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# Notes%20L%20BP - Transfer Orbits Lambert Arcs Two...

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Unformatted text preview: Transfer Orbits: Lambert Arcs Two approaches to mission planning: (a) Given the transfer orbit Æ initial and final positions are specified; relate to the time of flight (b) Given the initial (departure) and final (target) points Æ determine the orbit that passes through the points Transfer Orbit Design (special class of boundary value problem) 1. Geometrical relationships Conic paths connecting two points that are fixed in space with focus at the attracting center 2. Analytical Relationships 3. Lambert’s Theorem L 1 Geometrical Relationships : Ellipse Given two fixed points 1 2 , P P ; center of force at point O Find: ellipse with focus at point O that connects 1 2 , P P If F is not specified infinite number of solutions exist Thus, find the locus of all possible F locations Pick one of the F sites and the ellipse is determined L 2 “space triangle” for the transfer Let 1 1 2 2 1 2 (chord) OP r OP r PP c = = = Since 1 P and 2 P must both lie on the same ellipse, F must be selected such that For ellipse with major axis 2 a , point F determined as the intersection of two circles centered at 1 P and 2 P with radii 1 2 a r − and 2 2 a r − L 3 1 2 r r 1 1 2 2 2 OP PF a OP P F + = = + (always true for an ellipse) OR 1 1 2 2 2 2 P F a r P F a r = − = − given 1 2 , r r if know “a” can solve for F 1...
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Notes%20L%20BP - Transfer Orbits Lambert Arcs Two...

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