State and derive Kepler's third law

Kepler's third law states that the square of the period of any planet is proportional to the cube of its orbital radius.To derive it, two equations are required: F=GMm/r^2 and F = mv^2/r. These are Newtons law of gravity and the centripetal force for an object moving in circular motion respectively.By equating the two you can see that GMm/r^2 = mv^2/r. the m's and r's (mass and radius) then cancel to give: GM/r = v^2.v^2 can be shown to be equal to (2pir/T)^2, which I would show in the video and this can be substituted in to finally show that: T^2 = 4pi^2r^3/GM. I can then expand on this question by asking the student to find the period of a planet with mass M and radius r.