Lagrange point in the context of 2001 QR322

In celestial mechanics, an orbit is the curved trajectory of an object under the influence of an attracting force. Known as an orbital revolution, examples include the trajectory of a planet around a star, a natural satellite around a planet, or an artificial satellite around an object or position in space such as a planet, moon, asteroid, or Lagrange point. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the center of mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion.

For most situations, orbital motion is adequately approximated by Newtonian mechanics, which explains gravity as a force obeying an inverse-square law. However, Albert Einstein's general theory of relativity, which accounts for gravity as due to curvature of spacetime, with orbits following geodesics, provides a more accurate calculation and understanding of the exact mechanics of orbital motion.

Deep Space Climate Observatory (DSCOVR; formerly known as Triana, unofficially known as GoreSat) is a National Oceanic and Atmospheric Administration (NOAA) space weather, space climate, and Earth observation satellite. It was launched by SpaceX on a Falcon 9 v1.1 launch vehicle on 11 February 2015, from Cape Canaveral. This is NOAA's first operational deep space satellite and became its primary system of warning Earth in the event of solar magnetic storms.

DSCOVR was originally proposed as an Earth observation spacecraft positioned at the Sun-Earth L₁ Lagrange point, providing live video of the sunlit side of the planet through the Internet as well as scientific instruments to study climate change. Political changes in the United States resulted in the mission's cancellation, and in 2001 the spacecraft was placed into storage.

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.

In astrodynamics, orbital station-keeping is keeping a spacecraft at a fixed distance from another spacecraft or celestial body. It requires a series of orbital maneuvers made with thruster burns to keep the active craft in the same orbit as its target. For many low Earth orbit satellites, the effects of non-Keplerian forces, i.e. the deviations of the gravitational force of the Earth from that of a homogeneous sphere, gravitational forces from Sun/Moon, solar radiation pressure and air drag, must be counteracted.For spacecraft in a halo orbit around a Lagrange point, station-keeping is even more fundamental, as such an orbit is unstable; without an active control with thruster burns, the smallest deviation in position or velocity would result in the spacecraft leaving orbit completely.

The giant-impact hypothesis, sometimes called the Theia Impact, is an astrogeology hypothesis for the formation of the Moon first proposed in 1946 by Canadian geologist Reginald Daly. The hypothesis suggests that the Proto-Earth collided with a Mars-sized co-orbital protoplanet likely from the L₄ or L₅ Lagrange points of the Earth's orbit approximately 4.5 billion years ago in the early Hadean eon (about 20 to 100 million years after the Solar System formed), and some of the ejected debris from the impact event later re-accreted to form the Moon. The impactor planet is sometimes called Theia, named after the mythical Greek Titan who was the mother of Selene, the goddess of the Moon.

Analysis of lunar rocks published in a 2016 report suggests that the impact might have been a direct hit, causing a fragmentation and thorough mixing of both parent bodies.

Theia (/ˈθiːə/ THEE-uh) is a hypothesized ancient planet in the early Solar System which, according to the giant-impact hypothesis, collided with the proto-Earth around 4.5 billion years ago, with some of the resulting ejected debris re-coalescing to form the Moon. Collision simulations support the idea that the two large low-shear-velocity provinces in the Earth's lower mantle may be remnants of Theia. Theia is hypothesized to have been about the size of Mars and likely formed at the L₄ or L₅ Lagrange points of the Earth's orbit, although some hypotheses debatably suggested it may have formed in the Outer Solar System and later migrated into the Earth's orbit, and might have provided much of Earth's water.

Early Earth, also known as Proto-Earth, is loosely defined as Earth in the first one billion years — or gigayear (10 y or Ga) — of its geological history, from its initial formation in the young Solar System at about 4.55 billion years ago (Gya), to the end of the Eoarchean era at approximately 3.5 Gya. On the geologic time scale, this comprises all of the Hadean eon and approximately one-third of the Archean eon, starting with the formation of the Earth about 4.6 Gya, and ended at the start of the Paleoarchean era 3.6 Gya.

