10-20 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} r&=2.3\times10^4\ut{ly}\\ v&=250\ut{km/s}=2.5\times10^5\ut{m/s}\\ t&=4.5\times10^9\ut{y}\\ \end{cases} $$ $$ \begin{cases} c&=299~792~458\ut{m/s}\\ 1\ut{d}&=86400\ut{s}\\ 1\ut{y}&=365.25\ut{d}=31~557~600\ut{s}\\ 1\ut{ly}&=9~460~730~472~580~800\ut{m} \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} T&=\frac{2\pi r}{v}\\ &=\frac{8703872034774336 \pi }{5}\ut{s}\\ &=\frac{6895226534 \pi }{125}\ut{y}\\ &\approx 1.732959441924145\times10^8\ut{y}\\ &\approx 1.7\times10^8\ut{y}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} \Ans&=\frac{t}{T}\\ &=\frac{4.4\times10^9\ut{y}}{\frac{6895226534 \pi }{125}\ut{y}}\\ &=\frac{281250000000}{3447613267 \pi }\\ &\approx 25.967139744502884\\ &\approx 26\\ \end{aligned} $$