Lagrangian point in the context of 2010 TK7

In astronomy, a trojan is a small celestial body (mostly asteroids) that shares the orbit of a larger body, remaining in a stable orbit approximately 60° ahead of or behind the main body near one of its Lagrangian points L₄ and L₅. Trojans can share the orbits of planets or of large moons.

Trojans are one type of co-orbital object. In this arrangement, a star and a planet orbit about their common barycenter, which is close to the center of the star because it is usually much more massive than the orbiting planet. In turn, a much smaller mass than both the star and the planet, located at one of the Lagrangian points of the star–planet system, is subject to a combined gravitational force that acts through this barycenter. Hence the smallest object orbits around the barycenter with the same orbital period as the planet, and the arrangement can remain stable over time.

The Jupiter trojans, commonly called trojan asteroids or simply trojans, are a large group of asteroids that share the planet Jupiter's orbit around the Sun. Relative to Jupiter, each trojan librates around one of Jupiter's stable Lagrange points: either L₄, existing 60° ahead of the planet in its orbit, or L₅, 60° behind. Jupiter trojans are distributed in two elongated, curved regions around these Lagrangian points with an average semi-major axis of about 5.2 AU.

The first Jupiter trojan discovered, 588 Achilles, was spotted in 1906 by German astronomer Max Wolf. More than 15,300 Jupiter trojans have been found as of October 2025. By convention, they are each named from Greek mythology after a figure of the Trojan War, hence the name "trojan". The total number of Jupiter trojans larger than 1 km in diameter is believed to be about 1 million, approximately equal to the number of asteroids larger than 1 km in the asteroid belt. Like main-belt asteroids, Jupiter trojans form families.

In lunar astronomy, libration is the cyclic variation in the apparent position of the Moon that is perceived by observers on the Earth and caused by changes between the orbital and rotational planes of the moon. It causes an observer to see slightly different hemispheres of the surface at different times. It is similar in both cause and effect to the changes in the Moon's apparent size because of changes in distance. It is caused by three mechanisms detailed below, two of which cause a relatively tiny physical libration via tidal forces exerted by the Earth. Such true librations are known as well for other moons with locked rotation.

The quite different phenomenon of a trojan asteroid's movement has been called Trojan libration, and Trojan libration point means Lagrangian point.

The Herschel Space Observatory was a space observatory built and operated by the European Space Agency (ESA). It was active from 2009 to 2013, and was the largest infrared telescope ever launched until the launch of the James Webb Space Telescope in 2021. Herschel carries a 3.5-metre (11.5 ft) mirror and instruments sensitive to the far infrared and submillimetre wavebands (55–672 μm). Herschel was the fourth and final cornerstone mission in the Horizon 2000 programme, following SOHO, Cluster II, XMM-Newton and Rosetta.

The observatory was carried into orbit by an Ariane 5 in May 2009, reaching the second Lagrangian point (L2) of the Earth–Sun system, 1,500,000 kilometres (930,000 mi) from Earth, about two months later. Herschel is named after Sir William Herschel, the discoverer of the infrared spectrum and planet Uranus, and his sister and collaborator Caroline Herschel.

The Mars trojans are a group of trojan objects that share the orbit of the planet Mars around the Sun. They can be found around the two Lagrangian points 60° ahead of and behind Mars. The origin of the Mars trojans is not well understood. One hypothesis suggests that they were primordial objects left over from the formation of Mars that were captured in its Lagrangian points as the Solar System was forming. However, spectral studies of the Mars trojans indicate this may not be the case. Another explanation involves asteroids chaotically wandering into the Mars Lagrangian points later in the Solar System's formation. This is also questionable considering the short dynamical lifetimes of these objects. The spectra of Eureka and two other Mars trojans indicates an olivine-rich composition. Since olivine-rich objects are rare in the asteroid belt it has been suggested that some of the Mars trojans are captured debris from a large orbit-altering impact on Mars when it encountered a planetary embryo.

Presently, this group contains 17 asteroids confirmed to be stable Mars trojans by long-term numerical simulations but only nine of them are accepted by the Minor Planet Center.

Neptune trojans are bodies that orbit the Sun near one of the stable Lagrangian points of Neptune, similar to the trojans of other planets. They therefore have approximately the same orbital period as Neptune and follow roughly the same orbital path. Thirty-one Neptune trojans are currently known, of which 27 orbit near the Sun–Neptune L₄ Lagrangian point 60° ahead of Neptune and four orbit near Neptune's L₅ region 60° behind Neptune. The Neptune trojans are termed 'trojans' by analogy with the Jupiter trojans.

The discovery of 2005 TN53 in a high-inclination (>25°) orbit was significant, because it suggested a "thick" cloud of trojans (Jupiter trojans have inclinations up to 40°), which is indicative of freeze-in capture instead of in situ or collisional formation. It is suspected that large (radius ≈ 100 km) Neptune trojans could outnumber Jupiter trojans of that size by an order of magnitude.

In astronomy, a co-orbital configuration is a configuration of two or more astronomical objects (such as asteroids, moons, or planets) orbiting at the same, or very similar, distance from their primary; i.e., they are in a 1:1 mean-motion resonance. (or 1:-1 if orbiting in opposite directions).

There are several classes of co-orbital objects, depending on their point of libration. The most common and best-known class is the trojan, which librates around one of the two stable Lagrangian points (Trojan points), L₄ and L₅, 60° ahead of and behind the larger body respectively. Another class is the horseshoe orbit, in which objects librate around 180° from the larger body. Objects librating around 0° are called quasi-satellites.

This is a list of active space probes which have escaped Earth orbit. It includes lunar space probes, but does not include space probes orbiting at the Sun–Earth Lagrangian points (for these, see List of objects at Lagrangian points). A craft is deemed "active" if it is still able to transmit usable data to Earth (regardless of whether it can receive commands).

