Although it is often said that a planet revolves around its star, the planet and the star in fact revolve around each other. The presence of the planet causes its star to wobble around their common center of mass.
However, this movement is tiny. As for the radial velocity method, the smaller the planet, the smaller the wobble of its star. Detecting it requires incredibly precise instruments. Space telescope are a must since the Earth’s atmosphere distorts light.
The European Space Agency’s Gaia satellite aims to measure the position of more than a billion celestial objects with unparalleled accuracy. One of Gaia’s scientific objectives is to discover and confirm exoplanets around stars in the solar neighbourhood by detecting the tiny motion of these stars. The next few years promise to be filled with discoveries of new exoplanets!