We call barycentre to the common center of gravity of a system of celestial bodies that show mutual attraction.
In the Earth-Moon system, because the Earth has a mass 81 times higher than that of the Moon, the barycenter is within the globe.
In the case of the Earth and the Sun, both bodies revolve around the exact center of the mass (similar to the center of gravity) between them. The Earth and the Sun are "connected" by the gravity that attracts them, but, compared to the size of the Sun, the Earth is tiny. Therefore, the barycenter between the Earth and the Sun is almost, but not exactly, the very center of the Sun.
In the case of a planet the size of Jupiter, which has 318 times more mass than Earth, the barycenter of Jupiter and the Sun is a little further from the center of the Sun. Therefore, as Jupiter revolves around the Sun , the Sun also revolves around this point slightly away from its center.
Because of this, a planet the size of Jupiter causes the Sun (or any star) to wobble. We can take advantage of this knowledge and look for large planets in other solar systems if we can detect this tiny type of wobble in the position of the stars.
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