Explanation Write formula for relation between the time measured in the astronaut’s clock and clock on the Earth. t ′ = γ t (I) Where, t ′ is time measured in clock on the airplane, t is the time measured in clock on the Earth, and γ = 1 1 − β 2 is relativistic factor and β = v c , here, v = 375 m / s is speed of the plan from the Earth’ frame and c is the speed of the light. With the use of binomial approximation theorem. ( 1 + x ) α ≈ 1 + α x Where, x is small number. Calculation: With the help of binomial approximation theorem. γ = 1 1 − β 2 γ = 1 ( 1 − β 2 ) 1 2 γ = ( 1 − β 2 ) − 1 2 γ = 1 + β 2 2 (II) Calculate time difference between clock in the plane and clock on the Earth by using equation (I). Δ t = t − t ′ = t − γ t = t ( γ − 1 ) (III) Substitute the value of the ( γ − 1 ) from equation (II) in equation (III)

Modern Physics for Scientists and Engineers

4th Edition

ISBN: 9781133103721

Author: Stephen T. Thornton, Andrew Rex

Publisher: Cengage Learning

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The theory of special relativity explains the connection between space and time to objects that move in a straight line at a constant speed. The objects move at the speed of light. When an object approaches light speed, its mass is endless and cannot mov…

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Time difference between the clock on airplane and clock on the earth during one side trip.

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