Derive kepler's third law

F = G(Mm/r^2)F = mv^2/rG(Mm/r^2) = mω^2rω = 2π/TG(Mm/r^2) = 4π^2mr/T^2GM/r^3 = 4π^2/T^2T^2 = r^3 (4π^2/GM)