Explanation Formula used: The increment of the equation is calculated as Δ D = f ( R + Δ R ) − f ( R ) . The differential of the function is calculated as d D = f ′ ( R ) d R . Calculation: Let, D is distance travelled by the airplane. Thus, D + Δ D is the distance travelled by spacecraft. Distance travelled by airplane in one orbit is same as the circumference of the earth. Distance travelled by airplane in one orbit is D = 2 π R . Where, R is the radius of the earth. Use the increment Method. D = 2 π R Let, the function f ( x ) is: f ( R ) = 2 π R Substitute, R = 6370 in f ( R ) = 2 π R . f ( 6370 ) = 2 π ( 6370 ) = 40 , 023.89 The increment is calculated in R is: f ( R + Δ R ) = 2 π ( R + Δ R ) . Substitute, R = 6370 and Δ R = 250 in f ( R + Δ R ) = 2 π ( R + Δ R ) . f ( 6370 + 250 ) = 2 π ( 6370 + 250 ) = 2 π ( 6620 ) = 41 , 594.69 Use Increment Method. Substitute, f ( 6370 ) = 40 , 023.89 and f ( 6620 ) = 41 , 594.69 in Δ D = f ( R + Δ R ) − f ( R )

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 24.8, Problem 25E

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The spacecraft travel in one orbit than an airplane that circles Earth at a low altitude.

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Chapter 24.8, Problem 24E

Chapter 24.8, Problem 26E

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Chapter 24 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

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