18. Recently, the TV series Three-Body Problem has become very popular on Netflix. The "three-body problem" itself is a classic problem in physics, and only certain special cases admit exact analytical solutions.
Consider a system in outer space consisting of three planets, each with mass m, located at the vertices of an equilateral triangle with side length a, as shown in the figure. The three planets form an isolated system. Each planet moves with uniform circular motion along the circumcircle of the triangle, orbiting the center of mass of the system. Find the period of rotation of this system.