Explanation Given: For a circular orbit, ∑ F n = m a n : F = m v 2 r F = G M m r 2 Then G M m r 2 = m v 2 r Or: v 2 = G M r Then ( v A ) c i r c 2 = ( 1068 × 10 − 12 ft 3 / l b ) ( 5.03 × 10 21 l b . s 2 / ft ) 1400 mi Or: ( v A ) c i r c = 4898.29 ft / s And ( v B ) c i r c 2 = ( 1068 × 10 − 12 ft 3 / l b ) ( 5.03 × 10 21 l b To determine (b) Amount by which its speed should be reduced as it approaches B to insert it into the smaller circular orbit.

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 12.2, Problem 12.89P

To determine

(a)

Speed of the vehicle when it approaches B on the elliptic path.

To determine

(b)

Amount by which its speed should be reduced as it approaches B to insert it into the smaller circular orbit.

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Chapter 12.2, Problem 12.88P

Chapter 12.2, Problem 12.90P

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Vector Mechanics for Engineers: Dynamics

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(a) Speed of the vehicle when it approaches B on the elliptic path.

Solution Summary: The author explains the speed of the vehicle when it approaches B on the elliptic path.