Essential University Physics: Volume 1 (3rd Edition)

Published by Pearson
ISBN 10: 0321993721
ISBN 13: 978-0-32199-372-4

Chapter 8 - Exercises and Problems - Page 143: 67


3.76 meters per century

Work Step by Step

We follow the book's recommendation to differentiate equation 8.4. We obtain: $T^2 = \frac{4\pi^2r^3}{GM}$ $2T (\frac{DT}{dt})=\frac{12\pi^2r^2}{GM}\times \frac{dr}{dt}$ Recall, the orbital period of the moon is 27.3 days, which equals $2.359\times10^6s$. The distance between the center of the earth and the moon is $384,400\times10^3 m$. Thus, we find: $\frac{dr}{dt}=\fbox{3.76 meters per century}$
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