The Hill sphere of an astronomical body is the region in which it dominates the attraction of satellites. To be retained by a planet, a moon must have an orbit that lies within the planet's Hill sphere. That moon would, in turn, have a Hill sphere of its own. Any object within that distance would tend to become a satellite of the moon, rather than of the planet itself. One simple view of the extent of the Solar System is the Hill sphere of the Sun with respect to local stars and the galactic nucleus. In more precise terms, the Hill sphere approximates the gravitational sphere of influence of a smaller body in the face of perturbations from a more massive body. It was defined by the American astronomer George William Hill, based on the work of the French astronomer Édouard Roche. It is sometimes termed the Roche sphere. In the example to the right, the Earth's Hill sphere extends between the Lagrange points and , which lie along the line of centers of the two bodies. The region of influence of the smaller body is shortest in that direction, and so it acts as the limiting factor for the size of the Hill sphere. Beyond that distance, a third object in orbit around the small object would spend at least part of its orbit outside the Hill sphere, and would be progressively perturbed by the tidal forces of the central body (e.g. the Sun), eventually ending up orbiting the latter. For any given energy of the third object (considered to have a negligible mass) there is a zero-velocity surface in space which cannot be passed. This is a contour of the Jacobi integral. When the energy is low, the zero-velocity surface surrounds the second body (the smaller of the two) completely, which means the third body cannot escape. At higher energy, there will be one or more gaps or bottlenecks by which the third object may escape the second object and go into orbit around the first object. If the energy is right at the border between these two cases, then the third object cannot escape, but the zero-velocity surface confining it touches a larger zero-velocity surface around the first object at one of the nearby Lagrange points (forming a cone-like point there). At the opposite side of the planet it gets close to the other Lagrange point. This