The phrase "gravitational influence" refers to the pull or force that gravity exerts on an object, causing it to move or be attracted towards another object. Full definition
It is held in place by the enormous gravitational influence of dark matter. (sciencedaily.com)
Those stellar motions can reveal the presence of unseen planets whose gravitational influence produces periodic patterns of motion in the host star's position. (scientificamerican.com)
The bottom panel shows a numerical model that matches the data remarkably well, from using the combined gravitational influence of luminous and dark matter. (keckobservatory.org)