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An astronomical body's Hill sphere is the region in which it dominates the attraction of satellites. The outer shell of that region constitutes a zero-velocity surface. 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.〔http://adsabs.harvard.edu/full/1965SvA.....8..787C〕 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 upon the work of the French astronomer Édouard Roche. For this reason, it is also known as the Roche sphere (not to be confused with the Roche limit). In the example to the right, the Hill sphere extends between the Lagrangian points and , which lie along the line of centers of the two bodies. The region of influence of the second 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 second (e.g. a satellite of Jupiter) 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. == Formula and examples == If the mass of the smaller body (e.g. Earth) is ''m'', and it orbits a heavier body (e.g. Sun) of mass ''M'' with a semi-major axis ''a'' and an eccentricity of ''e'', then the radius ''r'' of the Hill sphere for the smaller body (e.g. Earth) is, approximately : When eccentricity is negligible (the most favourable case for orbital stability), this becomes : In the Earth example, the Earth (5.97×1024 kg) orbits the Sun (1.99×1030 kg) at a distance of 149.6 million km. The Hill sphere for Earth thus extends out to about 1.5 million km (0.01 AU). The Moon's orbit, at a distance of 0.384 million km from Earth, is comfortably within the gravitational sphere of influence of Earth and it is therefore not at risk of being pulled into an independent orbit around the Sun. All stable satellites of the Earth (those within the Earth's Hill sphere) must have an orbital period shorter than seven months. The previous (eccentricity-ignoring) formula can be re-stated as follows: : This expresses the relation in terms of the volume of the Hill sphere compared with the volume of the second body's orbit around the first; specifically, the ratio of the masses is three times the ratio of the volume of these two spheres. A quick way of estimating the radius of the Hill sphere comes from replacing mass with density in the above equation: : where are the densities of the primary and secondary bodies, and are their radii. The second approximation is justified by the fact that, for most cases in the Solar System, happens to be close to one. (The Earth–Moon system is the largest exception, and this approximation is within 20% for most of Saturn's satellites.) This is also convenient, since many planetary astronomers work in and remember distances in units of planetary radii. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hill sphere」の詳細全文を読む スポンサード リンク
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