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lecture_35_36

# lecture_35_36 - 16.512 Rocket Propulsion Prof Manuel...

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16.512, Rocket Propulsion Prof. Manuel Martinez-Sanchez Lecture 35-36: Impulsive and Low-Thrust Maneuvers in Space See Lectures 3-4 of 16.522 (Space Propulsion) for coverage of Low Thrust Maneuvers and Re-positing within an orbit . We add here material on Hyperbolic Orbits and Interplanetary Transfer . Hyperbolic trajectories : r = p 1 ecos + θ e > 1 Asymptotes : = -1 ecos θ cos θ = - 1 e 1 1 cos e θ = θ = π − h P = µ still valid Instead of “semimajor axis” a>0 distance from perigee to “center” is (-a), and we still have E 0 2a µ = − > Also ( ) ( ) ( ) 2 2 p a 1 e a e 1 = = Similarly, distance |focus - center| is (-a)e (it is ae in ellipse) Turning angle : 1 1 1 1 2( ) 2cos 2 cos e 2 e π δ = π − π − θ = π − = 1 1 2sin e δ = 16.512, Rocket Propulsion Lecture 35-36 Prof. Manuel Martinez-Sanchez Page 1 of 7

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Miss distance or Impact Parameter ( ae) sin( ) ( ae)sin ∆ = π − θ = θ 2 1 ( ae) 1 e ∆ = or 2 P e e 1 ∆ = 2 2 e 1 e 2 P e 1 ∆ = Excess hyperbolic velocity ( ) ( ) 2 e 1 V 2E a p µ µ = = = used in many books, reports 2 3 "C " v = Orbit characterized by any pair of parameters, like (p, e) , , (v , (v p (v , ) θ , ) θ , ) , p ( ,v ) γ , p ( , ) γ δ Example : Given (v , -a = , ) 2 v µ 2 2 v e 1 a = = µ then 2 1 1 2 1 v 1 2sin 2cot e 1 2cot e δ = = = µ Planetary “Spheres of Influence” (SOI) Locus of points for which the ratio of (the Sun’s disturbing acceleration of the relative vehicle-planet motion) to (the planet-induced vehicle acceleration) equals the ratio of (the planet-induced acceleration of the relative vehicle-Sun motion) (the Sun-induced vehicle acceleration).
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lecture_35_36 - 16.512 Rocket Propulsion Prof Manuel...

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