An innovative planetary ring system is designed to encircle Mars to create a habitat that simulates Earth-like gravity conditions through its rotation. This system is placed at $2.00\times 10^5\ km$ from the center of Mars. Given that Mars has a mass of $6.42\times 10^{23}\ kg$, calculate the ring system's rotation period, T, in hours. (Let $G=6.67\times 10^{-11}\frac{N\ m^2}{kg^2}$)