The Moon does not orbit Earth's centre, and the Sun wobbles too
Earth and Moon actually circle a shared balance point, and it is not Earth's centre. That point sits about 4,671 km from the middle of our planet, roughly three quarters of the way to the surface. The Sun plays the same game with its planets, sometimes swinging its centre well outside its own glowing surface.
This balance point is the barycenter, from Greek words for weight and centre. It is not a thing but a location: the centre of mass around which two or more bodies orbit, and one focus of each body's elliptical path. When one partner is far heavier and the two are close, the barycenter lies inside the bigger body, so the small one seems to orbit while the big one merely wobbles. Earth and Moon are that kind of pair.
When masses are similar, the balance point falls in open space between them and both visibly circle it. Pluto and its moon Charon behave like this, as do many binary stars and double asteroids. The rule of thumb is that a partner pulls the barycenter outward in proportion to its mass and its distance.
For the Sun, only the four giants really matter; every other planet and dwarf planet is negligible. Line up Jupiter, Saturn, Uranus and Neptune on one side and the Sun's balance point would lie about 810,000 km above its surface. Earth alone could never manage that: even moved out to the distant orbit of Eris, it would leave the shared centre inside the Sun. Jupiter placed on Mercury's orbit, by contrast, would still shift it only about 55,000 km from the solar centre.
Astronomers anchor their master reference frame, the International Celestial Reference System, on the Solar System's barycenter rather than on the Sun. Relativity complicates matters, because clocks tick at different rates in different gravity, so a standard called Barycentric Coordinate Time imagines an ideal clock far outside the Solar System. For far-flung, highly eccentric objects, barycentric orbits are steadier than Sun-centred ones, since they barely shift with Jupiter's 11.8-year circuit.
Source: Barycenter (astronomy)
