Perturbation (astronomy) in the context of Mean longitude

Neptune is the eighth and farthest known planet orbiting the Sun. It is the fourth-largest planet in the Solar System by diameter, the third-most-massive planet, and the densest giant planet. It is 17 times the mass of Earth. Compared to Uranus, its neighbouring ice giant, Neptune is slightly smaller, but more massive and denser. Being composed primarily of gases and liquids, it has no well-defined solid surface. Neptune orbits the Sun once every 164.8 years at an orbital distance of 30.1 astronomical units (4.5 billion kilometres; 2.8 billion miles). It is named after the Roman god of the sea and has the astronomical symbol , representing Neptune's trident.

Neptune is not visible to the unaided eye and is the only planet in the Solar System that was not initially observed by direct empirical observation. Rather, unexpected changes in the orbit of Uranus led Alexis Bouvard to hypothesise that its orbit was subject to gravitational perturbation by an unknown planet. After Bouvard's death, the position of Neptune was mathematically predicted from his observations, independently, by John Couch Adams and Urbain Le Verrier. Neptune was subsequently directly observed with a telescope on 23 September 1846 by Johann Gottfried Galle within a degree of the position predicted by Le Verrier. Its largest moon, Triton, was discovered shortly thereafter, though none of the planet's remaining moons were located telescopically until the 20th century.

A meteor shower is a celestial event in which a number of meteors are observed to radiate, or originate, from one point in the night sky. These meteors are caused by streams of cosmic debris called meteoroids entering Earth's atmosphere at extremely high speeds on parallel trajectories. Most meteors are smaller than a grain of sand, so almost all of them disintegrate and never hit the Earth's surface. Very intense or unusual meteor showers are known as meteor outbursts and meteor storms, which produce at least 1,000 meteors an hour, most notably from the Leonids. The Meteor Data Centre lists over 900 suspected meteor showers of which about 100 are well established. Several organizations point to viewing opportunities on the Internet. NASA maintains a daily map of active meteor showers.

Historically, meteor showers were regarded as an atmospheric phenomenon. In 1794, Ernst Chladni proposed that meteors originated in outer space. The Great Meteor Storm of 1833 led Denison Olmsted to show it arrived as a cloud of space dust, with the streaks forming a radiant point in the direction of the constellation of Leo. In 1866, Giovanni Schiaparelli proposed that meteors came from comets when he showed that the Leonid meteor shower shared the same orbit as the Comet Tempel. Astronomers learned to compute the orbits of these clouds of cometary dust, including how they are perturbed by planetary gravity. Fred Whipple in 1951 proposed that comets are "dirty snowballs" that shed meteoritic debris as their volatiles are ablated by solar energy in the inner Solar System.

The scattered disc (or scattered disk) is a distant circumstellar disc in the Solar System that is sparsely populated by icy small Solar System bodies, which are a subset of the broader family of trans-Neptunian objects. The scattered-disc objects (SDOs) have orbital eccentricities ranging as high as 0.8, inclinations as high as 40°, and perihelia greater than 30 astronomical units (4.5×10 km; 2.8×10 mi). These extreme orbits are thought to be the result of gravitational "scattering" by the gas giants, and the objects continue to be subject to perturbation by the planet Neptune.

Although the closest scattered-disc objects approach the Sun at about 30–35 AU, their orbits can extend well beyond 100 AU. This makes scattered disc objects among the coldest and most distant known objects in the Solar System. The innermost portion of the scattered disc overlaps with a torus-shaped region of orbiting objects traditionally called the Kuiper belt, but its outer limits reach much farther away from the Sun and farther above and below the ecliptic than the Kuiper belt proper.

This is a list of parabolic and hyperbolic comets in the Solar System. Many of these comets may come from the Oort cloud, or perhaps even have interstellar origin. The Oort Cloud is not gravitationally attracted enough to the Sun to form into a fairly thin disk, like the inner Solar System. Thus, comets originating from the Oort Cloud can come from roughly any orientation (inclination to the ecliptic), and many even have a retrograde orbit. By definition, a hyperbolic orbit means that the comet will only travel through the Solar System once, with the Sun acting as a gravitational slingshot, sending the comet hurtling out of the Solar System entirely unless its eccentricity is otherwise changed. Comets orbiting in this way still originate from the Solar System, however. Typically comets in the Oort Cloud are thought to have roughly circular orbits around the Sun, but their orbital velocity is so slow that they may easily be perturbed by passing stars and the galactic tide. Astronomers have been discovering weakly hyperbolic comets that were perturbed out of the Oort Cloud since the mid-1800s.

Prior to finding a well-determined orbit for comets, the JPL Small-Body Database and the Minor Planet Center list comet orbits as having an assumed eccentricity of 1.0. (This is the eccentricity of a parabolic trajectory; hyperbolics will be those with eccentricity greater than 1.0.) In the list below, a number of comets discovered by the SOHO space telescope have assumed eccentricities of exactly 1.0, because most orbits are based on only an insufficient observation arc of several hours or minutes. The SOHO satellite observes the corona of the Sun and the area around it, and as a result often observes sungrazing comets, including the Kreutz sungrazers.

