A Mars satellite moving in an orbit of radius $9.4 imes 10^3~km$ takes $27540~s$ to complete one r

Question

A Mars satellite moving in an orbit of radius $9.4 	imes 10^3~km$ takes $27540~s$ to complete one revolution. Calculate the approximate mass of Mars. (Take $G = 6.67 	imes 10^{-11}~N~m^2~kg^{-2}$)

Professor PC Thomas Classes · Answer

According to Kepler's third law, $T^2 = \frac{4\pi^2 r^3}{GM}$. Rearranging gives $M = \frac{4\pi^2 r^3}{GT^2} = \frac{4 \pi^2 (9.4 	imes 10^6)^3}{6.67 	imes 10^{-11} 	imes (27540)^2} \approx 6.48 	imes 10^{23}~kg$.