Answer
$2.408\times 10^{5}\ s$
Work Step by Step
The acceleration of the stresses $a=20g$. Therefore;
$a=20\times 9.8\ m/s^2=196\ m/s^2$
Speed of the craft $v=\frac{1}{10}c =\frac{1}{10}(3\times 10^8\ m/s) =3\times 10^7\ m/s$
Therefore, the time taken to rotate $90^{\circ}$ is:
$t=\frac{T}{4}$
$t=\frac{1}{4}(\frac{2\pi R}{v})$
$t=\frac{1}{4}(\frac{2\pi (4.6\times 10^{12}\ m)}{3\times 10^7\ m/s})$
$t=2.408\times 10^{5}\ s$
