Answer:
2 pi R / T = speed of moon
m V^2 / R = G M m / R^2 centripetal force = gravitational force
V^2 / R = G M / R^2
4 pi^2 R^2 / (T^2 R) = G M / R^2 using first equation
R^3 = 1 / (4 pi^2) * G M T^2 we need to know G and M
R^3 = .0253 * 6.67E-11 * 5.98E24 T^2 = 1.01E13 * T^2
63.3 da = 5.47E6 sec
T^2 = 2.99E13 sec^2
R^3 = 1.01E13 * 2.99E13 = 3.02E26 = 302E24 m^3
R = 6.70E8 m from center of earth
Using 1609 m/mile
R = 416,000 miles
Note: our moon is about 239,00 miles away
So this distance is about 1.74 our earth-moon distance
If T^2 proportional R^3 (the moon period is 27.3 da)
63.3/27.3 = 2.32 2.32^2 = 5.38
416/239 = 1.74 1.74^3 = 5.27
Not exact but reasonably close