Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 37 - Relativity - Problems: 3a

Answer

$\beta = 0.999 999 50 $

Work Step by Step

First we'll use the time dilation equation and solve for Beta; $\Delta t=\Delta t_0 / \sqrt{1-\beta^2 }$ $\sqrt{1-\beta^2 } \Delta t=\Delta t_0 $ $\sqrt{1-\beta^2 } =\Delta t_0 / \Delta t $ $1-\beta^2 =(\Delta t_0 / \Delta t)^2 $ $\beta =\sqrt{1-(\Delta t_0 / \Delta t)^2} $ Our journey will take 1 year, ignoring the time it would take to turn around. Also, we would like earth to be 1000 years older. Therefore; $\beta =\sqrt{1-(1year / 1000years)^2} $ $\beta = 0.999 999 50 $
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