RADIAL VELOCITY (‘WOBBLE’) METHOD
Stars with planets will gravitationally tug on one another. A star’s wobble toward an observer blueshifts the observed light; movement away redshifts it.
A planetary system passing in front of a distant star will cause light to bend, resulting in multiple images that briefly brighten observations of the distant star.
A planet passing in front of its star will briefly dim the star.
Masking the light from a parent star can make its planets visible — here, four Jupiter-size planets of the star HR 8799 are visible in this image from the W.M. Keck Observatory.