The center of mass of the Earth-Moon system, is a point in space about which the Earth and Moon appear to orbit as they travel around the Sun. It is located exactly along the line that connects the center of the Earth with the center of the Moon. The average distance between the centers is 384,405 kilometers. The distance from the Earth's center to the barycenter is
D = M(moon)d(moon)/(M(earth) +M(moon) 0.012 x 384405/(1.00 + 0.012 4641 kilometerswhere the mass of the Earth is 1.0 and the mass of the Moon relative to the earth is 0.012. Now, the radius of the Earth is 6,378 kilometers, so that means that the barycenter is located INSIDE the Earth about 1707 kilometers below its surface. Does anything weird happen there? Not that anyone can tell.