The center of mass of a system is the average location of all its mass. Its motion is affected solely by external forces, such as gravity, and not by internal forces like a rigid body fracturing. Since gravity acts vertically downward, providing the only vertical acceleration for a falling body, there are no external horizontal forces at play. Consequently, even when a rigid body splits, no new horizontal forces are introduced, preventing the center of mass from moving horizontally. While individual fragments may exhibit horizontal motion, their collective center of mass will maintain its vertical trajectory and continued downward acceleration due to gravity.