newtonian mechanics - Earth-Moon system

While learning about motion of centre of mass, I came across this statement online,

It is also more accurate to say that the Earth and Moon together revolve about their common center of mass.

I am not able to understand this. Can anyone please explain this statement?

Answer

Suppose the Earth was stationary, and the Moon revolved around the centre of the Earth:

If $v$ is the orbital velocity of the Moon then at point $A$ the linear momentum of the Moon is $mv$. Half an orbit later, at point $B$, the velocity of the Moon is $-v$, because it's in the opposite direction, so the momentum of the Moon is $-mv$.

If the Earth is stationary then its momentum is zero, and that means the total momentum of the Earth Moon system is not conserved, because it's changing from $mv$ to $-mv$ every half an orbit. But if we take the Earth-Moon system as an isolated system then its momentum must be conserved so we have a contradiction. That means the Earth can't be stationary.

Obviously what happens is that the Earth moves as well as the Moon:

At any point in time the momentum of the Earth is equal and opposite to the momentum of the Moon, so the total momentum (in the centre of mass frame) is zero.

And that's why conservation of momentum requires both the Earth and the Moon to revolve around the centre of mass.