Discuss the motion of the centre of mass of the following binary systems in nature : (i) Binary stars, (ii) Diatomic molecules, and (iii) Earth-moon systems.

The motion of the center of mass in various binary systems can be described as follows: In binary star systems, two stars orbit around a common center of mass that is closer to the more massive star with their periodic motion influenced by gravitational attraction.
In diatomic molecules, the center of mass lies along the line connecting the two atoms, and its motion changes during vibrations, rotations, or reactions, affecting molecular interactions. In the Earth-Moon system, the center of mass is located inside the Earth, with both bodies orbiting this point, which influences tidal forces and their relative positions.