9-17 할리데이 11판 솔루션 일반물리학

$$ \put \begin{cases} M : \text{Moon}\\ E : \text{Earth}\\ \end{cases} $$ $$ \begin{cases} r_{E}&=0\\ r_{M}&=3.82\times10^8\ut{m}\\ m_E&=5.98\times10^{24}\ut{kg}\\ m_M&=7.36\times10^{22}\ut{kg}\\ R_E&=6.37\times10^6\ut{m}\\ \end{cases} $$ $$\ab{a}$$ $$r_\com=\frac{\Sigma rm}{M},$$ $$ \begin{aligned} r_\com&=\frac{r_Em_E+r_Mm_M}{m_E+m_M}\\ &=\frac{m_M}{m_E+m_M}r_M\\ &=\frac{1528}{329}\times10^6\ut{m}\\ &\approx 4.644376899696048\times10^6\ut{m}\\ &\approx 4.64\times10^6\ut{m}\\ &\approx 4.64\ut{Mm}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} \frac{R_E}{r_\com}&=\frac{6.37\times10^6\ut{m}}{\frac{1528}{329}\times10^6\ut{m}}\\ &=\frac{209573}{152800}\\ &\approx 1.3715510471204189\\ &\approx 1.37\\ &\approx 137\ut{\%}\\ \end{aligned} $$