The Moon does not orbit the centre of the Earth. Both bodies swing around a shared balance point about 4,670 kilometres from Earth's middle, which is still 1,700 kilometres underground.

The Earth is eighty-one times heavier, so the balance point sits eighty-one times closer to it — deep inside the planet, but not at its centre. That means the Earth is describing a small monthly circle of its own, and the wobble is real enough that it shifts the timing of astronomical observations and has to be taken out of the data.