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 134: 41

Answer

$F_E=9.6\times10^{17}N$ $\frac{F_E}{F_{SE}}=2.7\times10^{-5}$

Work Step by Step

$F_G=G\frac{m_1m_2}{r^2}$ Assuming right is positive and left is negative, the gravitational force of Jupiter and Saturn will be positive while the gravitational field of Venus and the sun will be negative. $m_E=5.98\times10^{24}kg$ $F_{SE}=-6.67\times10^{-11}\frac{Nm^2}{kg^2}\frac{1.99\times10^{30}kg\times 5.98\times10^{24}kg}{(150\times10^9m)^2}$ $=-3.53\times10^{22}N$ $F_{VE}=-6.67\times10^{-11}\frac{Nm^2}{kg^2}\frac{0.815\times 5.98\times10^{24}kg\times 5.98\times10^{24}kg}{(42\times10^9m)^2}$ $=-1.10\times10^{18}N$ $F_{JE}=6.67\times10^{-11}\frac{Nm^2}{kg^2}\frac{318\times 5.98\times10^{24}kg\times 5.98\times10^{24}kg}{(628\times10^9m)^2}=1.92\times10^{18}N$ $F_{SE}=6.67\times10^{-11}\frac{Nm^2}{kg^2}\frac{95.1\times 5.98\times10^{24}kg\times 5.98\times10^{24}kg}{(1280\times10^9m)^2}=1.38\times10^{17}N$ $F_E=-1.10\times10^{24}N+1.92\times10^{24}N+1.38\times10^{23}N=9.6\times10^{17}N$ $\frac{F_E}{F_{SE}}=\frac{9.6\times10^{17}N}{3.53\times10^{22}N}=2.7\times10^{-5}$
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