A faraway, imaginary planet has one moon which has a nearly circular periodic orbit. Let the distance between the surface of the imaginary planet and the center of the moon be \(2.075 \times 10^5\) km, and the planet has a radius of 4125 km and a mass of \(6.55 \times 10^{22}\) kg. How many days will it take the moon to travel one time around the imaginary planet? The gravitational constant is \(6.67 \times 10^{-11} \text{ N} \cdot \text{m}^2/\text{kg}^2\).\[T = \underline{\hspace{6cm}} \text{ days}\]

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