# Argument of periapsis

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, words such as perihelion (for heliocentric orbits), perigee (for geocentric orbits), periastron (for orbits around stars), and so on may replace the word periapsis. (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".

## Calculation

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

$${\displaystyle \omega =\arccos {{\mathbf {n} \cdot \mathbf {e} } \over {\mathbf {\left|n\right|} \mathbf {\left|e\right|} }}}$$
If ez < 0 then ω → 2πω.

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:

$${\displaystyle \omega =\arctan 2\left(e_{y},e_{x}\right)}$$
If the orbit is clockwise (i.e. (r × v)z < 0) then ω → 2πω.

where:

• ex and ey are the 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]

## References

1. ^ 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. doi:.
2. ^ Kreidberg, Laura (2015). "Batman: BAsic Transit Model cAlculatioN in Python". Publications of the Astronomical Society of the Pacific. 127 (957): 1161–1165. arXiv:. Bibcode:2015PASP..127.1161K . doi:10.1086/683602 .
3. ^ 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:. Bibcode:2013PASP..125...83E . doi:10.1086/669497 .

Categories: Orbits

Information as of: 21.06.2020 09:30:47 CEST

Source: Wikipedia (Authors [History])    License : CC-by-sa-3.0

Changes: All pictures and most design elements which are related to those, were removed. Some Icons were replaced by FontAwesome-Icons. Some templates were removed (like “article needs expansion) or assigned (like “hatnotes”). CSS classes were either removed or harmonized.
Wikipedia specific links which do not lead to an article or category (like “Redlinks”, “links to the edit page”, “links to portals”) were removed. Every external link has an additional FontAwesome-Icon. Beside some small changes of design, media-container, maps, navigation-boxes, spoken versions and Geo-microformats were removed.

Please note: Because the given content is automatically taken from Wikipedia at the given point of time, a manual verification was and is not possible. Therefore LinkFang.org does not guarantee the accuracy and actuality of the acquired content. If there is an Information which is wrong at the moment or has an inaccurate display please feel free to contact us: email.