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The **argument of periapsis** (also called **argument of perifocus** or **argument of pericenter**), symbolized as *ω*, is one of the orbital elements of an orbiting body. Parametrically, *ω* is the angle from the body's ascending node to its periapsis, measured in the direction of motion.

For specific types of orbits, terms such as **argument of perihelion** (for heliocentric orbits), **argument of perigee** (for geocentric orbits), **argument of periastron** (for orbits around stars), and so on, may be used (see apsis for more information).

An argument of periapsis of 0° means that the orbiting body will be at its closest approach to the central body at the same moment that it crosses the plane of reference from South to North. An argument of periapsis of 90° means that the orbiting body will reach periapsis at its northmost distance from the plane of reference.

Adding the argument of periapsis to the longitude of the ascending node gives the longitude of the periapsis. However, especially in discussions of binary stars and exoplanets, the terms "longitude of periapsis" or "longitude of periastron" are often used synonymously with "argument of periapsis".

In astrodynamics the **argument of periapsis***ω* can be calculated as follows:

- If
*e*< 0 then_{z}*ω*→ 2π −*ω*.

- If

where:

**n**is a vector pointing towards the ascending node (i.e. the*z*-component of**n**is zero),**e**is the eccentricity vector (a vector pointing towards the periapsis).

In the case of equatorial orbits (which have no ascending node), the argument is strictly undefined. However, if the convention of setting the longitude of the ascending node Ω to 0 is followed, then the value of *ω* follows from the two-dimensional case:

- If the orbit is clockwise (i.e. (
**r**×**v**)_{z}< 0) then*ω*→ 2π −*ω*.

- If the orbit is clockwise (i.e. (

where:

*e*and_{x}*e*are the_{y}*x*- and*y*-components of the eccentricity vector**e**.

In the case of circular orbits it is often assumed that the periapsis is placed at the ascending node and therefore *ω* = 0. However, in the professional exoplanet community, *ω* = 90° is more often assumed for circular orbits, which has the advantage that the time of a planet's inferior conjunction (which would be the time the planet would transit if the geometry were favorable) is equal to the time of its periastron.^{ [1] }^{ [2] }^{ [3] }

**Orbital elements** are the parameters required to uniquely identify a specific 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, each consisting of a set of six parameters, are commonly used in astronomy and orbital mechanics.

The **longitude of the ascending node** is one of the orbital elements used to specify the orbit of an object in space. It is the angle from a specified reference direction, called the *origin of longitude*, to the direction of the ascending node, as measured in a specified reference plane. The ascending node is the point where the orbit of the object passes through the plane of reference, as seen in the adjacent image. Commonly used reference planes and origins of longitude include:

In celestial mechanics, **true anomaly** is an angular parameter that defines the position of a body moving along a Keplerian orbit. It is the angle between the direction of periapsis and the current position of the body, as seen from the main focus of the ellipse.

In celestial mechanics, the **longitude of the periapsis**, also called **longitude of the pericenter**, of an orbiting body is the longitude at which the periapsis would occur if the body's orbit inclination were zero. It is usually denoted *ϖ*.

In celestial mechanics **true longitude** is the ecliptic longitude at which an orbiting body could actually be found if its inclination were zero. Together with the inclination and the ascending node, the true longitude can tell us the precise direction from the central object at which the body would be located at a particular time.

**Orbital inclination change** is an orbital maneuver aimed at changing the inclination of an orbiting body's orbit. This maneuver is also known as an **orbital plane change** as the plane of the orbit is tipped. This maneuver requires a change in the orbital velocity vector (delta-v) at the orbital nodes.

In astrodynamics, the **orbital eccentricity** of an astronomical object is a dimensionless parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptic orbit, 1 is a parabolic escape orbit, and greater than 1 is a hyperbola. The term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section. It is normally used for the isolated two-body problem, but extensions exist for objects following a rosette orbit through the Galaxy.

**Spacecraft flight dynamics** is the application of mechanical dynamics to model how the external forces acting on a space vehicle or spacecraft determine its flight path. These forces are primarily of three types: propulsive force provided by the vehicle's engines; gravitational force exerted by the Earth and other celestial bodies; and aerodynamic lift and drag.

In astronomy, a **resonant trans-Neptunian object** is a trans-Neptunian object (TNO) in mean-motion orbital resonance with Neptune. The orbital periods of the resonant objects are in a simple integer relations with the period of Neptune, e.g. 1:2, 2:3, etc. Resonant TNOs can be either part of the main Kuiper belt population, or the more distant scattered disc population.

In celestial mechanics, the **Kozai mechanism** is a dynamical phenomenon affecting the orbit of a binary system perturbed by a distant third body under certain conditions. It is also known as the **von Zeipel-Kozai-Lidov**, **Lidov–Kozai mechanism**, **Kozai–Lidov mechanism**, or some combination of Kozai, Lidov–Kozai, Kozai–Lidov or von Zeipel-Kozai-Lidov effect, oscillations, cycles, or resonance. This effect causes the orbit's argument of pericenter to oscillate about a constant value, which in turn leads to a periodic exchange between its eccentricity and inclination. The process occurs on timescales much longer than the orbital periods. It can drive an initially near-circular orbit to arbitrarily high eccentricity, and *flip* an initially moderately inclined orbit between a prograde and a retrograde motion.