This period of Earth's history involved the planet's formation from the solar nebula via a process known as accretion, and transition of the Earth's atmosphere from a hydrogen/helium-predominant primary atmosphere collected from the protoplanetary disk to a reductant secondary atmosphere rich in nitrogen, methane and CO₂. This time period included intense impact events as the young Proto-Earth, a protoplanet of about 0.63 Earth masses, began clearing the neighborhood, including the early Moon-forming collision with Theia — a Mars-sized co-orbital planet likely perturbed from the L₄ Lagrange point — around 0.032 Ga after formation of the Solar System, which resulted in a series of magma oceans and episodes of core formation. After formation of the core, meteorites or comets from the Outer Solar System might have delivered water and other volatile compounds to the Earth's mantle, crust and ancient atmosphere in an intense "late veneer" bombardment. As the Earth's planetary surface eventually cooled and formed a stable but evolving crust during the end-Hadean, most of the water vapor condensed out of the atmosphere and precipitated into a superocean that covered nearly all of the Earth's surface, transforming the initially lava planet Earth of the Hadean into an ocean planet at the early Archean, where the earliest known life forms appeared soon afterwards.

An Earth trojan is an asteroid that orbits the Sun in the vicinity of the Earth–Sun Lagrange points L₄ (leading 60°) or L₅ (trailing 60°), thus having an orbit similar to Earth's. Only two Earth trojans have so far been discovered. The name "trojan" was first used in 1906 for the Jupiter trojans, the asteroids that were observed near the Lagrangian points of Jupiter's orbit.

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.

A Uranus trojan is an asteroid that shares an orbit with Uranus and the Sun. Predicted in simulations earlier, two trojans have been discovered in Uranus’s Lagrangian point L₄ (leading Uranus).

(687170) 2011 QF99 was the first body to be classified as such a trojan in 2013, while in 2017 (636872) 2014 YX49 became the second.

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.

The Solar and Heliospheric Observatory (SOHO) is a European Space Agency (ESA) spacecraft built by a European industrial consortium led by Matra Marconi Space (now Airbus Defence and Space) that was launched on a Lockheed Martin Atlas IIAS launch vehicle on 2 December 1995, to study the Sun. It has also discovered more than 5,000 comets. It began normal operations in May 1996. It is a joint project between the European Space Agency (ESA) and NASA. SOHO was part of the International Solar Terrestrial Physics Program (ISTP). Originally planned as a two-year mission, SOHO continues to operate after 29 years in space; the mission has been extended until the end of 2025, subject to review and confirmation by ESA's Science Programme Committee.

In addition to its scientific mission, it is a main source of near-real-time solar data for space weather prediction. Along with Aditya-L1, Wind, Advanced Composition Explorer (ACE), Deep Space Climate Observatory (DSCOVR) and other satellites, SOHO is one of five spacecraft in the vicinity of the Earth–Sun L1 point, a point of gravitational balance located approximately 0.99 astronomical unit (AU) from the Sun and 0.01 AU from the Earth. In addition to its scientific contributions, SOHO is distinguished by being the first three-axis-stabilized spacecraft to use its reaction wheels as a kind of virtual gyroscope; the technique was adopted after an on-board emergency in 1998 that nearly resulted in the loss of the spacecraft.

A distant retrograde orbit (DRO), as most commonly conceived, is a spacecraft orbit around a moon that is highly stable because of its interactions with two Lagrange points (L₁ and L₂) of the planet–moon system.

In more general terms, an object of negligible mass can be in a DRO around the smaller body of any two-body system, such as planet–Sun or exoplanet–star.

A halo orbit is a periodic, non-planar orbit associated with one of the L₁, L₂ or L₃ Lagrange points in the three-body problem of orbital mechanics. Although a Lagrange point is just a point in empty space, its peculiar characteristic is that it can be orbited by a Lissajous orbit or by a halo orbit. These can be thought of as resulting from an interaction between the gravitational pull of the two planetary bodies and the Coriolis and centrifugal force on a spacecraft. Halo orbits exist in any three-body system, e.g., a Sun–Earth–orbiting satellite system or an Earth–Moon–orbiting satellite system. Continuous "families" of both northern and southern halo orbits exist at each Lagrange point. Because halo orbits tend to be unstable, station-keeping using thrusters may be required to keep a satellite on the orbit.

Most satellites in halo orbit serve scientific purposes, for example space telescopes.