University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 8 - Momentum, Impulse, and Collision - Problems - Exercises - Page 267: 8.52

Answer

The center of mass is a distance of $7.42\times 10^{8}~m$ from the center of the sun. Since the sun's radius is $6.96\times 10^8~m$, the center of mass lies outside the sun.

Work Step by Step

Let the center of the sun be at the origin. $x_{cm} = \frac{m_1x_1+m_2x_2}{m_1+m_2}$ $x_{cm} = \frac{0+(1.9\times 10^{27}~kg)(7.78\times 10^{11}~m)}{1.99\times 10^{30}~kg+1.9\times 10^{27}~kg}$ $x_{cm} = 7.42\times 10^{8}~m$ The center of mass is a distance of $7.42\times 10^{8}~m$ from the center of the sun. Since the sun's radius is $6.96\times 10^8~m$, the center of mass lies outside the sun.
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