Answer
The period of an artificial satellite orbiting very near the Earth’s surface is 84.2 minutes.
Work Step by Step
Let $s_1 = 6380 ~km$
Let $s_2 = 385,000 ~km$
Let $T_2 = 27.4 ~days$
$(\frac{T_1}{T_2})^2 = (\frac{s_1}{s_2})^3$
$T_1^2 = (\frac{6380 ~km}{385,000 ~km})^3\cdot (27.4 ~days)^2$
$T_1 = 0.05845 ~days$
We can convert this time to minutes.
$T_1 = (0.05845 ~days)(\frac{24 ~h}{1 ~day})(\frac{60 ~min}{1 ~h}) = 84.2 ~minutes$
The period of an artificial satellite orbiting very near the Earth’s surface is 84.2 minutes.