deletions | additions       diff --git a/The Moon.tex b/The Moon.tex  index 9bb8327..931f5ac 100644  --- a/The Moon.tex  +++ b/The Moon.tex 
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\begin{align}  \frac{G M_\oplus}{a_m^2} &= \frac{4\pi^2 a_m^2}{P_m^2 a_m} \\  P_m^2 &= \frac{4\pi^2 a_m^3}{G M_\oplus} \label{keplersthird}\\   a_m &= \left( \frac{G M_\oplus P_m^2}{4\pi^2} \right)^{1/3} \\  &= \left( \frac{6.7\times10^{-8} \times 6 \times 10^{27} \times (2.4\times 10^6)^2}{4\times 10} \right)^{1/3} \\  &= 3.9\times10^{10}~{\rm cm}  \end{align}  For future reference, here's Newton's version of Kepler's third law:     \begin{equation}   P_m^2 &= \frac{4\pi^2 a_m^3}{G M_\oplus}   \label{keplersthird}   \end{equation}  A more precise estimate is $a_m = 3.844 \times 10^{10}$~cm.  \item {\it What is the Moon's radius?}