Explanation Given: The maximum and minimum distance from center of the earth is shown in Figure (1). The mass of the earth M e = ( 5.976 ) × 10 24 kg . The gravitational constant is G = 66.73 × 10 − 12 m 3 / kg ⋅ s 2 From Figure (1) write the value for minimum distance r p . r p = 20 Mm 10 6 m 1 Mm = 20 ( 10 6 ) m From Figure (1) write the value for maximum distance r a . r a = 30 Mm 10 6 m 1 Mm = 30 ( 10 6 ) m Write the expression for maximum distance from the center of earth r a . r a = r 0 2 G M ( r 0 υ 0 2 ) − 1 (I) Here, minimum distance from the center of earth is r p and the initial speed of the rocket υ 0 , the gravitational constant is G and mass of the earth is M . From figure (I) write the expression for the altitude h . h = r p υ p = r a υ a h = r p υ A = r a υ B (II) Here, h is constant at any positions of the orbit , the speed of the rocket at apogee is υ a , the speed of the rocket at perigee is υ B , r p is the minimum distance from the center of earth or perigee and r a is the orbit maximum distance from the center of earth or apogee. Conclusion: Since, r 0 = r p and υ 0 = υ p . Substitute r p for r 0 and υ p for υ 0 in Equation (I). r a = r 0 2 G M ( r 0 υ 0 2 ) − 1 r a = r p 2 G M ( r p υ p 2 ) − 1 2 G M ( r p υ p 2 ) = r p r a + 1 2 G M ( r p υ p 2 ) = r p + r a r a υ p = 2 G M r a r p ( r p + r a ) (III)

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 13.7, Problem 126P

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The speed of the rocket when it is at B and at A .

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Chapter 13.7, Problem 124P

Chapter 13.7, Problem 127P

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Engineering Mechanics: Statics & Dynamics (14th Edition)

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The speed of the rocket when it is at B and at A .

Solution Summary: The author explains how to determine the speed of the rocket when it is at B and A.

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