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: 13.31

Answer

$2.3\times 10^{30}Kg,1.2 Ms $

Work Step by Step

We can calculate the required mass as follows: $T=\frac{2\pi r^{\frac{3}{2}}}{\sqrt{Gm}}$ This can be simplified and rearranged as: $m=\frac{4\pi^2 r^3}{T^2G}$ We plug in the known values to obtain: $m=\frac{4\pi^2(10.5\times 10^9)^3}{(544320)^2(6.673\times 10^{-11})}=2.3\times 10^{30}Kg$ As we know that the mass of the sun is $1.99\times 10^{30}Kg$ Now the mass of HD68988 can be determined as $\frac{2.31\times 10^{30}}{1.99\times 10^{30}}=1.2 \space times \space the\space mass\space of \space sun $
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