Thanks for the welcome CraigD. That formula is correct for a nontranslating circularly rotating system with Euclidean axioms. However, if you assume the system is moving uniformly and apply Galilean relativity to it, you'll find that the orbital period must increase. You can rationalize this by realizing that circular rotation that suddenly begins to translate "to the right" is now undergoing ellipsoidal rotation wherein the "smaller radius" of the ellipse is equal to the previous circle's radius. Also, when you employ Galilean relativity, you'll find that the orbital period increases by exactly the Lorentz factor, assuming Euclidean axioms.