# 4 Ch 7 Lambert's Problem r1 - MAE 583 Astrodynamics...

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3/2/114 Lambert’s ProblemK N VaughtMAE 583 AstrodynmicsPage 1MAE 583AstrodynamicsAstrodynamicsChapter 4: Lambert’s Problem(Vallado Ch. 7.6)rev1Reference (unless noted otherwise):Vallado, Fundamentals of Astrodynamics & Applications, 3ndEd.,Microcosm and Springer, 2007Figures and Tables used with permission – Do not distribute
3/2/114 Lambert’s ProblemK N VaughtMAE 583 AstrodynmicsPage 2MAE 583AstrodynamicsOutline4 Lambert’s Problem4.1 Lambert Geometry4.2 Minimum Energy Solution4.3 Solution Algorithm
3/2/114 Lambert’s ProblemK N VaughtMAE 583 AstrodynmicsPage 3MAE 583AstrodynamicsLambert’s ProblemAB!r0!r1!tApplication:• Suppose you (B) are taking supplies to theSpace Station (A).• You know the space station will be at r1attime Δt from now.• What trajectory will transfer you from r1to r2in Δt? What velocity do you need?Lambert’s Problem:• Determine the orbit given a specified transfertime and connecting two position vectors.
3/2/114 Lambert’s ProblemK N VaughtMAE 583 AstrodynmicsPage 4MAE 583AstrodynamicsP0Basic Lambert GeometryLambert’s Problem:Given two position vectors and transfer timedetermine the orbit connecting them.1) The two vectors determine the orbit plane.2) The angle θswept out during the transfer can be <360 degs or > 360 degs (less than or more thanone rev)3) Some Degenerate cases:1)θ=180°Infinitely many planes.2)θ=0°P0between F and P1Colinear3)θ=0°P0= P14) P0= c or P1= c4) The Semiperimeter (s) (of the triangle FP0P1) is:F!"cP1P0!

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