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Forces, Fields and Energy - Gravitational Fields

The distance between the centers of the Earth and the moon is 3.8 x 10^8 m. Assume that the moon moves in a circular orbit about the center of the Earth. Estimate the period of the orbit to the nearest day.
*Mass of earth = 6.0 x 10^24 kg
*1 day = 8.6 x 10^4 seconds
*Distance between the centers of Earth and Moon = 3.8 x 10^8 m

That above, is the problem. Common knowledge tells me that the answer will be 1 day, as it takes 24 hours for the Moon to orbit the Earth. I know therefore that the period will be 1 day, equivalent to 8.6 x 10^4 seconds, but the problem is that I do not know how to show this via working it out. I tried to calculate the angular velocity OMEGA, which is given by 2PI/f, and also using v = rOMEGA, but both of these quantities can only be found by knowing the time period, as frequency = 1/T, and velocity requires time to work out as well, (as far as I know) and time is the quantity that you are trying to work out.

Please could you help me out with this problem. Your response will be very much appreciated.
:)

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