Noun
Hill sphere (plural Hill spheres)
(astronomy) The region in which a given astronomical body dominates the attraction of satellites.
However, the resonance width (the range of semi-axes compatible with the resonance) is very narrow and only a few times larger than Pluto’s Hill sphere (gravitational influence). Source: Internet
When the comet passed Jupiter in the late 1960s or early 1970s, it happened to be near its aphelion, and found itself slightly within Jupiter's Hill sphere. Source: Internet