University Physics with Modern Physics (14th Edition)

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

Chapter 13 - Gravitation - Problems - Exercises - Page 426: 13.26

Answer

The orbital period of Vulcan would be 48 days.

Work Step by Step

Let $P_V$ be Vulcan's period. Let $R_V$ be Vulcan's orbital radius. Let $P_M$ be Mercury's period. Let $R_M$ be Mercury's orbital radius. We can use Kepler's third law to find Vulcan's period. $(\frac{P_V}{P_M})^2 = (\frac{R_V}{R_M})^3$ $P_V = P_M~(\frac{R_V}{R_M})^{3/2}$ $P_V = (88~days)~(\frac{2R_M/3}{R_M})^{3/2}$ $P_V = (88~days)~(\frac{2}{3})^{3/2}$ $P_V = 48~days$ The orbital period of Vulcan would be 48 days.
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