An Etymological Dictionary of Astronomy and Astrophysics

The spherical region around a → secondary in which the secondary’s gravity is more important for the motion of a particle about the secondary than the tidal influence of the → primary. The radius is described by the formula: r = a (m/3M)^1/3, where, in the case of the Earth, a is the semi-major axis of the orbit around the Sun, m is the mass of Earth, and M is the mass of the Sun. The Hill sphere for the Earth has a radius of 0.01
→ astronomical units (AU).
Therefore the Moon, lying at a distance of 0.0025 AU, is well within the Hill sphere of the Earth.

See also: Named for George William Hill (1838-1914), an American astronomer who described this sphere of influence; → sphere.