Conceptual Physics (12th Edition)

Published by Addison-Wesley
ISBN 10: 0321909100
ISBN 13: 978-0-32190-910-7

Chapter 10 - Think and Explain: 81

Answer

The closer the satellite is to the planet, the stronger the gravitational force between them. Gravity is an inverse-square law. At point A, the perigee, the satellite feels the greatest gravitational force. Also, the closer the satellite is to the planet, the smaller the PE and the greater the KE. We know this from conservation of energy of a body in orbit (page 198). This means that the greatest speed, velocity, momentum, and KE are also encountered at point A. The greatest gravitational PE is where the planet is farthest from the Earth's center, point C, the apogee of the orbit. The total energy, the sum of KE and PE, is conserved, i.e., constant at points ABCD. We know this from conservation of energy of a body in orbit (page 198). The angular momentum is also conserved because no external torques act on this 2-body system. Finally, the closer the satellite is to the planet, the stronger the gravitational force between them. The greater the net force on the satellite, the greater its acceleration, so the maximum acceleration is at point A.
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