Answer
The moon's orbital period is 26.0 days.
Work Step by Step
We can use the gravitational force to find the mass $m_p$ of the planet;
$F_g = \frac{G~m_p~m_m}{r^2}$
$m_p = \frac{F_g~r^2}{G~m_m}$
$m_p = \frac{(1.1\times 10^{19}~N)(1.5\times 10^8~m)^2}{(6.67\times 10^{-11}~m^3/kg~s^2)(9.4\times 10^{21}~kg)}$
$m_p = 3.95\times 10^{23}~kg$
We can use the equation for the orbital period to find the period in seconds;
$T^2 = \frac{4\pi^2~r^3}{G~m_p}$
$T = \sqrt{\frac{4\pi^2~r^3}{G~m_p}}$
$T = \sqrt{\frac{(4)(\pi^2)(1.5\times 10^8~m)^3}{(6.67\times 10^{-11}~m^3/kg~s^2)(3.95\times 10^{23}~kg)}}$
$T = 2.25\times 10^6~s$
We can convert the period to units of days:
$T = (2.25\times 10^6~s)(\frac{1~day}{(24~hr)(3600~s/hr)})$
$T = 26.0~days$
The moon's orbital period is 26.0 days.
