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 $2.00\times {10}^5\text{ km}$ from the center of Mars. Given that Mars has a mass of $6.42\times {10}^{23}\text{ kg}$, calculate the ring system's rotation period, T, in hours. (Let $G=6.67\times {10}^{-11}\frac{\text{N}\cdot {\text{m}}^2}{{\text{kg}}^2}$)