«The principle is like that of a see-saw, or teeter-totter. If two people of very different weights sit on opposite sides of the balance point (or “fulcrum“), the heavier one must sit closer to the balance point (…).
The balance point is the “center of mass” of the see-saw, just as the barycenter is the balance point of the Earth-Moon system. It is this point that actually moves around the Sun in what we call the orbit of the Earth, while the Earth and Moon each move around the barycenter, in their respective “orbits”. (…)
Just as the Moon moves around the Earth once every 27 1/3 days, as a result of the Earth’s pull on the Moon, the Earth moves “around the Moon” once every 27 1/3 days, as a result of the Moon’s pull on the Earth. More accurately, each moves around a point in between them, which would be the balance point between them, if they were on a seesaw, called the center of mass or barycenter of the Earth-Moon system. At any given time, the bodies are on opposite sides of the center of mass, moving in opposite directions. As shown in the diagram (below), each exerts a force on the other which, according to Newton’s Third Law of Motion (the Law of Action and Reaction), is equal and opposite to the force that the other is exerting on it; but although the forces are equal, their effects are not, because the more massive Earth is accelerated less by the same force, than the less massive Moon. (…)
As the Earth rotates to the east each day, the Moon appears to move to the west. (…) You would be compelled to move around the center of mass every month, because the Earth’s gravity holds you on the surface while it goes around the center of mass; but you are not just along for the ride, as the Moon is pulling on you with a force equal to 1/300,000th of your weight, in a way that would cause you to follow the path that the Earth makes around the barycenter, even if you weren’t firmly held to the Earth by its gravity.»