One way to find a planet
You've heard that Earth revolves around the sun. Well, that's not quite true! Here's what's really going on:
The exact center of all the material (that is, mass) that makes up an object—whether a planet or a pencil—is called its "center of gravity." For example, if you have a straight stick, like a ruler, there's a place at the middle where you can balance it on your finger. That's its center of gravity.
But the center of gravity may not be the point that looks like the middle of the object. Some parts of the object may be heavier (denser) than others. A sledge hammer is heavier on one end than the other. Its center of gravity is much closer to the heavy end than the lighter end.
To get an idea of where the center of gravity is, rest the ends of any object like the ruler or a pencil on one finger from each hand. Slowly move your fingers together without dropping the object. Your fingers will meet underneath the object's center of gravity. You can balance the object on one finger at that special place.
The actual center of gravity could be close to the surface if, for example, the object is flat like a ruler or a dinner plate. Or the center of gravity could be deep inside if the object is "three-dimensional," like a box or a ball. And if you let the object spin (like when you throw it), it will try to spin about that point.
What's a barycenter?
In the case of the Earth and the Sun, both bodies orbit around the very center of the mass (similar to center of gravity) between them. This point is called the "barycenter."
Earth and the Sun are "connected" by the gravity pulling them together. It's just like the light end and heavy end of the sledge hammer. Compared to the size of the Sun, though, Earth is about like a flea on a cat! So the center of mass between the Earth and the Sun is almost—but not quite—the very center of the Sun.
Jupiter, on the other hand, is 318 times as massive as Earth. Therefore, the barycenter of Jupiter and the Sun is a bit further from the Sun's center. So, as Jupiter revolves around the Sun, the Sun itself is actually revolving around this slightly off-center point, located just outside its surface.
The barycenter "wobble" gives us a way to find planets around other stars.
Thus, a planet the size of Jupiter will make its star wobble a tiny bit. This picture shows you that the center of mass of a star and the barycenter of a star and a planet can be slightly different points.
We can take advantage of this bit of knowledge and look for large planets in other solar systems by learning to detect this type of tiny wobble in the star's position.