Answer
Please see the work below.
Work Step by Step
We know that orbital speed is given as
$v=\sqrt{\frac{Gm}{r}}$
We plug in the known values to obtain:
$v=\sqrt{\frac{6.67\times 10^{-11}(1.989\times 10^{30})}{6371000}}$
We plug in the known values to obtain:
$v=4.56\times 10^6\frac{m}{s}$
Now we can find the time period as
$T=2\pi\sqrt{\frac{r^3}{Gm}}$
We plug in the known values to obtain:
$T=2\pi\sqrt{\frac{(6371000)^3}{(6.67\times 10^{-11})(1.989\times 10^{30})}}=8.7722s$
