Explanation Given: The maximum and minimum distance from center of the planet is shown in Figure (1). The mass of the planet M = 0.6 ( 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 = 6 Mm 10 6 m 1 Mm = 6 ( 10 6 ) m From Figure (1) write the value for maximum distance r a . r a = 100 Mm 10 6 m 1 Mm = 100 ( 10 6 ) m Write the expression for the minimum distance from the centre of Planet. r a = r 0 2 G M ( r 0 υ 0 2 ) − 1 (I) Here, minimum distance from the center of planet is r 0 and the initial speed of the rocket υ 0 and the gravitational constant is G and mass of the planet is M . From Figure (1) write the equation for the h . h = r p υ p = r a υ a h = r p υ B = r a υ A ' (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 p , r p is the minimum distance from the center of planet or perigee and r a is the orbit maximum distance from the center of planet or apogee. Write the expression for period of elliptical orbit. T = π r p υ p ( r p + r a ) r p r a (III) Here, period is T , r p is minimum distance from the center of planet or perigee and r a is the maximum distance from the center of planet or apogee. Write the expression for time required to travel from A to A ' . t = T 2 (IV) Here, period is T and time is t . 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 e ( r p υ p 2 ) M = 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 ) (V). Since, υ p = υ B . Substitute υ B for υ p , [ 100 ( 10 6 ) m ] for r a , [ 6 ( 10 6 ) m ] for r p , 66

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 13.7, Problem 130P

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The required free-flight speed rocket must have at A' and the time t required for the rocket to land, going from A' to B' .

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Chapter 13.7, Problem 129P

Chapter 13.7, Problem 131P

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Engineering Mechanics: Statics & Dynamics (14th Edition)

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The required free-flight speed rocket must have at A ' and the time t required for the rocket to land, going from A ' to B ' .

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The required free-flight speed rocket must have at A' and the time t required for the rocket to land, going from A' to B' .

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