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 135: 59

Answer

The period of an artificial satellite orbiting very near the Earth’s surface is 84.2 minutes.

Work Step by Step

Let $s_1 = 6380 ~km$ Let $s_2 = 385,000 ~km$ Let $T_2 = 27.4 ~days$ $(\frac{T_1}{T_2})^2 = (\frac{s_1}{s_2})^3$ $T_1^2 = (\frac{6380 ~km}{385,000 ~km})^3\cdot (27.4 ~days)^2$ $T_1 = 0.05845 ~days$ We can convert this time to minutes. $T_1 = (0.05845 ~days)(\frac{24 ~h}{1 ~day})(\frac{60 ~min}{1 ~h}) = 84.2 ~minutes$ The period of an artificial satellite orbiting very near the Earth’s surface is 84.2 minutes.
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