University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 37 - Relativity - Problems - Exercises - Page 1248: 37.7

Answer

See explanation.

Work Step by Step

The spacecraft clock, like the internal clock of a moving muon, measures the proper time $\Delta t_o$. It will show the shorter elapsed time. The value of $\gamma$ is $\frac{1}{\sqrt{1-u^{2}/c^{2}}}=1.000128$. The Earth folks measure a dilated time interval of $\gamma \Delta t_o $. The difference in elapsed time is $(\gamma-1)\Delta t_o=0.000128(365.25 days)(24hrs/day)=1.12 hours$.
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