = = Two possible transfer orbits to analyze are a) going from inner orbit at periapsis to outer orbit at apoapsis, and b) going from inner orbit at apoapsis to outer orbit at periapsis. a) 1 2 1.1 12.0068 pt p at a rr D U D U == Î 6.5534 .8321 t t U e = = Î (1 ) 1.29058 / ) ) 0.118236 / ) t pt tt t at e vD U T U ae e U T U µ + + To go from the inner orbit into this transfer orbit, then from the transfer orbit to the outer orbit, there are two delta-V’s required. The total delta-V for the maneuver is the sum of these two delta-V’s: __ 1 2 () total inner to transfer transfer to outer pt p a at VV V v v v v ∆= + = +− where 1 p v is the periapsis speed of the smallest ellipse, and 2 a v is the apoapsis speed of the largest ellipse. Î 0.311 / total VD U T U b) 1 2 1.99859 5 pt a at p D U D U Î 3.4993 .428859 t t U e = = Î ) .845537 / ) ) .337977 / ) t pt t at e U T U e U T U + + 1 2 total inner to transfer transfer to outer pt a p at V v v v v + = Î 0.443 / total U T U Î Case a) has a smaller total V so that is the best choice as a transfer orbit.

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#2) Problem 3.9, BMW: 1 2 3 1 15 rD U U r = = =∞ Î 1 2 1/ 1 / 15 cir cir vD U T U U T U = = 3 0 cir v = Determine the total delta-V required to go from a circle of radius 1 r to a circle of radius 2 r a) directly using a Hohmann transfer, and b) by first transferring to a trajectory where a r and then transferring to a circular orbit of radius 2 r . a) There is just one transfer orbit for this scenario: 1 15 pt at U U = = Î 8 .875 t t aD U e = = Î 1.36931 / .091287 / pt at U T U U T U = = __ 1 2 () total inner to transfer transfer to outer pt cir
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sln6 - EAS 4510 Homework#6 Solutions#1 Problem 3.8 BMW rp1...

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