the video below describes the gravitational effect of
a planet on the star it orbits

the narrator of the National Geographic documentary
states,

When a planet orbits a star, its gravitational force will pull the star off center; making it wobble from side to side . . .

to illustrate this phenomenon, the video references
the relative motions (or "the dance") of Jupiter and
the Sun,

The largest planet in our solar system is Jupiter . . . 500 million miles out from the Sun, it take 12 years to complete each orbit. As it travels round, Jupiter pulls our sun off-center by as much as half a million miles.