The Solar System

The total distance D_{total} = 238,857 miles.

Distance from the Earth's center to the barycenter (point O to point X) is defined as:

D_{barycenter} = \tfrac{M_{moon}}{ M_{moon} + M_{Earth}} \times D_{total}

Where if the mass of the Earth were one, the mass of the Moon relative to the earth would be 0.012. Substituting for values, we get the distance from Earth's center to the barycenter of the Earth-Moon system.

D_{barycenter} = 2,832.30 miles.

Since the radius of Earth is 3,959 miles, it means that the barycenter is located inside of Earth at about 1121 miles below the surface. Could anything weird happen in there at the level of barycenter? Well, it depends. Gravitational forces may loosen rocks a bit, push magmatic material up and that in turn could trigger an earthquake — but this is a conjecture not fully understood yet.