Measuring the change in a star's position in the sky in order to detect a planet orbiting that star is called the astrometric method.
Astrometry is a method of finding exoplanets (planets outside our Solar System) that are orbiting another star. This method consists of measuring a start's position in the sky precisely, observing the changes in position over time.
If a star has a planet orbiting it, the gravitational influence of the planet will cause the star to move in a very tiny elliptical or circular orbit (hence the need of precision). That's because both star and planet each orbit around their mutual centre of mass.
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