A protoplanet or planetary embryo is an astronomical body originated within a protoplanetary disk that has undergone internal melting to produce a differentiated interior.

Protoplanets are thought to form out of kilometer-sized planetesimals that gravitationally perturb each other's orbits and collide, gradually coalescing into larger bodies through a process known as "runaway growth". Once accumulated enough mass, protoplanets will begin to assume a spherical shape due to hydrostatic equilibrium and become dwarf planets, those of which that subsequently succeed in dominating their own orbit will become planets proper.

The celestial equator is the great circle of the imaginary celestial sphere on the same plane as the equator of Earth. By extension, it is also a plane of reference in the equatorial coordinate system. Due to the Earth's axial tilt, the celestial equator is currently inclined by about 23.44° with respect to the ecliptic (the plane of Earth's orbit), but has varied from about 22.0° to 24.5° over the past 5 million years due to Milankovitch cycles and perturbation from other planets.

An observer standing on the Earth's equator visualizes the celestial equator as a semicircle passing through the zenith, the point directly overhead. As the observer moves north (or south), the celestial equator tilts towards the opposite horizon. The celestial equator is defined to be infinitely distant (since it is on the celestial sphere); thus, the ends of the semicircle always intersect the horizon due east and due west, regardless of the observer's position on the Earth. At the poles, the celestial equator coincides with the astronomical horizon. At all latitudes, the celestial equator is a uniform arc or circle because the observer is only finitely far from the plane of the celestial equator, but infinitely far from the celestial equator itself.

A solar equinox is a moment in time when the Sun appears directly above the equator, rather than to its north or south. On the day of the equinox, the Sun appears to rise directly east and set directly west. This occurs twice each year, around 20 March and 23 September.

An equinox is equivalently defined as the time when the plane of Earth's equator passes through the geometric center of the Sun's disk. This is also the moment when Earth's rotation axis is directly perpendicular to the Sun-Earth line, tilting neither toward nor away from the Sun. In modern times, since the Moon (and to a lesser extent the planets) causes Earth's orbit to vary slightly from a perfect ellipse, the equinox is officially defined by the Sun's more regular ecliptic longitude rather than by its declination. The instants of the equinoxes are currently defined to be when the apparent geocentric longitude of the Sun is 0° and 180°.

In astronomy, an epoch or reference epoch is a moment in time used as a reference point for some time-varying astronomical quantity. It is useful for the celestial coordinates or orbital elements of a celestial body, as they are subject to perturbations and vary with time. These time-varying astronomical quantities might include, for example, the mean longitude or mean anomaly of a body, the node of its orbit relative to a reference plane, the direction of the apogee or aphelion of its orbit, or the size of the major axis of its orbit.

The main use of astronomical quantities specified in this way is to calculate other relevant parameters of motion, in order to predict future positions and velocities. The applied tools of the disciplines of celestial mechanics or its subfield orbital mechanics (for predicting orbital paths and positions for bodies in motion under the gravitational effects of other bodies) can be used to generate an ephemeris, a table of values giving the positions and velocities of astronomical objects in the sky at a given time or times.

In astronomy, an equinox is either of two places on the celestial sphere at which the ecliptic intersects the celestial equator. Although there are two such intersections, the equinox associated with the Sun's ascending node is used as the conventional origin of celestial coordinate systems and referred to simply as "the equinox". In contrast to the common usage of spring/vernal and autumnal equinoxes, the celestial coordinate system equinox is a direction in space rather than a moment in time.

In a cycle of about 25,800 years, the equinox moves westward with respect to the celestial sphere because of perturbing forces; therefore, in order to define a coordinate system, it is necessary to specify the date for which the equinox is chosen. This date should not be confused with the epoch. Astronomical objects show real movements such as orbital and proper motions, and the epoch defines the date for which the position of an object applies. Therefore, a complete specification of the coordinates for an astronomical object requires both the date of the equinox and of the epoch.

In celestial mechanics, a Kepler orbit (or Keplerian orbit, named after the German astronomer Johannes Kepler) is the motion of one body relative to another, as an ellipse, parabola, or hyperbola, which forms a two-dimensional orbital plane in three-dimensional space. A Kepler orbit can also form a straight line. It considers only the point-like gravitational attraction of two bodies, neglecting perturbations due to gravitational interactions with other objects, atmospheric drag, solar radiation pressure, a non-spherical central body, and so on. It is thus said to be a solution of a special case of the two-body problem, known as the Kepler problem. As a theory in classical mechanics, it also does not take into account the effects of general relativity. Keplerian orbits can be parametrized into six orbital elements in various ways.

