Hill sphere

Also known as Roche sphere

with regards to an astronomical body, the region in which it dominates the attraction of satellites

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Image: Earth-moon-gravitational-potential-3d.gif

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In sectional/side view, a two-dimensional representation of the three-dimensional concept of the Hill sphere, here showing the Earth's "gravity well" (gravitational potential of Earth, blue line), the same for the Moon (red line) and their combined potential (black thick line). Point P is the force free spot, where gravitational forces of Earth and Moon cancel. The sizes of Earth and Moon are in the proportion, but distances and energies are not to scale.