Explosion-centre of mass

Imagine a shell is fired making certain angle with horizontal direction. It is under the influence of gravitational force and allows the parabolic path. Let the shell explodes into fragments due to internal forces in its path. It will be found that different fragments will fly in different directions. But only one point in the system does not disturb its path, i.e., it follows in parabolic path. In the process of explosion, some changes may occur in momentum of individual fragments due to internal forces, but the centre of mass has its motion unaltered. From this once again it can be proved that centre of mass  solely depends on external force, but gravitational force is applied on the shell from the beginning which continues the motion of the shell in parabolic patThis figure shows the path of the shell under explosion as a parabolic path.