In physics, the centre of gravity is an arbitrary location in a body of matter where the total weight of the body can be assumed to be concentrated for simplicity in some calculations.
The centre of gravity is identical to the centre of mass, in a uniform gravitational field. And still, not always do the two points coincide. The centre of mass for the Moon is very near its geometric centre. Nevertheless, owing to the stronger gravitational force on the nearer side of the Moon the centre of gravity is slightly toward the Earth.