ONE WAY TO FIND A PLANET.~
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.
As seen from above, a
large planet orbits a star–or rather the star and planet orbit their
shared center of mass, or barycenter.
As seen from the side, a
large planet and star orbit their shared center of mass, or barycenter,
with the star seeming to shift back and forth.
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