College Physics (4th Edition)

Published by McGraw-Hill Education
ISBN 10: 0073512141
ISBN 13: 978-0-07351-214-3

Chapter 6 - Problems - Page 234: 108


$U = -2K$

Work Step by Step

The gravitational force provides the centripetal force to keep an object of mass $m$ in circular orbit: $\frac{GMm}{r^2} = \frac{mv^2}{r}$ $\frac{GMm}{r} = mv^2$ $\frac{1}{2}\frac{GMm}{r} = \frac{1}{2}mv^2$ $(-\frac{1}{2})(-\frac{GMm}{r}) = K$ $(-\frac{1}{2})(U) = K$ $U = -2K$
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