Explanation Given: The minimum distance and Viking Explorer at point A is shown in Figure (1). The Viking Explorer velocity at A 10 Mm/h . The mass of the mars M M = 0.1074 ( 5.976 ) × 10 24 kg . The gravitational constant is G = 66.73 × 10 − 12 m 3 / kg ⋅ s 2 . Write the value for the Viking Explorer velocity at A . υ A = 10 Mm/h = 10 Mm h ( ( 10 ) 6 m 1 Mm ) ( 1 h 3600 s ) = 10 ( 10 ) 6 3600 m/s Write the expression for the velocity of Viking Explorer in circular orbit. υ A ' = G M M r 0 (I) Here, minimum distance from center of mars is r 0 , and the velocity of Viking Explorer in circular orbit is υ A ' , the gravitational constant is G and mass of the mars is M M . Write the expression for the escape velocity of Viking Explorer in parabolic trajectory. υ A = 2 G M M r 0 (II) Here, minimum distance from center of mars is r 0 , and the velocity of Viking Explorer approaches point at A in parabolic trajectory is υ A ' , the gravitational constant is G and mass of the mars is M M . Write the expression for required sudden decrease in speed in Viking Explorer. Δ υ = υ A − υ A ' (III) Conclusion: Substitute 66.73 × 10 − 12 m 3 / kg ⋅ s 2 for G , 0.1074 ( 5.976 ) × 10 24 kg for M M and 10 ( 10 ) 6 3600 m/s for υ A in Equation (II). υ A = 2 G M M r 0 10 ( 10 ) 6 3600 = ( 2 ) [ 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 122P

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The radius r0 of the circular orbit and the required velocity at ΔυA so that Viking Explorer can then maintain a circular orbit.

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Chapter 13.7, Problem 121P

Chapter 13.7, Problem 123P

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Engineering Mechanics: Statics & Dynamics (14th Edition)

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The radius r 0 of the circular orbit and the required velocity at Δ υ A so that Viking Explorer can then maintain a circular orbit.

Solution Summary: The author determines the radius of the circular orbit and the required velocity at Delta

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The radius r0 of the circular orbit and the required velocity at ΔυA so that Viking Explorer can then maintain a circular orbit.

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