Universe sandbox 2 barycenter
A spherical geostationary satellite, however, would only need to be more than 6% of the density of water to support satellites of its own. In fact, in any low Earth orbit, a spherical body must be more dense than lead in order to fit inside its own Hill sphere, or else it will be incapable of supporting an orbit. A sphere of this size and mass would be denser than lead. ( September 2018) ( Learn how and when to remove this template message)Īn astronaut could not have orbited the Space Shuttle (with mass of 104 tonnes), where the orbit was 300 km above the Earth, because its Hill sphere at that altitude was only 120 cm in radius, much smaller than the shuttle itself. Unsourced material may be challenged and removed. Please help improve this article by adding citations to reliable sources. This section needs additional citations for verification. This was thought to explain the preponderance of retrograde moons around Jupiter however, Saturn has a more even mix of retrograde/prograde moons so the reasons are more complicated. The region of stability for retrograde orbits at a large distance from the primary is larger than the region for prograde orbits at a large distance from the primary. Detailed numerical calculations show that orbits at or just within the Hill sphere are not stable in the long term it appears that stable satellite orbits exist only inside 1/2 to 1/3 of the Hill radius. This third object should also be of small enough mass that it introduces no additional complications through its own gravity. The Hill sphere is only an approximation, and other forces (such as radiation pressure or the Yarkovsky effect) can eventually perturb an object out of the sphere. (The Earth–Moon system is the largest exception, and this approximation is within 20% for most of Saturn's satellites.) This is also convenient, because many planetary astronomers work in and remember distances in units of planetary radii. the Earth) is m happens to be close to one. the Sun), eventually ending up orbiting the latter.Ĭomparison of the Hill spheres and Roche limits of the Sun-Earth-Moon system (not to scale) with shaded regions denoting stable orbits of satellites of each body the Moon) 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. Beyond that distance, a third object in orbit around the second (e.g. 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. In the example to the right, Earth's Hill sphere extends between the Lagrangian points L 1 and L 2, which lie along the line of centers of the two bodies (the Earth and the Sun). It was defined by the American astronomer George William Hill, based on the work of the French astronomer Édouard Roche. 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. 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. Any object within that distance would tend to become a satellite of the moon, rather than of the planet itself. That moon would, in turn, have a Hill sphere of its own. To be retained by a planet, a moon must have an orbit that lies within the planet's Hill sphere. The outer shell of that region constitutes a zero-velocity surface. The Hill sphere of an astronomical body is the region in which it dominates the attraction of satellites.