Hill sphere

The Hill sphere is a way to understand how gravity works between objects in space. It shows the area around a planet, moon, or star where its gravity is stronger than the gravity of a bigger object it orbits. For example, Earth's Hill sphere is the region where Earth's gravity holds onto its moons and other small objects, instead of the Sun's stronger gravity pulling them away.

This idea was created by an American astronomer named George William Hill, who built on the work of a French astronomer named Édouard Roche. The Hill sphere helps scientists explain why some objects stay close to planets or stars and don’t drift away into space.

One way to think about the Solar System is that it ends at the edge of the Sun's Hill sphere. This edge is set by how the Sun's gravity interacts with the rest of the galaxy. For Earth, its Hill sphere stretches from one special point called L₁ to another called L₂, which are balance points between Earth and the Sun. Beyond these points, objects can be pulled away by the Sun’s gravity instead of staying with Earth.

Definition

The Hill sphere is a way to understand how far a planet or moon can pull objects toward itself without another, larger object pulling them away. It shows the area around a smaller object where its gravity is stronger than that of a bigger, nearby object, like the Sun or a planet.

In a solar system, every object pulls on every other object with gravity. When only two objects are considered, like the Sun and a planet, their movements can be calculated exactly. But when three or more objects are involved, it becomes very complex. The Hill sphere helps us estimate how much influence a smaller object has, especially when it is much lighter than the bigger object it orbits. This idea is useful for understanding the orbits of moons and other space objects.

Solar System semi-major axis eccentricity pericenter true anomaly periapsis apoapsis perigee apogee

Example and derivation

The Hill sphere is a way to figure out how far a planet or moon can keep other objects close to it, even when there is a bigger object nearby, like the Sun for Earth or Earth for the Moon. For example, Earth orbits the Sun, but the Moon stays close to Earth because it is inside Earth's Hill sphere. The Sun's Hill sphere is much larger because the Sun is so massive.

The formula to find the size of the Hill sphere looks at how gravity and the spin of the bigger object affect a small object. It helps us understand where small moons or satellites can stay safely without being pulled away by the bigger object.

Regions of stability

The Hill sphere is just an estimate and things like radiation pressure or the Yarkovsky effect can push objects out of it over time. For this to work well, the object (like a moon) should be small so its gravity doesn’t affect things much.

Far away from a big object, orbits that go backward stay steady over a larger area than orbits that go forward. People once thought this explained why Jupiter has more backward moons, but Saturn has a mix of both kinds, so it’s more complex. In a system with two planets, they need to be far enough apart—more than 2√3 apart—to stay stable. With three or more planets, if they’re too close (less than ten times apart), things get unstable because the extra planet messes things up.

Further examples

A Hill sphere can sometimes be so tiny that it's impossible to stay in orbit around an object. For example, an astronaut could not have orbited a very heavy spacecraft 300 km above Earth because its Hill sphere would have been only about the size of a small chair—far too small to hold the spacecraft.

In our Solar System, the planet with the largest Hill sphere is Neptune, stretching about 116 million km. If a mysterious object called Planet Nine exists, its Hill sphere could be even larger—over ten times Neptune’s!

Even small objects like asteroids have Hill spheres, though they shrink quickly with less mass. For instance, a big asteroid named 1 Ceres has a Hill sphere reaching up to 220,000 km.

Some planets outside our Solar System, called “hot Jupiters,” also have large Hill spheres. One such planet, HD 209458 b, has a Hill sphere about eight times wider than the planet itself! Even very small planets far close to their stars still have Hill spheres much larger than the planets.

Hill spheres for the Solar System

The following table and logarithmic plot show the size of the Hill spheres of some objects in our Solar System. The numbers were calculated using a special formula and data from the JPL DE405 ephemeris and the NASA Solar System Exploration website.