In most applications, there is a large central body, the center of mass of which is assumed to be the center of mass of the entire system. By decomposition, the orbits of two objects of similar mass can be described as Kepler orbits around their common center of mass, their barycenter.

A sednoid is a trans-Neptunian object with a large semi-major axis, a distant perihelion and a highly eccentric orbit, similar to that of the dwarf planet Sedna. The consensus among astronomers is that there are only four objects that are known from this population: Sedna, 2012 VP113, 541132 Leleākūhonua, and 2023 KQ14. All four have perihelia greater than 60 AU. The sednoids are also classified as detached objects, since their perihelion distances are large enough that Neptune's gravity does not strongly influence their orbits. Some astronomers consider the sednoids to be Inner Oort Cloud (IOC) objects. The inner Oort cloud, or Hills cloud, lies at 1,000–10,000 AU from the Sun.

One attempt at a precise definition of sednoids is any body with a perihelion greater than 50 AU and a semi-major axis greater than 150 AU.However, this definition applies to the objects 2013 SY99, 2020 MQ53, and 2021 RR205 which have perihelia beyond 50 AU and semi-major axes over 700 AU. Despite this, astronomers do not classify these objects as sednoids because their orbits still experience gradual orbital migration as a result of perturbations by galactic tides and Neptune's weak gravitational influence.

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.

Lunar theory attempts to account for the motions of the Moon. There are many small variations (or perturbations) in the Moon's motion, and many attempts have been made to account for them. After centuries of being problematic, lunar motion can now be modeled to a very high degree of accuracy (see section Modern developments).

Namaka (full designation (136108) Haumea II) is the smaller, inner moon of the trans-Neptunian dwarf planet Haumea. Discovered by Michael E. Brown and the Keck Observatory adaptive optics team in the fall of 2005, it is named after Nāmaka, a water spirit and one of the daughters of Haumea in Hawaiian mythology. Namaka follows a highly elliptical orbit that is highly tilted by roughly 13 degrees with respect to Haumea's equator. Namaka is heavily perturbed by both the gravitational influence of Haumea's larger, outer moon Hiʻiaka and the variable gravitational field of Haumea's elongated shape.

With a diameter of around 150 km (93 mi), Namaka is predicted to have an irregular shape and a chaotic rotation. It has a reflective surface made of fresh water ice, similar to that of Haumea and Hiʻiaka. Like Hiʻiaka, Namaka is believed to be a fragment of Haumea that was ejected in the aftermath of a giant impact 4.4 billion years ago.

Weywot (formal designation (50000) Quaoar I) is the only known moon of the trans-Neptunian dwarf planet Quaoar. It was discovered by Michael Brown and Terry-Ann Suer using images taken by the Hubble Space Telescope on 14 February 2006. It is named after the Tongva sky god and son of Quaoar. Weywot is about 165 km (103 mi) in diameter and orbits Quaoar every 12.4 days at an average distance of 13,300 km (8,300 mi). Weywot is thought to play a role in maintaining Quaoar's outer ring by gravitationally influencing it in an orbital resonance.

Detached objects are a dynamical class of minor planets in the outer reaches of the Solar System and belong to the broader family of trans-Neptunian objects (TNOs). These objects have orbits whose points of closest approach to the Sun (perihelion) are sufficiently distant from the gravitational influence of Neptune that they are only moderately affected by Neptune and the other known planets: This makes them appear to be "detached" from the rest of the Solar System, except for their attraction to the Sun.

In this way, detached objects differ substantially from most other known TNOs, which form a loosely defined set of populations that have been perturbed to varying degrees onto their current orbit by gravitational encounters with the giant planets, predominantly Neptune. Detached objects have larger perihelia than these other TNO populations, including the objects in orbital resonance with Neptune, such as Pluto, the classical Kuiper belt objects in non-resonant orbits such as Makemake, and the scattered disk objects like Eris.

PSR B1257+12 c, alternatively designated PSR B1257+12 B, also named Poltergeist, is an extrasolar planet approximately 2,300 light-years away in the constellation of Virgo. It was one of the first planets ever discovered outside the Solar System, and is one of three pulsar planets known to be orbiting the pulsar Lich.

Over four times as massive as the Earth, it circles the primary at a distance of 0.36 AU with an orbital period of approximately 66 days. Because it and Phobetor have very similar masses and orbit close to each other, they were expected to cause measurable perturbations in each other's orbits. Detecting such perturbations confirmed that the planets were real. Accurate masses of the two planets, as well as their inclinations, were calculated from how much the planets perturb each other.

Orbital elements are the parameters required to uniquely identify orbit. In celestial mechanics these elements are considered in two-body systems using a Kepler orbit. There are many different ways to mathematically describe the same orbit, but certain schemes are commonly used in astronomy and orbital mechanics.

A real orbit and its elements change over time due to gravitational perturbations by other objects and the effects of general relativity. A Kepler orbit is an idealized, mathematical approximation of the orbit at a particular time.