Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 5 - Circular Motion; Gravitation - General Problems: 81

Answer

a) $3.86\times10^3m/s$ b) $4.4\times10^4s$

Work Step by Step

a) The speed of a satellite orbiting the Earth is given by $v=\sqrt{\frac{GM_{Earth}}{r}}$. For the GPS satellites, $r=R_{Earth}+(11000)(1852km)=2.68\times10^7m$. $$v=\sqrt{(6.67\times10^{-11}Nm^2/kg^2)\frac{5.97\times10^{24}kg}{2.68\times10^7m}}=3.86\times10^3m/s$$ b) The period can be found from the speed and the radius. $$v=\frac{2\pi r}{T}$$ $$T=\frac{2\pi r}{v}=\frac{2\pi(2.68\times10^7m)}{3.86\times10^3m/s}=4.4\times10^4s$$
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