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 - Problems - Page 134: 46

Answer

$v = 5.97\times 10^3~m/s$

Work Step by Step

Let's use 6380 km as the radius of the Earth. Then the satellite's orbital radius $r$ is 6380 km + 4800 km which is 11,180 km. The force of gravity provides the centripetal force to keep the satellite moving in a circle: $\frac{m_s~v^2}{r} = \frac{G~m_E~m_s}{r^2}$ $v^2 = \frac{G~m_E}{r}$ $v= \sqrt{\frac{G~m_E}{r}} = \sqrt{\frac{(6.67\times 10^{-11}~N\cdot m^2/kg^2)(5.98\times 10^{24}~kg)}{(1.118\times 10^7~m)}}$ $v = 5.97\times 10^3~m/s$
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