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: 45

Answer

The shuttle should be moving at a speed of 7460 m/s when it releases the satellite.

Work Step by Step

Let's use 6380 km as the Earth's radius. Then the orbital radius $r$ is 6380 km + 780 km which is 7160 km. The force of gravity provides the centripetal force for the satellite to move in a circle around the Earth. $\frac{mv^2}{r} = \frac{GMm}{r^2}$ $v = \sqrt{\frac{GM}{r}}$ $v = \sqrt{\frac{(6.67 \times 10^{-11} ~N\cdot m^2/kg^2)(5.98 \times 10^{24} ~kg)}{7.16\times 10^6 ~m}}$ $v = 7460 ~m/s$ The shuttle should be moving at a speed of 7460 m/s when it releases the satellite.
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