## University Physics with Modern Physics (14th Edition)

Published by Pearson

# Chapter 13 - Gravitation - Problems - Exercises - Page 426: 13.27

#### Answer

(a) The orbital speed is $8.27\times 10^4~m/s$. (b) The orbital period of the planet is 14.5 days.

#### Work Step by Step

(a) We can find the mass of the star. $M = (0.85)(1.989\times 10^{30}~kg)$ $M = 1.69\times 10^{30}~kg$ We can find the orbital radius of the planet. $R = (0.11)(1.50\times 10^{11}~m)$ $R = 1.65\times 10^{10}~m$ We can find the orbital speed of the planet. $v = \sqrt{\frac{G~M}{R}}$ $v = \sqrt{\frac{(6.67\times 10^{-11}~m^3/kg~s^2)(1.69\times 10^{30}~kg)}{1.65\times 10^{10}~m}}$ $v = 8.27\times 10^4~m/s$ The orbital speed is $8.27\times 10^4~m/s$ (b) We can find the orbital period of the planet. $T = \frac{distance}{speed}$ $T = \frac{2\pi~R}{v}$ $T = \frac{(2\pi)(1.65\times 10^{10}~m)}{8.27\times 10^4~m/s}$ $T = 1.25\times 10^6~s = 14.5~days$ The orbital period of the planet is 14.5 days.

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