Explanation Given information: h p = 300 k m . r v r = 3.44 k m / s . r g = 42140 k m . Formula used: G M = g R 2 F = m a = m v c i r c 2 r Calculation: As we have, R = 6370 k m , So, r A = 6370 k m + 300 k m ⇒ r A = 6.67 × 10 6 m , and ⇒ r C = 42.14 × 10 6 m We know that, G M = g R 2 . Put the values in the above equation: ⇒ G M = ( 9.81 m / s ) ( 6.37 × 10 6 m ) 2 ⇒ G M = 398.1 × 10 12 m 3 / s 2 We also know for any circular orbit: ⇒ F n = m a n = m v c i r c 2 r ⇒ F n = G M m r 2 = m m v 2 c i r c r ⇒ v c i r c = G M r Now velocity at A: ⇒ ( v A ) c i r c = G M r A = ( 398.1 × 10 12 m 3 / s 3 ) ( 6.67 × 10 6 m ) ⇒ 7.726 × 10 3 m / s ⇒ v A = ( v A ) c i r c + ( v A ) R ⇒ 7

Vector Mechanics for Engineers: Dynamics

11th Edition

ISBN: 9780077687342

Author: Ferdinand P. Beer, E. Russell Johnston Jr., Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 13.2, Problem 13.107P

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The angle at which the rocket will cross the intended orbit at point C at given condition.

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Chapter 13.2, Problem 13.106P

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Chapter 13 Solutions

Vector Mechanics for Engineers: Dynamics

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The angle at which the rocket will cross the intended orbit at point C at given condition.

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