Notes_LA%20BP - LA 1 Transfer Orbits: Lambert Arcs Two...

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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 LA 1
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Analytical Relationships Objective: expression for p ; e Given the following trig identity Sub above 5 expressions into trip identity and produce a quadratic in p () ( ) ( ) 22 12 1 2 2 1c o s 2 o s o s 0 ac p r r a r r p ar r φφ φ −− + ⎡⎤ ⎣⎦ + −= LA 2 any conic o s p r e θ = + 1 1 21 2 cos 1 cos cos( ) 1 p e r p ee r θθ ∗∗ =− = +=− Also known: 2 11 2 2c o s ae a p cr r r = I
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Use 12 2 s r rc = ++ to rewrite term in brackets ()( ) ( ) 1 2 21 c o s 2 2 2 ar r rr ssc a ac φ +− =
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This note was uploaded on 12/22/2010 for the course A&AE 532 taught by Professor Kathleenhowell during the Spring '10 term at Purdue University-West Lafayette.

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Notes_LA%20BP - LA 1 Transfer Orbits: Lambert Arcs Two...

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