MAE 161A 2009 - Lecture 9

# MAE 161A 2009 - Lecture 9 - Lecture 9 News HW 4 posted...

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Slide 1 © Wirz MAE 161A Lecture 9 News HW 4 posted today Midterm Next Thursday Review on Friday Last Lecture Kepler’s Problem between initial and final state vectors Today Interplanetary Missions Reading Bate: Ch 8 Chobotov: Ch 12

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Slide 2 © Wirz MAE 161A State Vectors – r(t), v(t)
Slide 3 © Wirz MAE 161A Kepler’s Problem Statement: Given the spacecraft position and velocity at t o , find its position and velocity at t. Note: Possible to progress time or anomaly Solution technique: Given: and Find: oo r t v t r t v t r ( t o ) v ( t o ) Convert back to: r ( t ), v ( t ) Progress time or anomaly ( t o ) ( t ) Find Orbit Parameters (e.g., a, e, i, , , )

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Slide 4 © Wirz MAE 161A © R. Wirz UCLA, MAE 161a Today’s Lecture Interplanetary Missions
Slide 5 © Wirz MAE 161A Interplanetary Missions A. Geocentric Escape Use hyperbolic escape trajectory B. Heliocentric transfer a.k.a. “cruise stage” Use elliptic transfer from basic equations, hyperbolic for faster transfers May use “gravity assist” for V maneuvers We must use rendezvous equations to time the launch escape Since the launch vehicle is used to escape the Earth’s Sphere of Influence (SOI) C. Planetocentric Encounter Hyperbolic arrival

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Slide 6 © Wirz MAE 161A Patched Conics Interplanetary Missions can be analyzed using the method of “Patched Conics” Essentially ties together the conic orbit shapes needed to conduct the mission Geocentric Escape (hyperbola)
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## This note was uploaded on 10/17/2010 for the course MAE 161 taught by Professor Richard during the Spring '10 term at UCLA.

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MAE 161A 2009 - Lecture 9 - Lecture 9 News HW 4 posted...

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