Explanation Given: The maximum and minimum distance from center of the planet 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 For orbit A C from Figure (1) write the value for minimum distance r p . r p = 10 Mm 10 6 m 1 Mm = 10 ( 10 6 ) m For orbit A C from Figure (1) write the value for maximum distance r a . r a = 8 Mm + 8 Mm 10 6 m 1 Mm = 16 ( 10 6 ) m For orbit A B from Figure (1) write the value for minimum distance r p . r p = 8 Mm 10 6 m 1 Mm = 8 ( 10 6 ) m For orbit A B from Figure (1) write the value for maximum distance r a . r a = 10 Mm 10 6 m 1 Mm = 10 ( 10 6 ) m Write the expression for the maximum distance from the centre of Earth or apogee. r a = r 0 2 G M e ( r 0 υ 0 2 ) − 1 (I) Here, minimum distance from the center of earth is r 0 and the initial speed of the rocket υ 0 , the gravitational constant is G and mass of the earth is M e . Write the expression for the altitude h . h = r p υ p = r a υ a h = r p υ p = r a ( υ A ) A 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. Write the expression for required change in speed. Δ υ = ( υ A ) A B − ( υ A ) A C (III) 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 e ( r 0 υ 0 2 ) − 1 r a = r p 2 G M e ( r p υ p 2 ) − 1 2 G M e ( r p υ p 2 ) = r p r a + 1 2 G M e ( r p υ p 2 ) = r p + r a r a υ p = 2 G M e r a r p ( r p + r a ) (IV). Since, υ p = ( υ A ) A C . For orbit A C Substitute ( υ A ) A C for υ p , [ 16 ( 10 6 ) m ] for r a , [ 10 ( 10 6 ) m ] for r p , 66.73 × 10 − 12 m 3 / kg ⋅ s 2 for G and ( 5

Engineering Mechanics: Dynamics (14th Edition)

14th Edition

ISBN: 9780133915389

Author: Russell C. Hibbeler

Publisher: PEARSON

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Applied Fluid Mechanics

A fluid is a substance that is continuously deformed by the application of shear stress. The rate of deformation of a fluid depends on its viscosity. The fluid tries to flow when it interacts with some other system.

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Chapter 13.7, Problem 132P

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The change in the speed when rocket reaches at A so that rocket can travel in an elliptical orbit AB .

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Chapter 13.7, Problem 131P

Chapter 13.7, Problem 3CP

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Chapter 13 Solutions

Engineering Mechanics: Dynamics (14th Edition)

Ch. 13.4 - In each case, determine its velocity when t = 2 s...Ch. 13.4 - In each case, determine its velocity at s = 8 m if...Ch. 13.4 - Determine the initial acceleration of the 10-kg...Ch. 13.4 - Write the equations of motion in the x and y...Ch. 13.4 - The motor winds n the cable with a constant...Ch. 13.4 - If motor M exerts a force of F = (10t2 + 100) N on...Ch. 13.4 - A spring of stiffness k = 500 N/m is mounted...Ch. 13.4 - The spring has a stiffness k = 200 N/m and is...Ch. 13.4 - Block B rests upon a smooth surface. If the...Ch. 13.4 - The 6-lb particle is subjected to the action of...

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The change in the speed when rocket reaches at A so that rocket can travel in an elliptical orbit A B .

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Chapter 13 Solutions