Answer
$7.05\times10^3s$
Work Step by Step
The speed of an object in a circular orbit of radius $r$ around mass $M$ is given by $v=\sqrt{\frac{GM}{r}}$ and also $v=\frac{2\pi r}{T}$, where $T$ is the period of orbiting object. Equate both expressions and solve for $T$.
$$v=\sqrt{\frac{GM}{r}}=\frac{2\pi r}{T}$$
$$T=2\pi \sqrt{\frac{r^3}{GM}}=2\pi \sqrt{\frac{(1.74\times10^6m+9.5\times10^4m)^3}{(6.67\times10^{-11}Nm^2/kg^2)(7.35\times10^{22}m)}}$$
$$=7.05\times10^3s$$