lecture24 - Orbital maneuvers Changing orbits in-plane: a ,...

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Unformatted text preview: Orbital maneuvers Changing orbits in-plane: a , e , , plane change: i , In planning a maneuver, usually the two most important quantities are total v (fuel consumption), total time of transfer (to complete the ma- neuvers), though other considerations may come into play. Maneuvers are approximated as either continu- ous or impulsive ; we concentrate on the latter because analysis is easier. We also look at only the simplest kinds of transfer: changing only one element. L. Healy ENAE404 Spring 2007 Lecture 24 (Apr. 24) 1 Hohmann transfer Simplest in-plane transfer is the Hohmann trans- fer, that is, two burns tangent v k v when = 0. Transfer ellipse semimajor axis a t = r i + r f 2 going from apogee to perigee or vice versa. Time of transfer is half an orbit of transfer ellipse, T t = v u u t ( r i + r f ) 3 2 3 . The total v going from and to circular orbits, v tot = s r i v u u t 2 r f r i + r f- 1 + s r f 1- v u u t 2 r i r i + r f . L. Healy ENAE404 Spring 2007 Lecture 24 (Apr. 24) 2 Bi-elliptic transfer and one tangent burn A Bi-elliptic transfer is two back-to-back Hohmann transfers, temporarily going to a higher alti- tude than the final orbit and coming back down. If r f /r i > 11 . 94 bi-elliptic could be lower v than a straight Hohmann, but will take longer. Pick r b . A one tangent burn transfer eliminates require- ment of v parallel to v at one burn. Faster, uses more fuel than Hohmann. Pick b , solve for transfer ellipse elements e t = 1- cos b 1 a t = r i 1 e t with the- used for perigee departure, + for apogee. v a is the same as Hohmann, v b re- quires 2D vector analysis. Flight time requires Keplers equation....
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lecture24 - Orbital maneuvers Changing orbits in-plane: a ,...

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