Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 13 - Newton's Theory of Gravity - Exercises and Problems: 28

Answer

The orbital radius of the planet which orbits Vega is 18.5 R

Work Step by Step

We can write an expression for the orbital radius $R$ of the earth. Let $M_s$ be the mass of the sun. $T^2 = \frac{4\pi^2~R^3}{G~M_s}$ $R^3 = \frac{G~M_s~T^2}{4\pi^2}$ $R = (\frac{G~M_s~T^2}{4\pi^2})^{1/3}$ We then write an expression for the orbital radius $R_p$ of the planet which orbits Vega. $(55~T)^2 = \frac{4\pi^2~R_p^3}{G~(2.1~M_s)}$ $R_p^3 = \frac{G~(2.1~M_s)~(55~T)^2}{4\pi^2}$ $R_p = (\frac{G~(2.1~M_s)~(55~T)^2}{4\pi^2})^{1/3}$ We can divide the orbital radius $R_p$ of the planet orbiting Vega by the orbital radius $R$ of the earth. $\frac{R_p}{R} = [(2.1)(55)^2]^{1/3}$ $R_p = 18.5~R$ Therefore, orbital radius of the planet which orbits Vega is 18.5 R
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