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 133: 30

Answer

$ 3.46\times10^8 m$.

Work Step by Step

Let the distance from Earth to the spacecraft be x, and from the spacecraft to the moon be L-x, where L is the Earth-moon distance. The magnitude of the force of gravity exerted on the spacecraft by the Earth is: $$\frac{Gm_{earth}m_{spacecraft}}{x^2}$$ The magnitude of the force of gravity exerted on the spacecraft by the moon is: $$\frac{Gm_{moon}m_{spacecraft}}{(L-x)^2}$$ Set the two expressions equal and solve. $$x=L\frac{\sqrt{ m_{earth}}}{ \sqrt{ m_{earth}}+ \sqrt{ m_{moon}}}=3.46\times10^8 m$$
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