A binary star wobbles back and forth because each star orbits the common center of mass (barycenter) of the system. This mutual gravitational pull causes both stars to move in elliptical orbits around this shared point, resulting in a periodic "wobble" motion as seen from a distance

. More specifically:

• Each star in the binary system moves around the barycenter. When one star moves toward us, the other moves away, causing observable Doppler shifts in their spectral lines (blueshift and redshift), which oscillate back and forth as the stars orbit each other

• The wobble is essentially the star's motion around the barycenter, not a simple linear path but a small orbit or oscillation caused by the gravitational influence of its companion star

• This wobble can be detected as changes in the star’s position on the sky or as variations in its radial velocity (speed toward or away from us)

Thus, the cause of the wobble is the gravitational interaction between the two stars in the binary system, making each star orbit their common center of mass and producing the characteristic back-and-forth motion observed.