Even the small mass of the earth determines the course of the Sun

The Sun is not the actual center of the solar system that the planets orbit around. The planets…and the Sun…actually orbit around the center of mass of the solar system. Since the Sun is by far the most massive object in the solar system the center of mass of the solar system is usually very near the sun and might be located around the surface of the Sun. Because of this the sun appears to wobble as it moves in its orbit and this phenomena can be used to help detect planets orbiting around others stars that we can see.

(The Great Courses – The Search of Exoplanets: What Astronomers Know)

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