University Physics with Modern Physics (14th Edition)

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

Chapter 13 - Gravitation - Problems - Discussion Questions - Page 424: Q13.7


Choice D, $\frac{T}{\sqrt{3}}$.

Work Step by Step

We see from equation 13.12 how the period T depends on the mass of the central body (i.e, here, the mass of the star): $T=\frac{2\pi r^{3/2}}{\sqrt{GM}}$. Increasing the star’s mass, M, by 3 will produce a new factor of $\sqrt{3}$ in the denominator, and reduce the period by that factor.
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