Answer
The period is $~~97~$ minutes.
Work Step by Step
We can find the speed:
$\frac{GMm}{r^2} = \frac{mv^2}{r}$
$v^2 = \frac{GM}{r}$
$v = \sqrt{\frac{GM}{r}}$
$v = \sqrt{\frac{(6.67\times 10^{-11}~N~m^2/kg^2)(5.98\times 10^{24}~kg)}{(6.37\times 10^6~m)+(6.40\times 10^5~m)}}$
$v = 7540~m/s$
We can find the period:
$T = \frac{2\pi~r}{v}$
$T = \frac{(2\pi)~(6.37\times 10^6~m+6.40\times 10^5~m)}{7540~m/s}$
$T = 5841.5~s$
$T = 97~min$
The period is $~~97~$ minutes.
