In Astronomy, the barycenter is a term used for the centre of mass of two or more bodies, usually bodies orbiting around each other, such as the Earth and the Moon. We say that planets orbit stars, but that’s not the whole truth. Planets and stars actually orbit around their common centre of mass.
All objects have a centre of mass. The centre of mass is the exact centre of all the material an object is made at which it can be balanced. Sometimes the centre of mass is directly in the centre of an object. With some symmetrical objects, it is easy to find the middle of the object to balance.
Some objects may have more mass distributed to other parts. A sledge hammer, for example, has most of its mass on one end, so its center of mass is much closer its heavy end.
The moon does not simply just orbit the Earth. They both orbit the barycenter. If two objects of a similar size are orbiting each other, the barycenter will be between them. The barycenter is usually closest to the object with the most mass. Because the Earth is in fact considerably larger than the moon, the barycenter is inside the Earth close to the the centre.
The fact that the barycenter isn’t in the middle of the Earth causes the Earth to wobble on it’s axis. Effectively, thanks to the gravity of the moon, the Earth is orbiting a point inside itself.
So, Where is the barycenter between Earth and the sun? Well, the sun has lots of mass. In comparison, Earth’s mass is very small. That means the sun is like the head of the sledgehammer. So, the barycenter between Earth and the sun is very close to the center of the sun.
Our entire solar system also has a barycenter. The sun, Earth, and all of the planets in the solar system orbit around this barycenter. It is the center of mass of every object in the solar system combined.
Our solar system’s barycenter constantly changes position. Its position depends on where the planets are in their orbits. The solar system’s barycenter can range from being near the center of the sun to being outside the surface of the sun. As the sun orbits this moving barycenter, it wobbles around.