Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 13 - Gravitation - Problems - Page 383: 61b

Answer

At greater heights, the energy for lifting is greater than the kinetic energy for orbiting.

Work Step by Step

The gravitational potential energy at the Earth's surface is $U_s = -\frac{GMm}{R}$ The gravitational potential energy at a height $h$ above the Earth's surface is $U_h = -\frac{GMm}{R+h}$ The kinetic energy of a satellite in orbit at a height of $h$ above the Earth's surface is $K_h = \frac{GMm}{2(R+h)}$ As the height increases, the energy required to lift the satellite increases while the kinetic energy of an orbiting satellite decreases. Therefore, at greater heights, the energy for lifting is greater than the kinetic energy for orbiting.
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