Hill sphere
The region around a planet or other body where its own gravity, rather than the Sun's, controls what orbits it.
Every body in the Solar System is pulled by the Sun while also holding on to things with its own gravity. The Hill sphere is the zone around a planet, moon or asteroid in which its own pull dominates, so that a moon, a spacecraft or a ring of debris can stay in orbit around it instead of being drawn off into an orbit of its own around the Sun.
The size depends on two things: the body's mass compared with the Sun's, and its distance from the Sun. A heavier body, and one farther out, has a larger Hill sphere. Earth's reaches out about 1.5 million kilometres, roughly four times the distance to the Moon, which orbits comfortably inside it. The small asteroid Bennu, about 250 metres in radius, has a Hill sphere only about 29.5 kilometres in radius, which made orbiting it a delicate task for NASA's OSIRIS-REx spacecraft.
In practice, long-lasting orbits sit well inside the Hill sphere; near its edge the Sun's influence makes orbits wander and escape.
The idea matters for how planets form, too. A growing planet can gather up only material that strays within its zone of gravitational influence, so the Hill sphere helps set how wide a lane of the protoplanetary disc a young planet can clear, and how far out it can hold on to moons.