Physics (10th Edition)

Published by Wiley
ISBN 10: 1118486897
ISBN 13: 978-1-11848-689-4

Chapter 5 - Dynamics of Uniform Circular Motion - Problems - Page 139: 31

Answer

$v_A=7700m/s$ $v_B=7503m/s$

Work Step by Step

The earth's radius is $6371km$ and its mass $M=5.98\times10^{24}kg$. The gravitational constant $G=6.67\times10^{-11}Nm^2/kg^2$ Satellite A is $360km$ above the earth's surface. So the distance from satellite A to the earth's center is $r_A=6371+360=6731km=6.73\times10^6m$ Satellite B is $720km$ above the earth's surface. So the distance from satellite B to the earth's center is $r_B=6371+720=7091km=7.09\times10^6m$ The orbital speed of each satellite is $$v_A=\sqrt{\frac{GM}{r_A}}=7700m/s$$ $$v_B=\sqrt{\frac{GM}{r_B}}=7503m/s$$
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