Hill sphere

That moon would, in turn, have a Hill sphere of its own.

The radius of the Hill sphere is given in the adjacent table.

An astronomical body's Hill sphere 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.

The radius of the Uranus's Hill sphere is approximately 73 million km.

Jupiter is massive, with a surface gravity two and a half times that of Earth, so its Hill sphere is very large.

In contrast to true satellites, quasi-satellite orbits lie outside the planet's Hill sphere, and are unstable.

However, the Sun's Hill sphere, the effective range of its gravitational dominance, is believed to extend up to a thousand times farther.

Alternatively, the increasing perturbations by the Sun at the growing apocenters push them beyond the Hill sphere.

All stable satellites of the Earth (those within the Earth's Hill sphere) must have an orbital period shorter than 7 months.

The Hill sphere extends between the Lagrangian points and , which lie along the line of centers of the two bodies.

A quick way of estimating the radius of the Hill sphere comes from replacing mass with density in the above equation:

Within the Hill sphere, the region of stability for retrograde orbits at a large distance from the primary is larger than that for prograde orbits.

In practice, the satellite's semi-major axis is compared with the planet's Hill sphere (that is, the sphere of its gravitational influence) .

When the comet passed Jupiter in the late 1960s or early 1970s, it happened to be near its aphelion, and found itself slightly within Jupiter's Hill sphere.

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.

Dust and debris could extend out to Rhea's Hill sphere, but were thought to be denser nearer the moon, with three narrow rings of higher density.

The volume of space within which an object can be said to orbit Jupiter is defined by Jupiter's Hill sphere (also called the Roche sphere).

More precisely, the Hill sphere approximates the gravity sphere of influence of a smaller body in the face of perturbations from a more massive body.

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 search covered nearly the entire Hill sphere, but scattered light from Mars excluded the inner few arcminutes where the satellites Phobos and Deimos reside.

However, the resonance width (the range of semi-axes compatible with the resonance) is very narrow and only a few times larger than Pluto's Hill sphere (gravitational influence).

The Hill sphere for Jupiter is the largest sphere, centered at Jupiter, within which the sum of the three forces is always directed towards Jupiter.

Neptune has the largest Hill sphere in the solar system, owing primarily to its large distance from the Sun; this allows it to retain control of such distant moons.

Most recently, Scott S. Sheppard and David C. Jewitt surveyed the Hill sphere of Mars for irregular satellites.