The craft are further grouped by mission status – "en-route", "mission in progress" or "mission complete" – based on their primary mission. For example, though Voyager 1 is still contactable en-route to the Oort Cloud and has exited the Solar System, it is listed as "mission complete" because its primary task of studying Jupiter and Saturn has been accomplished. Once a probe has reached its first primary target, it is no longer listed as "en route" regardless of whether further travel is involved.

Chang'e 4 (/tʃɑːŋˈə/; Chinese: 嫦娥四号; pinyin: Cháng'é Sìhào; lit. 'Chang'e No. 4') is a robotic spacecraft mission in the Chinese Lunar Exploration Program of the CNSA. It made a soft landing on the far side of the Moon, the first spacecraft to do so, on 3 January 2019.

A communication relay satellite, Queqiao, was first launched to a halo orbit near the Earth–Moon L₂ point in May 2018. The robotic lander and Yutu-2 (Chinese: 玉兔二号; pinyin: Yùtù Èrhào; lit. 'Jade Rabbit No. 2') rover were launched on 7 December 2018 and entered lunar orbit on 12 December 2018, before landing on the Moon's far side. On 15 January it was announced that seeds had sprouted in the lunar lander's biological experiment, the first plants to sprout on the Moon. The mission is the follow-up to Chang'e 3, the first Chinese landing on the Moon.

This is a list of Jupiter trojans that lie in the Greek camp, an elongated curved region around the leading Lagrangian point (L₄), 60° ahead of Jupiter in its orbit.

All the asteroids at Jupiter's L₄ point have names corresponding to participants on the Greek side of the Trojan War, except for 624 Hektor, which was named before this naming convention was instituted. Correspondingly, 617 Patroclus is a Greek-named asteroid at the "Trojan" (L₅) Lagrangian point. In 2018, at its 30th General Assembly in Vienna, the International Astronomical Union amended this naming convention, allowing Jupiter trojans with an H larger than 12 (that is, a mean diameter smaller than approximately 22 kilometers, for an assumed albedo of 0.057) to be named after Olympic athletes, as the number of known Jupiter trojans, currently more than 10,000, far exceeds the number of available names of heroes from the Trojan War in Greek mythology.

This is a list of Jupiter trojans that lie in the Trojan camp, an elongated curved region around the trailing L₅ Lagrangian point, 60° behind Jupiter in its orbit.

All the asteroids at the trailing L₅ point have names corresponding to participants on the Trojan side of the Trojan War, except for 617 Patroclus, which was named before this naming convention was instituted. Correspondingly, 624 Hektor is a Trojan-named asteroid at the "Greek" (L₄) Lagrangian point. In 2018, at its 30th General Assembly in Vienna, the International Astronomical Union amended this naming convention, allowing for Jupiter trojans with H larger than 12 (that is, a mean diameter smaller than approximately 22 kilometers, for an assumed albedo of 0.057) to be named after Olympic athletes, as the number of known Jupiter trojans, currently more than 10,000, far exceeds the number of available names of heroes from the Trojan War in Greek mythology.

In astronomy, the Roche lobe is the region around a star in a binary system within which orbiting material is gravitationally bound to that star. It is an approximately teardrop-shaped region bounded by a critical gravitational equipotential, with the apex of the teardrop pointing towards the other star (the apex is at the L₁ Lagrangian point of the system).

The Roche lobe is different from the Roche sphere, which approximates the gravitational sphere of influence of one astronomical body in the face of perturbations from a more massive body around which it orbits. It is also different from the Roche limit, which is the distance at which an object held together only by gravity begins to break up due to tidal forces. The Roche lobe, Roche limit, and Roche sphere are named after the French astronomer Édouard Roche.

(101429) 1998 VF₃₁ (provisional designation 1998 VF₃₁) is a sub-kilometer asteroid that orbits near Mars's L₅ Lagrangian point, on average trailing 60° behind it. Its orbit is highly stable, and was originally thought to be spectroscopically similar to 5261 Eureka, suggesting they may both be primordial Martian asteroids.

Spectroscopic observations through 2007 indicate that it has a large proportion of metal and achondrites on its surface (either with or without a mesosiderite contribution); which could also indicate that the surface regolith has undergone space weathering. These observations also reveal differences in the spectra with 5261 Eureka, suggesting they may not be related to each other after all.

(687170) 2011 QF₉₉ is a minor planet from the outer Solar System and the first known Uranus trojan to be discovered. It measures approximately 60 kilometers (37 miles) in diameter, assuming an albedo of 0.05. It was first observed 29 August 2011 during a deep survey of trans-Neptunian objects conducted with the Canada–France–Hawaii Telescope, but its identification as a Uranian trojan was not announced until 2013.

2011 QF₉₉ temporarily orbits near Uranus's L₄ Lagrangian point (leading Uranus). It will continue to librate around L₄ for at least 70,000 years and will remain a Uranus co-orbital for up to three million years. 2011 QF₉₉ is thus a temporary Uranus trojan—a centaur captured some time ago.

(612243) 2001 QR₃₂₂, prov. designation: 2001 QR₃₂₂, is a minor planet and the first Neptune trojan discovered, by American astronomer Marc Buie of the Deep Ecliptic Survey at Cerro Tololo Observatory in Chile on 21 August 2001. It orbits ahead of Neptune at its L₄ Lagrangian point and measures approximately 132 kilometers (82 miles) in diameter.

Other Neptune trojans have been discovered since. A study by American astronomers Scott Sheppard and Chad Trujillo from the Carnegie Institution suggests that Neptune could possibly have twenty times more trojans than Jupiter.