The **perifocal coordinate** (**PQW**) **system** is a frame of reference for an orbit. The frame is centered at the focus of the orbit, i.e. the celestial body about which the orbit is centered. The unit vectors and lie in the plane of the orbit. is directed towards the periapsis of the orbit and has a true anomaly of 90 degrees past the periapsis. The third unit vector is the angular momentum vector and is directed orthogonal to the orbital plane such that:

**Orbit determination** is the estimation of orbits of objects such as moons, planets, and spacecraft. One major application is to allow tracking newly observed asteroids and verify that they have not been previously discovered. The basic methods were discovered in the 17th century and have been continuously refined.

In astronomy, a **co-orbital configuration** is a configuration of two or more astronomical objects orbiting at the same, or very similar, distance from their primary, i.e. they are in a 1:1 mean-motion resonance..

In celestial mechanics, a **Kepler orbit** 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 celestial mechanics, **apsidal precession** is the precession of the line connecting the apsides of an astronomical body's orbit. The apsides are the orbital points closest (periapsis) and farthest (apoapsis) from its primary body. The apsidal precession is the first time derivative of the argument of periapsis, one of the six main orbital elements of an orbit. Apsidal precession is considered positive when the orbit's axis rotates in the same direction as the orbital motion. An **apsidal period** is the time interval required for an orbit to precess through 360°.

**HIP 79431 b** is an extrasolar planet discovered by the W. M. Keck Observatory in 2010. The planet is found in an M type dwarf star catalogued as HIP 79431 and is located within the Scorpius constellation approximately 47 light years away from the Earth. Its orbital period lasts about 111.7 days and has an orbital eccentricity of 0.29. The planet is the 6th giant planet to be detected in the Doppler surveys of M dwarfs and is considered to be one of the most massive planets found around M dwarf stars.

**Nodal precession** is the precession of the orbital plane of a satellite around the rotational axis of an astronomical body such as Earth. This precession is due to the non-spherical nature of a rotating body, which creates a non-uniform gravitational field. The following discussion relates to low Earth orbit of artificial satellites, which have no measurable effect on the motion of Earth. The nodal precession of more massive, natural satellites like the Moon is more complex.

A **sednoid** is a trans-Neptunian object with a perihelion well beyond the Kuiper cliff at 47.8 AU. Only four objects are known from this population: 90377 Sedna, 2012 VP113, 541132 Leleākūhonua (2015 TG_{387}), and 2021 RR205, but it is suspected that there are many more. All four have perihelia greater than 55 AU. These objects lie outside an apparently nearly empty gap in the Solar System and have no significant interaction with the planets. They are usually grouped with the detached objects. Some astronomers, such as Scott Sheppard, consider the sednoids to be **inner Oort cloud objects** (OCOs), though the inner Oort cloud, or Hills cloud, was originally predicted to lie beyond 2,000 AU, beyond the aphelia of the four known sednoids.

**Planet Nine** is a hypothetical ninth planet in the outer region of the Solar System. Its gravitational effects could explain the peculiar clustering of orbits for a group of extreme trans-Neptunian objects (ETNOs), bodies beyond Neptune that orbit the Sun at distances averaging more than 250 times that of the Earth. These ETNOs tend to make their closest approaches to the Sun in one sector, and their orbits are similarly tilted. These alignments suggest that an undiscovered planet may be shepherding the orbits of the most distant known Solar System objects. Nonetheless, some astronomers question this conclusion and instead assert that the clustering of the ETNOs' orbits is due to observational biases, resulting from the difficulty of discovering and tracking these objects during much of the year.

The hypothetical Planet Nine would modify the orbits of extreme trans-Neptunian objects via a combination of effects. On very long timescales exchanges of angular momentum with Planet Nine cause the perihelia of anti-aligned objects to rise until their precession reverses direction, maintaining their anti-alignment, and later fall, returning them to their original orbits. On shorter timescales mean-motion resonances with Planet Nine provides phase protection, which stabilizes their orbits by slightly altering the objects' semi-major axes, keeping their orbits synchronized with Planet Nine's and preventing close approaches. The inclination of Planet Nine's orbit weakens this protection, resulting in a chaotic variation of semi-major axes as objects hop between resonances. The orbital poles of the objects circle that of the Solar System's Laplace plane, which at large semi-major axes is warped toward the plane of Planet Nine's orbit, causing their poles to be clustered toward one side.

- ↑ Iglesias-Marzoa, Ramón; López-Morales, Mercedes; Jesús Arévalo Morales, María (2015). "Thervfit
*Code*: A Detailed Adaptive Simulated Annealing Code for Fitting Binaries and Exoplanets Radial Velocities".*Publications of the Astronomical Society of the Pacific*.**127**(952): 567–582. arXiv: 1505.04767 . Bibcode:2015PASP..127..567I. doi: 10.1086/682056 . - ↑ Kreidberg, Laura (2015). "Batman: BAsic Transit Model cAlculatioN in Python".
*Publications of the Astronomical Society of the Pacific*.**127**(957): 1161–1165. arXiv: 1507.08285 . Bibcode:2015PASP..127.1161K. doi:10.1086/683602. S2CID 7954832. - ↑ Eastman, Jason; Gaudi, B. Scott; Agol, Eric (2013). "EXOFAST: A Fast Exoplanetary Fitting Suite in IDL".
*Publications of the Astronomical Society of the Pacific*.**125**(923): 83. arXiv: 1206.5798 . Bibcode:2013PASP..125...83E. doi:10.1086/669497. S2CID 118627052.

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