al phy

Since the moon and the statellite orbit the same object, i.e. the Earth, kelper's 3rd law can be used in this case.

(T^2)/(R^3) is constant,
[ (Tm)^2 ] / [ (Rm)^3 ] = [ (Ts)^2 ] / [ (Rs)^3 ],

where
Tm = Period of the moon;
Ts = Period of the statellite;
Rm = Orbital radius of the moon;
Rs = Orbital radius of the statellite.

By substitution,
Ts = 0.1661 days = 3.987 hrs = 4 hrs