All the places that I've seen an answer to this question simply state that it's because there is a stronger gravitational pull on the near side of the moon, facing the earth. But I'm wondering how this gravitational pull actually manages to shift the centre of gravity of the moon, and how does it tie into the idea that the centre of gravity is where a body's weight is evenly distributed?
Answer
The near side of the moon experiences more gravity because it is closer to Earth. The force of gravity from the Earth acting on the moon has an inverse relationship to the distance between the two bodies. So the part of the moon that is closer to Earth experiences greater gravity than the far side of the moon.
If there were no other bodies of mass acting on the moon, then the centre of gravity would be the centre of mass. But that's not the case here.
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