Answer
$2.73\times10^{-3} m/s^2$
Work Step by Step
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 $
$g=\frac{4\pi^2 R }{T^2}=\frac{4\pi^2 (384400\times10^3) }{(2.36\times10^6)^2}=2.73\times10^{-3} m/s^2$
