Hill sphere

The region around an astronomical body where its gravity dominates satellite motion relative to a more massive body's pull. Its approximate size depends on the body's mass, its orbit, and the mass of the larger body.

Hill radius: An approximate radius of the region in which a body can retain orbiting satellites against a larger body's gravity. It gives the standard quantitative estimate for the Hill sphere's scale.
Natural satellite: A naturally occurring object that orbits a planet, dwarf planet, or other nonstellar body. A satellite must remain within its primary's gravitational domain to avoid capture by the larger body.
George William Hill: An American astronomer and mathematician known for foundational work in lunar and planetary motion. Hill's analysis of the restricted three-body problem underlies the sphere's name and classical treatment.
Roche limit: The minimum distance at which a body held together by self-gravity can survive a larger body's tidal forces. It concerns disruption by tides, whereas the Hill sphere concerns retention against an external body's pull.
Restricted three-body problem: A model of two massive bodies and a third body whose mass is negligible. It supplies the dynamical framework used to define gravitational dominance.
Earth's Hill sphere: The region around Earth in which Earth's gravity can retain orbiting objects against the Sun's pull. It provides a concrete example of the scale available for Earth's satellites.
Édouard Roche: A French mathematician and astronomer who studied the stability of bodies near planets. His work on Roche limits and lobes established a closely related way to describe gravitational boundaries.
Laplace sphere of influence: An approximate region in which a body's gravity dominates spacecraft motion for patched-conic trajectory calculations. This alternative boundary is optimized for trajectory planning, not satellite stability.
Lagrange point: A location in a rotating two-body system where gravitational and inertial effects permit a small object to remain fixed relative to the bodies. The L1 and L2 points mark approximate escape boundaries for stable satellite motion.
Moon: Earth's only permanent natural satellite, orbiting at an average distance of about 384,400 kilometers. Its orbit lies far inside Earth's Hill sphere, illustrating a long-lived satellite orbit.

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