Newton's 2nd Law for a body with constant mass is the well-known formula:

Newton's law of gravity for the force acting on body m in orbit about M:

where r_hat is the radial unit vector pointing from mass M to m. Set these equal, and the motion of the orbiting body (small m) is:

For a circular orbit of radius R you can replace the acceleration vector using:

and from that derive a formula for the period of the orbit versus orbital velocity and mass M. Not sure what else you're looking for.