Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 5 - Circular Motion; Gravitation - General Problems: 86

Answer

Mass of the core = $5.2\times10^39kg$ It is $2.6\times10^9$ solar masses

Work Step by Step

The speed of an orbiting object is given by $v=\sqrt{\frac{GM}{r}}$. Solve the equation for $M$. $$v=\sqrt{\frac{GM}{r}}$$ $$M=\frac{rv^2}{G}=\frac{(5.7\times10^17m)(7.8\times10^5m/s)^2}{6.67\times10^{-11}Nm^2/kg^2}=5.2\times10^{39}kg$$ The number of solar masses is found by dividing the mass by the solar mass. $$=\frac{M_{galaxy}}{M_{Sun}}=\frac{5.2\times10^{39}kg}{2\times10^{30}kg}=2.6\times10^9$$
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