Answer
$r = 4.6\times 10^{12}~m$
Work Step by Step
We can find the minimum turning radius:
$a = \frac{v^2}{r}$
$r = \frac{v^2}{a}$
$r = \frac{(0.1~c)^2}{20~g}$
$r = \frac{[(0.1)~(3.0\times 10^8~m/s)]^2}{(20)(9.8~m/s^2)}$
$r = 4.6\times 10^{12}~m$