## Essential University Physics: Volume 1 (3rd Edition)

$2.73\times10^{-3} m/s^2$
a) Recall, $g=\frac{GM}{R^2}$. Using this, we find that the equation for period simplifies to: $T ^2 = \frac{4\pi^2 R^3}{GM}$ $\frac{T^2GM}{R^3}=4\pi^2$ $\frac{T^2g}{R}=4\pi^2$ $g=\frac{4\pi^2 R }{T^2}=\frac{4\pi^2 (384400\times10^3) }{(2.36\times10^6)^2}=2.73\times10^{-3} m/s^2$