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 - Page 136: 84

Answer

See answer.

Work Step by Step

The relationship between the sun's period T, mean distance r, and the galaxy’s mass M is derived in Example 5-14. $$M=\frac{4 \pi ^2 r^3}{GT^2}$$ Substitute the values given to get the mass of the galaxy. $$M=\frac{4 \pi ^2 (30000*9.5\times10^{15}m)^3}{G(200\times10^6 y*3.15\times10^7 s/y)^2}\approx3\times10^{41}kg$$ Dividing that mass by the mass of our sun, there would be about $2\times10^{11}$ stars in the galaxy.
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