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 - Problems - Page 135: 65

Answer

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Work Step by Step

Use Kepler’s third law to find the mean orbital radius of Halley’s comet, using Earth’s data. $$(\frac{r_1}{r_2})^3=(\frac{T_1}{T_2})^2$$ $$r_1=r_2 (\frac{T_1}{T_2})^{2/3}$$ $$r_{Halley}=r_{Earth} (\frac{T_{Halley}}{T_{Earth}})^{2/3}$$ $$r_{Halley}=(150\times10^6 km) (\frac{76y}{1y})^{2/3}=2690\times10^6 km $$ This value is the average of the nearest and farthest distances of Halley’s comet from the sun. Assuming that the nearest distance is zero, the farthest distance is twice the value calculated, or $5.4\times10^{9}km$. As we see from Table 5-2, it’s out near Pluto, so it is (barely) in the solar system.
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