Question

Where is the centre of mass of the Earth-moon system?

Answer 1

1. Gravitational force binds the moon and the earth together. The "pericenter" of the earth-moon system is the center of mass, and it is always close to the bigger body. This center is around $1068$ miles ($1719$ kilometers) from the earth's surface.
2. While it may seem that the moon rotates around the earth, in fact, both objects really revolve around a single center of mass. The earth's interior is where the earth's center of mass is located because it has a far larger mass than the moon. The earth-moon system's center of mass travels in an elliptical orbit around the sun