Trojan (celestial body)

A Trojan is a small celestial body that shares an orbit with a much larger object. Most Trojans are asteroids, but they can also be moons. These objects are a specific type of co-orbital object. This means they follow the same orbital path as a larger primary body. They do not crash into the larger object because they stay in stable positions. These positions are located approximately 60 degrees ahead of or behind the main body. This unique arrangement allows them to remain in a steady orbit for a very long time.

This stability happens because of how gravity works in a three-body system. In space, a star and a planet orbit around a shared center called a barycenter. The star is usually much more massive, so the barycenter is close to the star's center. A small Trojan is subject to the combined gravitational force of both the star and the planet. This force acts through that central barycenter. Because of this combined pull, the tiny Trojan orbits the barycenter with the same orbital period as the planet. This mathematical balance keeps the Trojan in its specific spot along the orbit.

These special spots are known as Lagrangian points, named after the mathematician Joseph-Louis Lagrange. In 1772, Lagrange discovered two constant-pattern solutions to the general three-body problem. These patterns are called collinear and equilateral solutions. In a restricted three-body problem, one mass is considered negligible or very small. This small mass can occupy five specific positions known as Lagrange points. The Trojans specifically occupy the L4 and L5 points. These points are located 60 degrees ahead of and 60 degrees behind the planet.

Humanity first understood these points through math before seeing them in the sky. On February 12, 1906, astronomer Max Wolf discovered the asteroid 588 Achilles. At the same time, Carl Charlier noticed the asteroid was caught in a point of Jupiter. This was the first time Lagrange's theoretical calculations were proven to work in practice. Since then, astronomers have found many other Trojans. Most of these are found near Jupiter, but they also exist near other planets. We have found nine Mars Trojans, 31 Neptune Trojans, and two Uranus Trojans. We have also identified two Earth Trojans and one Saturn Trojan.

The Jupiter Trojans are the most famous and numerous group. They are divided into two distinct camps based on their position. The group located ahead of Jupiter is called the Greek camp. The group located behind Jupiter is called the Trojan camp. These names come from figures in the Trojan War of Greek mythology. By convention, asteroids in the Greek camp are named after Greek characters. Those in the Trojan camp are named after Trojan characters. There are two exceptions to this rule: 624 Hektor and 617 Patroclus.

Jupiter's Trojans are incredibly abundant in our solar system. Astronomers estimate there are more than one million Jupiter Trojans larger than one kilometer. So far, scientists have catalogued more than 7,000 of them. It is estimated that the number of Jovian Trojans is about as large as the number of asteroids in the main asteroid belt. Other planets have fewer, but they are still significant. For example, the large Neptunian Trojans are expected to outnumber the large Jupiter Trojans by an order of magnitude. Even Earth has Trojans, such as 2010 TK7, which was confirmed in 2011.

Trojans can also exist in systems involving moons rather than planets. This happens when a large planet has a moon, and smaller Trojan moons share that moon's orbit. All known Trojan moons are part of the Saturn system. For instance, Telesto and Calypso are Trojans of the moon Tethys. Similarly, Helene and Polydeuces are Trojans of the moon Dione. The stability of these systems depends on the masses of the objects involved. A system is more likely to be long-lived if the star is much larger than the planet, and the planet is much larger than the Trojan.