243_Dynamics 11ed Manual

243_Dynamics 11ed Manual - = f 8 Mm = r p 8 Mm = G 66.73 10...

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Engineering Mechanics - Dynamics Chapter 13 Problem 13-127 A rocket is in free-flight elliptical orbit around the planet Venus. Knowing that the periapsis and apoapsis of the orbit are r p and a p , respectively, determine (a) the speed of the rocket at point A' , (b) the required speed it must attain at A just after braking so that it undergoes a free-flight circular orbit around Venus, and (c) the periods of both the circular and elliptical orbits. The mass of Venus is a times the mass of the earth. Units Used: Mm 10 3 km = Given: a 0.816 = a p 26 Mm
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Unformatted text preview: = f 8 Mm = r p 8 Mm = G 66.73 10 12 m 3 kg s 2 = M e 5.976 10 24 kg = Solution: M v aM e = M v 4.876 10 24 kg = OA' OA 2 GM p OA v 2 1 = a p r p 2 GM v r p v A 2 1 = v A 1 a p r p r p 2 + 2 r p a p r p + ( ) a p GM v = v A 7.89 km s = v' A r p v A a p = v' A 2.43 km s = v'' A GM v r p = v'' A 6.38 km s = Circular Orbit: T c 2 r p v'' A = T c 2.19 hr = Elliptic Orbit: T e r p v A r p a p + ( ) r p a p = T e 6.78 hr = 241...
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This note was uploaded on 08/16/2011 for the course EGN 3321 taught by Professor Christianfeldt during the Spring '08 term at University of Central Florida.

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